Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP187^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:07:06 AM UTC 2026

% Result   : Theorem 129.52s 39.01s
% Output   : Refutation 132.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :  278
% Syntax   : Number of formulae    : 1292 ( 836 unt;   0 typ;  11 def)
%            Number of atoms       : 3135 (1310 equ;   0 cnn)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives : 15207 (1054   ~; 348   |; 202   &;12529   @)
%                                         (   0 <=>;1074  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   8 avg)
%            Number of types       :   27 (  26 usr)
%            Number of type conns  :  106 ( 106   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   81 (  77 usr;  17 con; 0-5 aty)
%            Number of variables   : 4989 (  38   ^;4667   !; 273   ?;4989   :)
%                                         (   0  !>;   0  ?*;   0  @-;  11  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(produc1462499409ion_pi_type,type,
    produc1462499409ion_pi: $tType ).

thf(produc691362330ubject_type,type,
    produc691362330ubject: $tType ).

thf(produc1834551554reeRes_type,type,
    produc1834551554reeRes: $tType ).

thf(produc405342261i_name_type,type,
    produc405342261i_name: $tType ).

thf(produc629157763_pi_pi_type,type,
    produc629157763_pi_pi: $tType ).

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

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

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

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

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

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

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

thf(produc2008547984reeRes_type,type,
    produc2008547984reeRes: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(piNil_decl,type,
    piNil: pi ).

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

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

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

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

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

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

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

thf(late_TauR_decl,type,
    late_TauR: late_freeRes ).

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

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

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

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

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

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

thf(fresh_543891186ion_pi_decl,type,
    fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).

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

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

thf(fresh_1641682979reeRes_decl,type,
    fresh_1641682979reeRes: name > late_freeRes > $o ).

thf(fresh_81631222sidual_decl,type,
    fresh_81631222sidual: name > late_residual > $o ).

thf(fresh_717452603ubject_decl,type,
    fresh_717452603ubject: name > late_subject > $o ).

thf(fresh_1963366730reeRes_decl,type,
    fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).

thf(fresh_820177506ubject_decl,type,
    fresh_820177506ubject: name > produc865358760ubject > $o ).

thf(fresh_1627595501_pi_pi_decl,type,
    fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).

thf(fresh_2007541374s_name_decl,type,
    fresh_2007541374s_name: name > produc2052722628s_name > $o ).

thf(fresh_1847501388Res_pi_decl,type,
    fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).

thf(fresh_493808761reeRes_decl,type,
    fresh_493808761reeRes: name > produc1357834675reeRes > $o ).

thf(fresh_1498103185ubject_decl,type,
    fresh_1498103185ubject: name > produc214645451ubject > $o ).

thf(fresh_1953561446t_name_decl,type,
    fresh_1953561446t_name: name > produc1998742700t_name > $o ).

thf(fresh_994896692ect_pi_decl,type,
    fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).

thf(fresh_1638563217reeRes_decl,type,
    fresh_1638563217reeRes: name > produc355105483reeRes > $o ).

thf(fresh_495373993ubject_decl,type,
    fresh_495373993ubject: name > produc1359399907ubject > $o ).

thf(produc1531804426reeRes_decl,type,
    produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).

thf(produc607574050ubject_decl,type,
    produc607574050ubject: name > late_subject > produc865358760ubject ).

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

thf(produc1701355766s_name_decl,type,
    produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).

thf(produc1177552196Res_pi_decl,type,
    produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).

thf(produc1244821099reeRes_decl,type,
    produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).

thf(produc320590723ubject_decl,type,
    produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).

thf(produc1647375838t_name_decl,type,
    produc1647375838t_name: late_subject > name > produc1998742700t_name ).

thf(produc324947500ect_pi_decl,type,
    produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).

thf(produc242091907reeRes_decl,type,
    produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).

thf(produc1465345179ubject_decl,type,
    produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).

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

thf(collec1051790738_pi_pi_decl,type,
    collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).

thf(strong2129052853vative_decl,type,
    strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).

thf(strong743114133lation_decl,type,
    strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).

thf(member558706512_pi_pi_decl,type,
    member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).

thf(p_decl,type,
    p: pi ).

thf(pqr_decl,type,
    pqr: pi ).

thf(p2_decl,type,
    p2: pi ).

thf(q_decl,type,
    q: pi ).

thf(qr_decl,type,
    qr: pi ).

thf(q2_decl,type,
    q2: pi ).

thf(r_decl,type,
    r: pi ).

thf(rel_decl,type,
    rel: set_Pr1834926343_pi_pi ).

thf(alpha_decl,type,
    alpha: late_freeRes ).

thf(a_decl,type,
    a: name ).

thf(x_decl,type,
    x: name ).

thf(y_decl,type,
    y: name ).

thf(sk1_decl,type,
    sk1: pi > name ).

thf(sk2_decl,type,
    sk2: late_subject > name ).

thf(sk3_decl,type,
    sk3: late_freeRes > name ).

thf(sk4_decl,type,
    sk4: late_subject > name ).

thf(sk5_decl,type,
    sk5: late_subject > name ).

thf(sk6_decl,type,
    sk6: name > name ).

thf(sk7_decl,type,
    sk7: ( product_prod_pi_pi > $o ) > ( product_prod_pi_pi > $o ) > product_prod_pi_pi ).

thf(sk19_decl,type,
    sk19: product_prod_pi_pi > pi ).

thf(sk20_decl,type,
    sk20: product_prod_pi_pi > pi ).

thf(sk208_decl,type,
    sk208: product_prod_pi_pi > pi ).

thf(sk209_decl,type,
    sk209: product_prod_pi_pi > pi ).

thf(sk1_def,definition,
    ( sk1
    = ( ^ [A: pi] :
        @+[B: name] : ( fresh_name_pi @ B @ A ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( ^ [A: late_subject] :
        @+[B: name] : ( fresh_717452603ubject @ B @ A ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( ^ [A: late_freeRes] :
        @+[B: name] : ( fresh_1641682979reeRes @ B @ A ) ) ) ).

thf(sk4_def,definition,
    ( sk4
    = ( ^ [A: late_subject] :
        @+[B: name] :
          ( A
          = ( late_InputS @ B ) ) ) ) ).

thf(sk5_def,definition,
    ( sk5
    = ( ^ [A: late_subject] :
        @+[B: name] :
          ( A
          = ( late_BoundOutputS @ B ) ) ) ) ).

thf(sk6_def,definition,
    ( sk6
    = ( ^ [A: name] :
        @+[B: name] : ( fresh_name_name @ B @ A ) ) ) ).

thf(sk7_def,definition,
    ( sk7
    = ( ^ [A: product_prod_pi_pi > $o,B: product_prod_pi_pi > $o] :
        @+[C: product_prod_pi_pi] :
          ( ( B @ C )
         != ( A @ C ) ) ) ) ).

thf(sk19_def,definition,
    ( sk19
    = ( ^ [A: product_prod_pi_pi] :
        @+[B: pi] :
        ? [C: pi] :
          ( A
          = ( product_Pair_pi_pi @ B @ C ) ) ) ) ).

thf(sk20_def,definition,
    ( sk20
    = ( ^ [A: product_prod_pi_pi] :
        @+[B: pi] :
          ( A
          = ( product_Pair_pi_pi @ ( sk19 @ A ) @ B ) ) ) ) ).

thf(sk208_def,definition,
    ( sk208
    = ( ^ [A: product_prod_pi_pi] :
        @+[B: pi] :
        ? [C: pi] :
          ( A
          = ( product_Pair_pi_pi @ B @ C ) ) ) ) ).

thf(sk209_def,definition,
    ( sk209
    = ( ^ [A: product_prod_pi_pi] :
        @+[B: pi] :
          ( A
          = ( product_Pair_pi_pi @ ( sk208 @ A ) @ B ) ) ) ) ).

thf(142,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) )
     => ~ ( ( A != D )
          | ( B != E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_outputIneqTrans) ).

thf(892,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) )
     => ~ ( ( A != D )
          | ( B != E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(168,axiom,
    ! [A: late_subject > pi > $o,B: late_subject,C: pi] :
      ( ! [D: late_subject] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: late_subject] :
            ( ! [H: late_subject] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: late_subject] :
              ( ! [F: late_subject] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: late_subject] :
                ( ( fresh_717452603ubject @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: late_subject] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: late_subject] :
                  ( ! [H: late_subject] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: late_subject] :
                    ( ! [H: late_subject] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: late_subject] :
                      ( ! [G: late_subject] : ( A @ G @ D )
                     => ( ! [G: late_subject] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: late_subject] :
                        ( ! [G: late_subject] : ( A @ G @ D )
                       => ( ! [G: late_subject] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: late_subject] :
                          ( ( fresh_717452603ubject @ D @ F )
                         => ( ! [G: late_subject] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: late_subject] :
                            ( ! [F: late_subject] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_pi_Ostrong__induct) ).

thf(1036,plain,
    ! [A: late_subject > pi > $o,B: late_subject,C: pi] :
      ( ! [D: late_subject] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: late_subject] :
            ( ! [H: late_subject] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: late_subject] :
              ( ! [F: late_subject] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: late_subject] :
                ( ( fresh_717452603ubject @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: late_subject] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: late_subject] :
                  ( ! [H: late_subject] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: late_subject] :
                    ( ! [H: late_subject] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: late_subject] :
                      ( ! [G: late_subject] : ( A @ G @ D )
                     => ( ! [G: late_subject] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: late_subject] :
                        ( ! [G: late_subject] : ( A @ G @ D )
                       => ( ! [G: late_subject] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: late_subject] :
                          ( ( fresh_717452603ubject @ D @ F )
                         => ( ! [G: late_subject] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: late_subject] :
                            ( ! [F: late_subject] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(268,axiom,
    late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_cPar1_Ohyps) ).

thf(1625,plain,
    late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(116,axiom,
    ! [A: late_residual] :
      ~ ( late_transitions @ piNil @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_nilCases_H) ).

thf(710,plain,
    ! [A: late_residual] :
      ~ ( late_transitions @ piNil @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(711,plain,
    ~ ? [A: late_residual] : ( late_transitions @ piNil @ A ),
    inference(miniscope,[status(thm)],[710]) ).

thf(712,plain,
    ! [A: late_residual] :
      ~ ( late_transitions @ piNil @ A ),
    inference(cnf,[status(esa)],[711]) ).

thf(1712,plain,
    ! [A: late_residual] :
      ( ~ $true
      | ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
       != ( late_transitions @ piNil @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1625,712]) ).

thf(1713,plain,
    ! [A: late_residual] :
      ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
     != ( late_transitions @ piNil @ A ) ),
    inference(simp,[status(thm)],[1712]) ).

thf(1716,plain,
    ! [A: late_residual] :
      ( ( q != piNil )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 )
       != A ) ),
    inference(simp,[status(thm)],[1713]) ).

thf(1718,plain,
    q != piNil,
    inference(simp,[status(thm)],[1716]) ).

thf(191,axiom,
    late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062) ).

thf(1154,plain,
    late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(10762,plain,
    ! [A: late_residual] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
       != ( late_transitions @ piNil @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1154,712]) ).

thf(10763,plain,
    ! [A: late_residual] :
      ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
     != ( late_transitions @ piNil @ A ) ),
    inference(simp,[status(thm)],[10762]) ).

thf(10784,plain,
    ! [A: late_residual] :
      ( ( ( par @ ( par @ p @ q ) @ r )
       != piNil )
      | ( ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) )
       != A ) ),
    inference(simp,[status(thm)],[10763]) ).

thf(10785,plain,
    ( ( par @ ( par @ p @ q ) @ r )
   != piNil ),
    inference(simp,[status(thm)],[10784]) ).

thf(233,axiom,
    ! [A: pi,B: pi,C: set_Pr1834926343_pi_pi] :
      ( ! [D: late_subject,E: name,F: pi] :
          ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ F ) )
         => ( ( fresh_name_pi @ E @ B )
           => ? [G: pi] :
                ( ( late_transitions @ B @ ( late_BoundR @ D @ E @ G ) )
                & ( strong2129052853vative @ G @ F @ D @ E @ C ) ) ) )
     => ( ! [D: late_freeRes,E: pi] :
            ( ( late_transitions @ A @ ( late_FreeR @ D @ E ) )
           => ? [F: pi] :
                ( ( late_transitions @ B @ ( late_FreeR @ D @ F ) )
                & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ C ) ) )
       => ( strong743114133lation @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_simCases) ).

thf(1454,plain,
    ! [A: pi,B: pi,C: set_Pr1834926343_pi_pi] :
      ( ! [D: late_subject,E: name,F: pi] :
          ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ F ) )
         => ( ( fresh_name_pi @ E @ B )
           => ? [G: pi] :
                ( ( late_transitions @ B @ ( late_BoundR @ D @ E @ G ) )
                & ( strong2129052853vative @ G @ F @ D @ E @ C ) ) ) )
     => ( ! [D: late_freeRes,E: pi] :
            ( ( late_transitions @ A @ ( late_FreeR @ D @ E ) )
           => ? [F: pi] :
                ( ( late_transitions @ B @ ( late_FreeR @ D @ F ) )
                & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ C ) ) )
       => ( strong743114133lation @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(65,axiom,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( mismatch @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_pi_Odistinct_I9_J) ).

thf(476,plain,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( mismatch @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(477,plain,
    ~ ? [A: name,B: name,C: pi] :
        ( piNil
        = ( mismatch @ A @ B @ C ) ),
    inference(miniscope,[status(thm)],[476]) ).

thf(478,plain,
    ! [C: pi,B: name,A: name] :
      ( piNil
     != ( mismatch @ A @ B @ C ) ),
    inference(cnf,[status(esa)],[477]) ).

thf(479,plain,
    ! [C: pi,B: name,A: name] :
      ( ( mismatch @ A @ B @ C )
     != piNil ),
    inference(lifteq,[status(thm)],[478]) ).

thf(26,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi] :
      ~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_nilSim_I1_J) ).

thf(347,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi] :
      ~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(175,axiom,
    late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Free_Ohyps) ).

thf(1099,plain,
    late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(170,axiom,
    alpha = late_TauR,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_cClose2_Ohyps_I14_J) ).

thf(1046,plain,
    alpha = late_TauR,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(1047,plain,
    alpha = late_TauR,
    inference(lifteq,[status(thm)],[1046]) ).

thf(1734,plain,
    late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ),
    inference(rewrite,[status(thm)],[1099,1047]) ).

thf(104,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_resTrans_I1_J) ).

thf(601,plain,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(602,plain,
    ~ ? [A: name,B: name,C: pi,D: late_residual] : ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
    inference(miniscope,[status(thm)],[601]) ).

thf(603,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
    inference(cnf,[status(esa)],[602]) ).

thf(8495,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D )
       != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1734,603]) ).

thf(8496,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D )
     != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[8495]) ).

thf(8508,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( output @ A @ B @ C ) )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( D
       != ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[8496]) ).

thf(8514,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( output @ A @ B @ C ) )
     != ( par @ p @ ( par @ q @ r ) ) ),
    inference(simp,[status(thm)],[8508]) ).

thf(210,axiom,
    ! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
      ( ( late_BoundR @ A @ B @ C )
     != ( late_FreeR @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_residual_Odistinct_I1_J) ).

thf(1237,plain,
    ! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
      ( ( late_BoundR @ A @ B @ C )
     != ( late_FreeR @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(77,axiom,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_subject_Ofresh_I2_J) ).

thf(518,plain,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(154,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( ( fresh_name_pi @ F @ E )
           => ( ( F != B )
             => ( ( F != C )
               => ( ( fresh_name_pi @ F @ D )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_transitions_OComm2) ).

thf(941,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( ( fresh_name_pi @ F @ E )
           => ( ( F != B )
             => ( ( F != C )
               => ( ( fresh_name_pi @ F @ D )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(178,axiom,
    ! [A: set_Pr1834926343_pi_pi] :
      ( ( collec1051790738_pi_pi
        @ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Collect__mem__eq) ).

thf(1108,plain,
    ! [A: set_Pr1834926343_pi_pi] :
      ( ( collec1051790738_pi_pi
        @ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(1109,plain,
    ! [A: set_Pr1834926343_pi_pi] :
      ( ( collec1051790738_pi_pi
        @ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
      = A ),
    inference(cnf,[status(esa)],[1108]) ).

thf(1110,plain,
    ! [A: set_Pr1834926343_pi_pi] :
      ( ( collec1051790738_pi_pi
        @ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[1109]) ).

thf(27,axiom,
    ! [A: late_freeRes] :
      ~ ! [B: name] :
          ~ ( fresh_1641682979reeRes @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_name__exists__fresh) ).

thf(350,plain,
    ! [A: late_freeRes] :
      ~ ! [B: name] :
          ~ ( fresh_1641682979reeRes @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(351,plain,
    ~ ~ ! [A: late_freeRes] :
        ? [B: name] : ( fresh_1641682979reeRes @ B @ A ),
    inference(miniscope,[status(thm)],[350]) ).

thf(352,plain,
    ! [A: late_freeRes] : ( fresh_1641682979reeRes @ ( sk3 @ A ) @ A ),
    inference(cnf,[status(esa)],[351]) ).

thf(11,axiom,
    ! [A: name,B: name,C: set_Pr1834926343_pi_pi,D: pi] :
      ( ( A != B )
     => ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_matchNilLeft) ).

thf(298,plain,
    ! [A: name,B: name,C: set_Pr1834926343_pi_pi,D: pi] :
      ( ( A != B )
     => ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(299,plain,
    ! [A: name,B: name] :
      ( ( A != B )
     => ! [C: set_Pr1834926343_pi_pi,D: pi] : ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) ) ),
    inference(miniscope,[status(thm)],[298]) ).

thf(300,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: name,A: name] :
      ( ( A = B )
      | ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) ) ),
    inference(cnf,[status(esa)],[299]) ).

thf(301,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: name,A: name] :
      ( ( A = B )
      | ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) ) ),
    inference(lifteq,[status(thm)],[300]) ).

thf(99,axiom,
    x != a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_cClose2_Ohyps_I5_J) ).

thf(585,plain,
    x != a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(586,plain,
    x != a,
    inference(polarity_switch,[status(thm)],[585]) ).

thf(587,plain,
    x != a,
    inference(lifteq,[status(thm)],[586]) ).

thf(1965,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: name,A: name] :
      ( ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) )
      | ( A != a )
      | ( B != x ) ),
    inference(paramod_ordered,[status(thm)],[301,587]) ).

thf(1966,plain,
    ! [C: pi,B: set_Pr1834926343_pi_pi,A: name] :
      ( ( strong743114133lation @ piNil @ B @ ( match @ A @ x @ C ) )
      | ( A != a ) ),
    inference(pattern_uni,[status(thm)],[1965:[bind(A,$thf( A )),bind(B,$thf( x ))]]) ).

thf(2199,plain,
    ! [B: pi,A: set_Pr1834926343_pi_pi] : ( strong743114133lation @ piNil @ A @ ( match @ a @ x @ B ) ),
    inference(simp,[status(thm)],[1966]) ).

thf(217,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( fresh_name_pi @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_freshFreeDerivative_I2_J) ).

thf(1322,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( fresh_name_pi @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(192,axiom,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( sum @ A @ B )
     != ( res @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_pi_Odistinct_I81_J) ).

thf(1155,plain,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( sum @ A @ B )
     != ( res @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(1156,plain,
    ~ ? [A: pi,B: pi,C: name,D: pi] :
        ( ( sum @ A @ B )
        = ( res @ C @ D ) ),
    inference(miniscope,[status(thm)],[1155]) ).

thf(1157,plain,
    ! [D: pi,C: name,B: pi,A: pi] :
      ( ( sum @ A @ B )
     != ( res @ C @ D ) ),
    inference(cnf,[status(esa)],[1156]) ).

thf(1158,plain,
    ! [D: pi,C: name,B: pi,A: pi] :
      ( ( sum @ A @ B )
     != ( res @ C @ D ) ),
    inference(lifteq,[status(thm)],[1157]) ).

thf(263,axiom,
    fresh_name_pi @ x @ p,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_cClose2_Ohyps_I3_J) ).

thf(1596,plain,
    fresh_name_pi @ x @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(113,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Late__Semantics_OPar1B) ).

thf(683,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(231,axiom,
    ! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
          ( ( fresh_1641682979reeRes @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_residual_Ostrong__induct) ).

thf(1443,plain,
    ! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
          ( ( fresh_1641682979reeRes @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(187,axiom,
    ! [A: late_freeRes] :
      ( ! [B: name,C: name] :
          ( A
         != ( late_OutputR @ B @ C ) )
     => ( A = late_TauR ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_freeRes_Oexhaust) ).

thf(1142,plain,
    ! [A: late_freeRes] :
      ( ! [B: name,C: name] :
          ( A
         != ( late_OutputR @ B @ C ) )
     => ( A = late_TauR ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(54,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
      ~ ( strong743114133lation @ piNil @ A @ ( input @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_nilSim_I2_J) ).

thf(440,plain,
    ! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
      ~ ( strong743114133lation @ piNil @ A @ ( input @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(248,axiom,
    ! [A: pi,B: pi,C: name,D: name] :
      ( ( subs @ ( sum @ A @ B ) @ C @ D )
      = ( sum @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_simps_I7_J) ).

thf(1533,plain,
    ! [A: pi,B: pi,C: name,D: name] :
      ( ( subs @ ( sum @ A @ B ) @ C @ D )
      = ( sum @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(21,axiom,
    ! [A: name,B: pi] :
      ( ( fresh_name_pi @ A @ ( bang @ B ) )
      = ( fresh_name_pi @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_pi_Ofresh_I10_J) ).

thf(332,plain,
    ! [A: name,B: pi] :
      ( ( fresh_name_pi @ A @ ( bang @ B ) )
      = ( fresh_name_pi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(333,plain,
    ! [B: pi,A: name] :
      ( ( fresh_name_pi @ A @ ( bang @ B ) )
      = ( fresh_name_pi @ A @ B ) ),
    inference(cnf,[status(esa)],[332]) ).

thf(334,plain,
    ! [B: pi,A: name] :
      ( ( fresh_name_pi @ A @ ( bang @ B ) )
      = ( fresh_name_pi @ A @ B ) ),
    inference(lifteq,[status(thm)],[333]) ).

thf(15,axiom,
    ! [A: pi] :
      ~ ! [B: name] :
          ~ ( fresh_name_pi @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_name__exists__fresh) ).

thf(311,plain,
    ! [A: pi] :
      ~ ! [B: name] :
          ~ ( fresh_name_pi @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(312,plain,
    ~ ~ ! [A: pi] :
        ? [B: name] : ( fresh_name_pi @ B @ A ),
    inference(miniscope,[status(thm)],[311]) ).

thf(313,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ A ) @ A ),
    inference(cnf,[status(esa)],[312]) ).

thf(4,axiom,
    ! [A: name,B: pi] :
      ( ( fresh_name_pi @ A @ ( tau @ B ) )
      = ( fresh_name_pi @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_pi_Ofresh_I3_J) ).

thf(274,plain,
    ! [A: name,B: pi] :
      ( ( fresh_name_pi @ A @ ( tau @ B ) )
      = ( fresh_name_pi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(275,plain,
    ! [B: pi,A: name] :
      ( ( fresh_name_pi @ A @ ( tau @ B ) )
      = ( fresh_name_pi @ A @ B ) ),
    inference(cnf,[status(esa)],[274]) ).

thf(276,plain,
    ! [B: pi,A: name] :
      ( ( fresh_name_pi @ A @ ( tau @ B ) )
      = ( fresh_name_pi @ A @ B ) ),
    inference(lifteq,[status(thm)],[275]) ).

thf(1728,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ A ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[313,276]) ).

thf(1729,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ A ) ) @ A ),
    inference(pattern_uni,[status(thm)],[1728:[bind(A,$thf( tau @ E )),bind(B,$thf( sk1 @ ( tau @ E ) )),bind(C,$thf( E ))]]) ).

thf(1732,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ A ) ) @ A ),
    inference(simp,[status(thm)],[1729]) ).

thf(3007,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ C ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[334,1732]) ).

thf(3008,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ A ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3007:[bind(A,$thf( sk1 @ ( tau @ ( bang @ F ) ) )),bind(B,$thf( F )),bind(C,$thf( bang @ F ))]]) ).

thf(3073,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ A ) ) ) @ A ),
    inference(simp,[status(thm)],[3008]) ).

thf(3161,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ A ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3073,334]) ).

thf(3162,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ A ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3161:[bind(A,$thf( bang @ G )),bind(B,$thf( sk1 @ ( tau @ ( bang @ ( bang @ G ) ) ) )),bind(C,$thf( G ))]]) ).

thf(3178,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ A ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3162]) ).

thf(3392,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ C ) ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[334,3178]) ).

thf(3393,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3392:[bind(A,$thf( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ H ) ) ) ) )),bind(B,$thf( H )),bind(C,$thf( bang @ H ))]]) ).

thf(3394,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3393]) ).

thf(4727,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3394,334]) ).

thf(4728,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4727:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4747,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4728]) ).

thf(169,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
      ( ! [D: pi,E: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ D @ E ) @ ( par @ E @ D ) ) @ A )
     => ( ! [D: pi,E: pi,F: name] :
            ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ D @ E ) @ A )
           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ F @ D ) @ ( res @ F @ E ) ) @ A ) )
       => ( strong743114133lation @ ( par @ B @ C ) @ A @ ( par @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_parSym) ).

thf(1041,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
      ( ! [D: pi,E: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ D @ E ) @ ( par @ E @ D ) ) @ A )
     => ( ! [D: pi,E: pi,F: name] :
            ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ D @ E ) @ A )
           => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ F @ D ) @ ( res @ F @ E ) ) @ A ) )
       => ( strong743114133lation @ ( par @ B @ C ) @ A @ ( par @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(239,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name] :
      ( ( subs @ ( match @ A @ B @ C ) @ D @ E )
      = ( match @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_simps_I5_J) ).

thf(1486,plain,
    ! [A: name,B: name,C: pi,D: name,E: name] :
      ( ( subs @ ( match @ A @ B @ C ) @ D @ E )
      = ( match @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(43,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( bang @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_pi_Odistinct_I77_J) ).

thf(405,plain,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( bang @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(406,plain,
    ~ ? [A: name,B: name,C: pi,D: pi] :
        ( ( mismatch @ A @ B @ C )
        = ( bang @ D ) ),
    inference(miniscope,[status(thm)],[405]) ).

thf(407,plain,
    ! [D: pi,C: pi,B: name,A: name] :
      ( ( mismatch @ A @ B @ C )
     != ( bang @ D ) ),
    inference(cnf,[status(esa)],[406]) ).

thf(408,plain,
    ! [D: pi,C: pi,B: name,A: name] :
      ( ( mismatch @ A @ B @ C )
     != ( bang @ D ) ),
    inference(lifteq,[status(thm)],[407]) ).

thf(163,axiom,
    ! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
      ( ! [D: late_freeRes] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
            ( ! [H: late_freeRes] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: late_freeRes] :
              ( ! [F: late_freeRes] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                ( ( fresh_1641682979reeRes @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: late_freeRes] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                  ( ! [H: late_freeRes] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                    ( ! [H: late_freeRes] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: late_freeRes] :
                      ( ! [G: late_freeRes] : ( A @ G @ D )
                     => ( ! [G: late_freeRes] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: late_freeRes] :
                        ( ! [G: late_freeRes] : ( A @ G @ D )
                       => ( ! [G: late_freeRes] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: late_freeRes] :
                          ( ( fresh_1641682979reeRes @ D @ F )
                         => ( ! [G: late_freeRes] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: late_freeRes] :
                            ( ! [F: late_freeRes] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_pi_Ostrong__inducts) ).

thf(977,plain,
    ! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
      ( ! [D: late_freeRes] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
            ( ! [H: late_freeRes] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: late_freeRes] :
              ( ! [F: late_freeRes] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                ( ( fresh_1641682979reeRes @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: late_freeRes] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                  ( ! [H: late_freeRes] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                    ( ! [H: late_freeRes] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: late_freeRes] :
                      ( ! [G: late_freeRes] : ( A @ G @ D )
                     => ( ! [G: late_freeRes] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: late_freeRes] :
                        ( ! [G: late_freeRes] : ( A @ G @ D )
                       => ( ! [G: late_freeRes] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: late_freeRes] :
                          ( ( fresh_1641682979reeRes @ D @ F )
                         => ( ! [G: late_freeRes] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: late_freeRes] :
                            ( ! [F: late_freeRes] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(121,axiom,
    fresh_name_pi @ y @ p,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_cClose2_Ohyps_I8_J) ).

thf(730,plain,
    fresh_name_pi @ y @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(266,axiom,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( A != C )
       => ( fresh_name_pi @ A @ ( subs @ B @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_fresh__fact1) ).

thf(1618,plain,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( A != C )
       => ( fresh_name_pi @ A @ ( subs @ B @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(85,axiom,
    late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_cClose2_Ohyps_I1_J) ).

thf(543,plain,
    late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(153,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_resTrans_I2_J) ).

thf(938,plain,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(939,plain,
    ~ ? [A: name,B: name,C: pi,D: late_residual] : ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
    inference(miniscope,[status(thm)],[938]) ).

thf(940,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
    inference(cnf,[status(esa)],[939]) ).

thf(10557,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
       != ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[543,940]) ).

thf(10558,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
     != ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ) ),
    inference(simp,[status(thm)],[10557]) ).

thf(10562,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( input @ A @ B @ C ) )
       != p )
      | ( ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 )
       != D ) ),
    inference(simp,[status(thm)],[10558]) ).

thf(10567,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( input @ A @ B @ C ) )
     != p ),
    inference(simp,[status(thm)],[10562]) ).

thf(14,axiom,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Late__Semantics1_Osubject_Oinject_I2_J) ).

thf(308,plain,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(256,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
     => ( fresh_name_pi @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_fresh__prodD_I2_J) ).

thf(1569,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
     => ( fresh_name_pi @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(202,axiom,
    ! [A: name,B: pi] :
      ( piNil
     != ( res @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_pi_Odistinct_I15_J) ).

thf(1205,plain,
    ! [A: name,B: pi] :
      ( piNil
     != ( res @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(57,axiom,
    ! [A: pi,B: pi] :
      ( ( ( bang @ A )
        = ( bang @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_pi_Oinject_I9_J) ).

thf(449,plain,
    ! [A: pi,B: pi] :
      ( ( ( bang @ A )
        = ( bang @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(1,conjecture,
    ? [A: pi] :
      ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ A ) )
      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ? [A: pi] :
        ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ A ) )
        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(269,plain,
    ~ ? [A: pi] :
        ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ A ) )
        & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(112,axiom,
    ! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
          ( ( fresh_1641682979reeRes @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_residual_Ostrong__inducts) ).

thf(677,plain,
    ! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
          ( ( fresh_1641682979reeRes @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(214,axiom,
    ! [A: name,B: pi,C: late_residual] :
      ~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_mismatchTrans) ).

thf(1257,plain,
    ! [A: name,B: pi,C: late_residual] :
      ~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(1258,plain,
    ~ ? [A: name,B: pi,C: late_residual] : ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
    inference(miniscope,[status(thm)],[1257]) ).

thf(1259,plain,
    ! [C: late_residual,B: pi,A: name] :
      ~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
    inference(cnf,[status(esa)],[1258]) ).

thf(3418,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ~ $true
      | ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
       != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1625,1259]) ).

thf(3419,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
     != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ),
    inference(simp,[status(thm)],[3418]) ).

thf(3425,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( ( mismatch @ A @ A @ B )
       != q )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 )
       != C ) ),
    inference(simp,[status(thm)],[3419]) ).

thf(3429,plain,
    ! [B: pi,A: name] :
      ( ( mismatch @ A @ A @ B )
     != q ),
    inference(simp,[status(thm)],[3425]) ).

thf(82,axiom,
    ! [A: name,B: name,C: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Output) ).

thf(533,plain,
    ! [A: name,B: name,C: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(1812,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ A ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1732,276]) ).

thf(1813,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ A ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[1812:[bind(A,$thf( tau @ F )),bind(B,$thf( sk1 @ ( tau @ ( tau @ F ) ) )),bind(C,$thf( F ))]]) ).

thf(1816,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ A ) ) ) @ A ),
    inference(simp,[status(thm)],[1813]) ).

thf(3037,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ C ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[334,1816]) ).

thf(3038,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ A ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3037:[bind(A,$thf( sk1 @ ( tau @ ( tau @ ( bang @ G ) ) ) )),bind(B,$thf( G )),bind(C,$thf( bang @ G ))]]) ).

thf(3086,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ A ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3038]) ).

thf(3307,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3086,276]) ).

thf(3308,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3307:[bind(A,$thf( tau @ H )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(3337,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3308]) ).

thf(4408,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3337,276]) ).

thf(4409,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4408:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4440,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4409]) ).

thf(155,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ E @ A )
       => ( fresh_717452603ubject @ E @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_freshBoundDerivative_I1_J) ).

thf(945,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ E @ A )
       => ( fresh_717452603ubject @ E @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(24,axiom,
    ! [A: name,B: late_freeRes,C: late_subject] :
      ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_fresh__prod) ).

thf(340,plain,
    ! [A: name,B: late_freeRes,C: late_subject] :
      ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(84,axiom,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
      ( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_prod__cases) ).

thf(538,plain,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
      ( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(243,axiom,
    ! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
      ( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
     => ( ( ( late_transitions @ C @ D )
         => ( ( A != B )
           => ( E @ A @ B ) ) )
       => ( E @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_mismatchCases) ).

thf(1497,plain,
    ! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
      ( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
     => ( ( ( late_transitions @ C @ D )
         => ( ( A != B )
           => ( E @ A @ B ) ) )
       => ( E @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(226,axiom,
    x != y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_cClose2_Ohyps_I6_J) ).

thf(1364,plain,
    x != y,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(1365,plain,
    x != y,
    inference(polarity_switch,[status(thm)],[1364]) ).

thf(1366,plain,
    y != x,
    inference(lifteq,[status(thm)],[1365]) ).

thf(1957,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: name,A: name] :
      ( ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) )
      | ( A != x )
      | ( B != y ) ),
    inference(paramod_ordered,[status(thm)],[301,1366]) ).

thf(1958,plain,
    ! [C: pi,B: set_Pr1834926343_pi_pi,A: name] :
      ( ( strong743114133lation @ piNil @ B @ ( match @ A @ y @ C ) )
      | ( A != x ) ),
    inference(pattern_uni,[status(thm)],[1957:[bind(A,$thf( A )),bind(B,$thf( y ))]]) ).

thf(2195,plain,
    ! [B: pi,A: set_Pr1834926343_pi_pi] : ( strong743114133lation @ piNil @ A @ ( match @ x @ y @ B ) ),
    inference(simp,[status(thm)],[1958]) ).

thf(441,plain,
    ~ ? [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] : ( strong743114133lation @ piNil @ A @ ( input @ B @ C @ D ) ),
    inference(miniscope,[status(thm)],[440]) ).

thf(442,plain,
    ! [D: pi,C: name,B: name,A: set_Pr1834926343_pi_pi] :
      ~ ( strong743114133lation @ piNil @ A @ ( input @ B @ C @ D ) ),
    inference(cnf,[status(esa)],[441]) ).

thf(4609,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ a @ x @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2199,442]) ).

thf(4610,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ a @ x @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4609]) ).

thf(4630,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ a @ x @ B )
       != ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4610]) ).

thf(4638,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ a @ x @ A )
     != ( input @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4630]) ).

thf(63,axiom,
    ! [A: name,B: name,C: late_subject] :
      ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_fresh__prod) ).

thf(470,plain,
    ! [A: name,B: name,C: late_subject] :
      ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(471,plain,
    ! [C: late_subject,B: name,A: name] :
      ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(cnf,[status(esa)],[470]) ).

thf(472,plain,
    ! [C: late_subject,B: name,A: name] :
      ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[471]) ).

thf(3011,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[334,313]) ).

thf(3012,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ A ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3011:[bind(A,$thf( sk1 @ ( bang @ E ) )),bind(B,$thf( E )),bind(C,$thf( bang @ E ))]]) ).

thf(3076,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ A ) ) @ A ),
    inference(simp,[status(thm)],[3012]) ).

thf(3129,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ A ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3076,334]) ).

thf(3130,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ A ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3129:[bind(A,$thf( bang @ F )),bind(B,$thf( sk1 @ ( bang @ ( bang @ F ) ) )),bind(C,$thf( F ))]]) ).

thf(3146,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ A ) ) ) @ A ),
    inference(simp,[status(thm)],[3130]) ).

thf(3287,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ A ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3146,334]) ).

thf(3288,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ A ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3287:[bind(A,$thf( bang @ G )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( bang @ G ) ) ) )),bind(C,$thf( G ))]]) ).

thf(3303,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ A ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3288]) ).

thf(4192,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3303,334]) ).

thf(4193,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4192:[bind(A,$thf( bang @ H )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(4200,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4193]) ).

thf(5130,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4200,276]) ).

thf(5131,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5130:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(5163,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5131]) ).

thf(215,axiom,
    ! [A: name,B: pi,C: late_subject,D: name,E: pi] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [F: pi,G: name,H: name] :
            ( ( ( res @ A @ B )
              = ( res @ H @ F ) )
           => ! [I: pi] :
                ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
               => ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
                 => ( G = H ) ) ) )
       => ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
              ( ( ( res @ A @ B )
                = ( res @ J @ F ) )
             => ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
               => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
                 => ( ( fresh_717452603ubject @ J @ G )
                   => ( ( J != H )
                     => ( ( fresh_name_pi @ H @ F )
                       => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_resCasesB_H) ).

thf(1260,plain,
    ! [A: name,B: pi,C: late_subject,D: name,E: pi] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [F: pi,G: name,H: name] :
            ( ( ( res @ A @ B )
              = ( res @ H @ F ) )
           => ! [I: pi] :
                ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
               => ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
                 => ( G = H ) ) ) )
       => ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
              ( ( ( res @ A @ B )
                = ( res @ J @ F ) )
             => ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
               => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
                 => ( ( fresh_717452603ubject @ J @ G )
                   => ( ( J != H )
                     => ( ( fresh_name_pi @ H @ F )
                       => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(223,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: late_subject] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_717452603ubject @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_simCasesCont) ).

thf(1342,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: late_subject] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_717452603ubject @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(5142,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4200,334]) ).

thf(5143,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5142:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(5161,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5143]) ).

thf(3319,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3086,334]) ).

thf(3320,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3319:[bind(A,$thf( bang @ H )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(3335,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3320]) ).

thf(270,plain,
    ! [A: pi] :
      ( ~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ A ) )
      | ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ),
    inference(cnf,[status(esa)],[269]) ).

thf(1737,plain,
    ! [A: pi] :
      ( ~ $true
      | ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ A ) )
       != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1734,270]) ).

thf(1738,plain,
    ! [A: pi] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ A ) )
       != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ) ),
    inference(simp,[status(thm)],[1737]) ).

thf(1740,plain,
    ! [A: pi] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( ( par @ ( par @ p @ q ) @ r )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( ( late_FreeR @ late_TauR @ A )
       != ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[1738]) ).

thf(1743,plain,
    ! [A: pi] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( ( par @ ( par @ p @ q ) @ r )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( late_TauR != late_TauR )
      | ( A != pqr ) ),
    inference(simp,[status(thm)],[1740]) ).

thf(1746,plain,
    ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
    | ( ( par @ ( par @ p @ q ) @ r )
     != ( par @ p @ ( par @ q @ r ) ) ) ),
    inference(simp,[status(thm)],[1743]) ).

thf(184,axiom,
    fresh_name_pi @ x @ ( par @ q @ r ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_cClose2_Ohyps_I4_J) ).

thf(1127,plain,
    fresh_name_pi @ x @ ( par @ q @ r ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(225,axiom,
    ! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
      ( ! [D: late_freeRes] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
            ( ! [H: late_freeRes] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: late_freeRes] :
              ( ! [F: late_freeRes] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                ( ( fresh_1641682979reeRes @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: late_freeRes] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                  ( ! [H: late_freeRes] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                    ( ! [H: late_freeRes] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: late_freeRes] :
                      ( ! [G: late_freeRes] : ( A @ G @ D )
                     => ( ! [G: late_freeRes] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: late_freeRes] :
                        ( ! [G: late_freeRes] : ( A @ G @ D )
                       => ( ! [G: late_freeRes] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: late_freeRes] :
                          ( ( fresh_1641682979reeRes @ D @ F )
                         => ( ! [G: late_freeRes] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: late_freeRes] :
                            ( ! [F: late_freeRes] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_pi_Ostrong__induct) ).

thf(1359,plain,
    ! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
      ( ! [D: late_freeRes] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
            ( ! [H: late_freeRes] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: late_freeRes] :
              ( ! [F: late_freeRes] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                ( ( fresh_1641682979reeRes @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: late_freeRes] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                  ( ! [H: late_freeRes] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: late_freeRes] :
                    ( ! [H: late_freeRes] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: late_freeRes] :
                      ( ! [G: late_freeRes] : ( A @ G @ D )
                     => ( ! [G: late_freeRes] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: late_freeRes] :
                        ( ! [G: late_freeRes] : ( A @ G @ D )
                       => ( ! [G: late_freeRes] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: late_freeRes] :
                          ( ( fresh_1641682979reeRes @ D @ F )
                         => ( ! [G: late_freeRes] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: late_freeRes] :
                            ( ! [F: late_freeRes] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(247,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_name_pi @ C @ E )
           => ( ( fresh_name_pi @ F @ A )
             => ( ( fresh_name_pi @ F @ E )
               => ( ( C != B )
                 => ( ( fresh_name_pi @ C @ G )
                   => ( ( F != B )
                     => ( ( fresh_name_pi @ F @ D )
                       => ( ( C != F )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_transitions_OClose1) ).

thf(1529,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_name_pi @ C @ E )
           => ( ( fresh_name_pi @ F @ A )
             => ( ( fresh_name_pi @ F @ E )
               => ( ( C != B )
                 => ( ( fresh_name_pi @ C @ G )
                   => ( ( F != B )
                     => ( ( fresh_name_pi @ F @ D )
                       => ( ( C != F )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(52,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( ( mismatch @ A @ B @ C )
        = ( mismatch @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_pi_Oinject_I5_J) ).

thf(434,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( ( mismatch @ A @ B @ C )
        = ( mismatch @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(435,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( ( mismatch @ A @ B @ C )
        = ( mismatch @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(cnf,[status(esa)],[434]) ).

thf(436,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( ( mismatch @ A @ B @ C )
        = ( mismatch @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(lifteq,[status(thm)],[435]) ).

thf(206,axiom,
    fresh_name_pi @ y @ r,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26__092_060open_062y_A_092_060sharp_062_AR_092_060close_062) ).

thf(1228,plain,
    fresh_name_pi @ y @ r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(139,axiom,
    ! [A: name,B: pi,C: late_residual] :
      ( ( late_transitions @ ( res @ A @ B ) @ C )
     => ( ! [D: pi,E: name,F: name] :
            ( ( ( res @ A @ B )
              = ( res @ F @ D ) )
           => ! [G: pi] :
                ( ( C
                  = ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) )
               => ( ( late_transitions @ D @ ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) )
                 => ( E = F ) ) ) )
       => ( ! [D: pi,E: late_subject,F: name,G: pi,H: name] :
              ( ( ( res @ A @ B )
                = ( res @ H @ D ) )
             => ( ( C
                  = ( late_BoundR @ E @ F @ ( res @ H @ G ) ) )
               => ( ( late_transitions @ D @ ( late_BoundR @ E @ F @ G ) )
                 => ( ( fresh_717452603ubject @ H @ E )
                   => ( ( H != F )
                     => ( ( fresh_name_pi @ F @ D )
                       => ~ ( fresh_717452603ubject @ F @ E ) ) ) ) ) ) )
         => ~ ! [D: pi,E: late_freeRes,F: pi,G: name] :
                ( ( ( res @ A @ B )
                  = ( res @ G @ D ) )
               => ( ( C
                    = ( late_FreeR @ E @ ( res @ G @ F ) ) )
                 => ( ( late_transitions @ D @ ( late_FreeR @ E @ F ) )
                   => ~ ( fresh_1641682979reeRes @ G @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_resCases_H) ).

thf(829,plain,
    ! [A: name,B: pi,C: late_residual] :
      ( ( late_transitions @ ( res @ A @ B ) @ C )
     => ( ! [D: pi,E: name,F: name] :
            ( ( ( res @ A @ B )
              = ( res @ F @ D ) )
           => ! [G: pi] :
                ( ( C
                  = ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) )
               => ( ( late_transitions @ D @ ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) )
                 => ( E = F ) ) ) )
       => ( ! [D: pi,E: late_subject,F: name,G: pi,H: name] :
              ( ( ( res @ A @ B )
                = ( res @ H @ D ) )
             => ( ( C
                  = ( late_BoundR @ E @ F @ ( res @ H @ G ) ) )
               => ( ( late_transitions @ D @ ( late_BoundR @ E @ F @ G ) )
                 => ( ( fresh_717452603ubject @ H @ E )
                   => ( ( H != F )
                     => ( ( fresh_name_pi @ F @ D )
                       => ~ ( fresh_717452603ubject @ F @ E ) ) ) ) ) ) )
         => ~ ! [D: pi,E: late_freeRes,F: pi,G: name] :
                ( ( ( res @ A @ B )
                  = ( res @ G @ D ) )
               => ( ( C
                    = ( late_FreeR @ E @ ( res @ G @ F ) ) )
                 => ( ( late_transitions @ D @ ( late_FreeR @ E @ F ) )
                   => ~ ( fresh_1641682979reeRes @ G @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(42,axiom,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_subject_Ofresh_I1_J) ).

thf(402,plain,
    ! [A: name,B: name] :
      ( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(403,plain,
    ! [B: name,A: name] :
      ( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    inference(cnf,[status(esa)],[402]) ).

thf(404,plain,
    ! [B: name,A: name] :
      ( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
      = ( fresh_name_name @ A @ B ) ),
    inference(lifteq,[status(thm)],[403]) ).

thf(161,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( B != C )
       => ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Open) ).

thf(973,plain,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( B != C )
       => ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(18,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( mismatch @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_pi_Odistinct_I39_J) ).

thf(320,plain,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( mismatch @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(92,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_pi_Odistinct_I75_J) ).

thf(565,plain,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(3151,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( tau @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ C ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[276,3073]) ).

thf(3152,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ A ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3151:[bind(A,$thf( sk1 @ ( tau @ ( bang @ ( tau @ G ) ) ) )),bind(B,$thf( G )),bind(C,$thf( tau @ G ))]]) ).

thf(3165,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ A ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3152]) ).

thf(3346,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3165,276]) ).

thf(3347,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3346:[bind(A,$thf( tau @ H )),bind(B,$thf( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(3363,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3347]) ).

thf(4571,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3363,334]) ).

thf(4572,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4571:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4607,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4572]) ).

thf(173,axiom,
    ! [A: name > pi > $o,B: name,C: pi] :
      ( ! [D: name] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: name] :
            ( ! [H: name] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: name] :
              ( ! [F: name] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: name] :
                ( ( fresh_name_name @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: name] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: name] :
                  ( ! [H: name] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: name] :
                    ( ! [H: name] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: name] :
                      ( ! [G: name] : ( A @ G @ D )
                     => ( ! [G: name] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: name] :
                        ( ! [G: name] : ( A @ G @ D )
                       => ( ! [G: name] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: name] :
                          ( ( fresh_name_name @ D @ F )
                         => ( ! [G: name] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: name] :
                            ( ! [F: name] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_pi_Ostrong__inducts) ).

thf(1055,plain,
    ! [A: name > pi > $o,B: name,C: pi] :
      ( ! [D: name] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: name] :
            ( ! [H: name] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: name] :
              ( ! [F: name] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: name] :
                ( ( fresh_name_name @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: name] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: name] :
                  ( ! [H: name] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: name] :
                    ( ! [H: name] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: name] :
                      ( ! [G: name] : ( A @ G @ D )
                     => ( ! [G: name] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: name] :
                        ( ! [G: name] : ( A @ G @ D )
                       => ( ! [G: name] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: name] :
                          ( ( fresh_name_name @ D @ F )
                         => ( ! [G: name] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: name] :
                            ( ! [F: name] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(118,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( res @ A @ B )
     != ( bang @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_pi_Odistinct_I89_J) ).

thf(716,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( res @ A @ B )
     != ( bang @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(717,plain,
    ~ ? [A: name,B: pi,C: pi] :
        ( ( res @ A @ B )
        = ( bang @ C ) ),
    inference(miniscope,[status(thm)],[716]) ).

thf(718,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( res @ A @ B )
     != ( bang @ C ) ),
    inference(cnf,[status(esa)],[717]) ).

thf(719,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( res @ A @ B )
     != ( bang @ C ) ),
    inference(lifteq,[status(thm)],[718]) ).

thf(33,axiom,
    ! [A: name,B: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_Late__Semantics1_Osubject_Oinject_I1_J) ).

thf(370,plain,
    ! [A: name,B: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(371,plain,
    ! [B: name,A: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    inference(cnf,[status(esa)],[370]) ).

thf(372,plain,
    ! [B: name,A: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    inference(lifteq,[status(thm)],[371]) ).

thf(3119,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( tau @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( bang @ C ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[276,3076]) ).

thf(3120,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ A ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3119:[bind(A,$thf( sk1 @ ( bang @ ( tau @ F ) ) )),bind(B,$thf( F )),bind(C,$thf( tau @ F ))]]) ).

thf(3133,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ A ) ) ) @ A ),
    inference(simp,[status(thm)],[3120]) ).

thf(3193,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ A ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3133,334]) ).

thf(3194,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ A ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3193:[bind(A,$thf( bang @ G )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( bang @ G ) ) ) )),bind(C,$thf( G ))]]) ).

thf(3210,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ A ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3194]) ).

thf(3601,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3210,276]) ).

thf(3602,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3601:[bind(A,$thf( tau @ H )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(3618,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3602]) ).

thf(5032,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3618,276]) ).

thf(5033,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5032:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(5064,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5033]) ).

thf(3615,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ C ) ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[334,3210]) ).

thf(3616,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3615:[bind(A,$thf( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ H ) ) ) ) )),bind(B,$thf( H )),bind(C,$thf( bang @ H ))]]) ).

thf(3617,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3616]) ).

thf(127,axiom,
    ! [A: name,B: late_residual] :
      ~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_resZeroTrans) ).

thf(749,plain,
    ! [A: name,B: late_residual] :
      ~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(750,plain,
    ~ ? [A: name,B: late_residual] : ( late_transitions @ ( res @ A @ piNil ) @ B ),
    inference(miniscope,[status(thm)],[749]) ).

thf(751,plain,
    ! [B: late_residual,A: name] :
      ~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
    inference(cnf,[status(esa)],[750]) ).

thf(29,axiom,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( mismatch @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_pi_Ofresh_I6_J) ).

thf(357,plain,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( mismatch @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(4952,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3617,276]) ).

thf(4953,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4952:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4984,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4953]) ).

thf(348,plain,
    ~ ? [A: set_Pr1834926343_pi_pi,B: pi] : ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
    inference(miniscope,[status(thm)],[347]) ).

thf(349,plain,
    ! [B: pi,A: set_Pr1834926343_pi_pi] :
      ~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
    inference(cnf,[status(esa)],[348]) ).

thf(2349,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ a @ x @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2199,349]) ).

thf(2350,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ a @ x @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2349]) ).

thf(2351,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ a @ x @ B )
       != ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2350]) ).

thf(2356,plain,
    ! [B: pi,A: pi] :
      ( ( match @ a @ x @ A )
     != ( tau @ B ) ),
    inference(simp,[status(thm)],[2351]) ).

thf(38,axiom,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_pi_Ofresh_I4_J) ).

thf(387,plain,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(388,plain,
    ! [D: pi,C: name,B: name,A: name] :
      ( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    inference(cnf,[status(esa)],[387]) ).

thf(389,plain,
    ! [D: pi,C: name,B: name,A: name] :
      ( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    inference(lifteq,[status(thm)],[388]) ).

thf(81,axiom,
    ( subst_name
    = ( ^ [A: name,B: name,C: name] : ( if_name @ ( A = B ) @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subst__name__def) ).

thf(531,plain,
    ( subst_name
    = ( ^ [A: name,B: name,C: name] : ( if_name @ ( A = B ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(532,plain,
    ( ( ^ [A: name,B: name,C: name] : ( if_name @ ( A = B ) @ C @ A ) )
    = subst_name ),
    inference(lifteq,[status(thm)],[531]) ).

thf(1628,plain,
    ! [A: name] :
      ( ( ^ [B: name,C: name] : ( if_name @ ( A = B ) @ C @ A ) )
      = ( subst_name @ A ) ),
    inference(func_ext,[status(esa)],[532]) ).

thf(107,axiom,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_pi_Odistinct_I85_J) ).

thf(619,plain,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(234,axiom,
    ! [A: name,B: pi,C: late_subject,D: name,E: pi] :
      ~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_BoundR @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_resTauBoundTrans) ).

thf(1462,plain,
    ! [A: name,B: pi,C: late_subject,D: name,E: pi] :
      ~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_BoundR @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(186,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ D )
     => ~ ! [E: name,F: name,G: pi] :
            ( ( ( A = E )
              & ( B = F )
              & ( C = G ) )
           => ( D
             != ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_outputCases_H) ).

thf(1132,plain,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ D )
     => ~ ! [E: name,F: name,G: pi] :
            ( ( ( A = E )
              & ( B = F )
              & ( C = G ) )
           => ( D
             != ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(91,axiom,
    ! [A: name > late_residual > $o,B: name,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: name] :
          ( ( fresh_name_name @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_residual_Ostrong__inducts) ).

thf(559,plain,
    ! [A: name > late_residual > $o,B: name,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: name] :
          ( ( fresh_name_name @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(3183,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( tau @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ C ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[276,3133]) ).

thf(3184,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ A ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3183:[bind(A,$thf( sk1 @ ( bang @ ( tau @ ( tau @ G ) ) ) )),bind(B,$thf( G )),bind(C,$thf( tau @ G ))]]) ).

thf(3197,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ A ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3184]) ).

thf(3434,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3197,276]) ).

thf(3435,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3434:[bind(A,$thf( tau @ H )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(3463,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3435]) ).

thf(4180,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3303,276]) ).

thf(4181,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4180:[bind(A,$thf( tau @ H )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(4202,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4181]) ).

thf(5180,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4202,276]) ).

thf(5181,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5180:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(5214,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5181]) ).

thf(160,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( ( fresh_name_pi @ F @ E )
           => ( ( fresh_name_pi @ C @ A )
             => ( ( fresh_name_pi @ C @ E )
               => ( ( F != B )
                 => ( ( fresh_name_pi @ F @ D )
                   => ( ( C != B )
                     => ( ( fresh_name_pi @ C @ G )
                       => ( ( F != C )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_transitions_OClose2) ).

thf(969,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( ( fresh_name_pi @ F @ E )
           => ( ( fresh_name_pi @ C @ A )
             => ( ( fresh_name_pi @ C @ E )
               => ( ( F != B )
                 => ( ( fresh_name_pi @ F @ D )
                   => ( ( C != B )
                     => ( ( fresh_name_pi @ C @ G )
                       => ( ( F != C )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(6,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( input @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_pi_Odistinct_I49_J) ).

thf(281,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( input @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(282,plain,
    ~ ? [A: name,B: name,C: pi,D: name,E: name,F: pi] :
        ( ( input @ A @ B @ C )
        = ( match @ D @ E @ F ) ),
    inference(miniscope,[status(thm)],[281]) ).

thf(283,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    inference(cnf,[status(esa)],[282]) ).

thf(284,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    inference(lifteq,[status(thm)],[283]) ).

thf(16,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( ( abs_fun_name_pi @ A @ B )
        = ( abs_fun_name_pi @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_abs__fun__eq1) ).

thf(314,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( ( abs_fun_name_pi @ A @ B )
        = ( abs_fun_name_pi @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(315,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( ( abs_fun_name_pi @ A @ B )
        = ( abs_fun_name_pi @ A @ C ) )
      = ( B = C ) ),
    inference(cnf,[status(esa)],[314]) ).

thf(316,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( ( abs_fun_name_pi @ A @ B )
        = ( abs_fun_name_pi @ A @ C ) )
      = ( B = C ) ),
    inference(lifteq,[status(thm)],[315]) ).

thf(97,axiom,
    ! [A: product_prod_pi_pi] :
      ~ ! [B: pi,C: pi] :
          ( A
         != ( product_Pair_pi_pi @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_old_Oprod_Oexhaust) ).

thf(577,plain,
    ! [A: product_prod_pi_pi] :
      ~ ! [B: pi,C: pi] :
          ( A
         != ( product_Pair_pi_pi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(578,plain,
    ~ ~ ! [A: product_prod_pi_pi] :
        ? [B: pi,C: pi] :
          ( A
          = ( product_Pair_pi_pi @ B @ C ) ),
    inference(miniscope,[status(thm)],[577]) ).

thf(579,plain,
    ! [A: product_prod_pi_pi] :
      ( A
      = ( product_Pair_pi_pi @ ( sk19 @ A ) @ ( sk20 @ A ) ) ),
    inference(cnf,[status(esa)],[578]) ).

thf(580,plain,
    ! [A: product_prod_pi_pi] :
      ( ( product_Pair_pi_pi @ ( sk19 @ A ) @ ( sk20 @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[579]) ).

thf(242,axiom,
    ! [A: name,B: name] :
      ( ( subs @ piNil @ A @ B )
      = piNil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_simps_I1_J) ).

thf(1494,plain,
    ! [A: name,B: name] :
      ( ( subs @ piNil @ A @ B )
      = piNil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(1495,plain,
    ! [B: name,A: name] :
      ( ( subs @ piNil @ A @ B )
      = piNil ),
    inference(cnf,[status(esa)],[1494]) ).

thf(1496,plain,
    ! [B: name,A: name] :
      ( ( subs @ piNil @ A @ B )
      = piNil ),
    inference(lifteq,[status(thm)],[1495]) ).

thf(1773,plain,
    ! [C: pi,B: name,A: name] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ ( res @ y @ ( par @ p2 @ piNil ) ) ) @ rel )
      | ( ( par @ ( par @ p @ q ) @ r )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( ( late_FreeR @ late_TauR @ C )
       != ( late_FreeR @ late_TauR @ pqr ) )
      | ( ( subs @ piNil @ A @ B )
       != ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ),
    inference(paramod_ordered,[status(thm)],[1496,1740]) ).

thf(1787,plain,
    ! [C: pi,B: name,A: name] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ ( res @ y @ ( par @ p2 @ piNil ) ) ) @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( late_TauR != late_TauR )
      | ( C != pqr )
      | ( ( subs @ piNil @ A @ B )
       != ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ),
    inference(simp,[status(thm)],[1773]) ).

thf(1801,plain,
    ! [B: name,A: name] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ piNil ) ) ) @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( subs @ piNil @ A @ B )
       != ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ),
    inference(simp,[status(thm)],[1787]) ).

thf(3213,plain,
    ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ piNil ) ) ) @ rel )
    | ( ( par @ p @ q )
     != p )
    | ( ( par @ q @ r )
     != r )
    | ( ( subs @ ( par @ q2 @ r ) @ x @ y )
     != piNil ) ),
    inference(rewrite,[status(thm)],[1801,1496]) ).

thf(3230,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( subs @ ( par @ q2 @ r ) @ x @ y )
       != piNil )
      | ( ( product_Pair_pi_pi @ ( sk19 @ A ) @ ( sk20 @ A ) )
       != ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ piNil ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[580,3213]) ).

thf(3231,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( subs @ ( par @ q2 @ r ) @ x @ y )
       != piNil )
      | ( ( sk19 @ A )
       != pqr )
      | ( ( sk20 @ A )
       != ( res @ y @ ( par @ p2 @ piNil ) ) ) ),
    inference(simp,[status(thm)],[3230]) ).

thf(176,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( output @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_pi_Odistinct_I31_J) ).

thf(1100,plain,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( output @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(22,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_freeRes_Ofresh_I1_J) ).

thf(335,plain,
    ! [A: name,B: name,C: name] :
      ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(336,plain,
    ! [C: name,B: name,A: name] :
      ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(cnf,[status(esa)],[335]) ).

thf(337,plain,
    ! [C: name,B: name,A: name] :
      ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[336]) ).

thf(3243,plain,
    ! [D: late_freeRes,C: name,B: name,A: name] :
      ( ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C ) )
      | ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
       != ( fresh_1641682979reeRes @ ( sk3 @ D ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[337,352]) ).

thf(3244,plain,
    ! [B: name,A: name] :
      ( ( fresh_name_name @ ( sk3 @ ( late_OutputR @ A @ B ) ) @ A )
      & ( fresh_name_name @ ( sk3 @ ( late_OutputR @ A @ B ) ) @ B ) ),
    inference(pattern_uni,[status(thm)],[3243:[bind(A,$thf( sk3 @ ( late_OutputR @ F @ G ) )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( late_OutputR @ F @ G ))]]) ).

thf(3265,plain,
    ! [B: name,A: name] :
      ( ( fresh_name_name @ ( sk3 @ ( late_OutputR @ A @ B ) ) @ A )
      & ( fresh_name_name @ ( sk3 @ ( late_OutputR @ A @ B ) ) @ B ) ),
    inference(cnf,[status(esa)],[3244]) ).

thf(3266,plain,
    ! [B: name,A: name] : ( fresh_name_name @ ( sk3 @ ( late_OutputR @ A @ B ) ) @ A ),
    inference(cnfConj,[status(thm)],[3265]) ).

thf(3268,plain,
    ! [B: name,A: name] : ( fresh_name_name @ ( sk3 @ ( late_OutputR @ A @ B ) ) @ A ),
    inference(simp,[status(thm)],[3266]) ).

thf(128,axiom,
    y != a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cClose2_Ohyps_I10_J) ).

thf(752,plain,
    y != a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(753,plain,
    y != a,
    inference(polarity_switch,[status(thm)],[752]) ).

thf(754,plain,
    y != a,
    inference(lifteq,[status(thm)],[753]) ).

thf(2009,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: name,A: name] :
      ( ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) )
      | ( B != a )
      | ( A != y ) ),
    inference(paramod_ordered,[status(thm)],[301,754]) ).

thf(2010,plain,
    ! [C: pi,B: set_Pr1834926343_pi_pi,A: name] :
      ( ( strong743114133lation @ piNil @ B @ ( match @ y @ A @ C ) )
      | ( A != a ) ),
    inference(pattern_uni,[status(thm)],[2009:[bind(A,$thf( y ))]]) ).

thf(2220,plain,
    ! [B: pi,A: set_Pr1834926343_pi_pi] : ( strong743114133lation @ piNil @ A @ ( match @ y @ a @ B ) ),
    inference(simp,[status(thm)],[2010]) ).

thf(75,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
      ~ ( strong743114133lation @ piNil @ A @ ( output @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_nilSim_I3_J) ).

thf(512,plain,
    ! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
      ~ ( strong743114133lation @ piNil @ A @ ( output @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(513,plain,
    ~ ? [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] : ( strong743114133lation @ piNil @ A @ ( output @ B @ C @ D ) ),
    inference(miniscope,[status(thm)],[512]) ).

thf(514,plain,
    ! [D: pi,C: name,B: name,A: set_Pr1834926343_pi_pi] :
      ~ ( strong743114133lation @ piNil @ A @ ( output @ B @ C @ D ) ),
    inference(cnf,[status(esa)],[513]) ).

thf(4651,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ y @ a @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2220,514]) ).

thf(4652,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ y @ a @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4651]) ).

thf(4661,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ y @ a @ B )
       != ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4652]) ).

thf(4669,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ y @ a @ A )
     != ( output @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4661]) ).

thf(1735,plain,
    ! [A: late_residual] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) )
       != ( late_transitions @ piNil @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1734,712]) ).

thf(1736,plain,
    ! [A: late_residual] :
      ( ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) )
     != ( late_transitions @ piNil @ A ) ),
    inference(simp,[status(thm)],[1735]) ).

thf(1739,plain,
    ! [A: late_residual] :
      ( ( ( par @ p @ ( par @ q @ r ) )
       != piNil )
      | ( ( late_FreeR @ late_TauR @ pqr )
       != A ) ),
    inference(simp,[status(thm)],[1736]) ).

thf(1741,plain,
    ( ( par @ p @ ( par @ q @ r ) )
   != piNil ),
    inference(simp,[status(thm)],[1739]) ).

thf(13,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_pi_Ofresh_I7_J) ).

thf(305,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(306,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(cnf,[status(esa)],[305]) ).

thf(307,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[306]) ).

thf(2383,plain,
    ! [D: pi,C: pi,B: pi,A: name] :
      ( ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) )
      | ( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
       != ( fresh_name_pi @ ( sk1 @ D ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[307,313]) ).

thf(2384,plain,
    ! [B: pi,A: pi] :
      ( ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ A )
      & ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ B ) ),
    inference(pattern_uni,[status(thm)],[2383:[bind(A,$thf( sk1 @ ( sum @ F @ G ) )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( sum @ F @ G ))]]) ).

thf(2443,plain,
    ! [B: pi,A: pi] :
      ( ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ A )
      & ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ B ) ),
    inference(cnf,[status(esa)],[2384]) ).

thf(2445,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ B ),
    inference(cnfConj,[status(thm)],[2443]) ).

thf(2447,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ B ),
    inference(simp,[status(thm)],[2445]) ).

thf(3033,plain,
    ! [D: pi,C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( sum @ C @ D ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[334,2447]) ).

thf(3034,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ A @ ( bang @ B ) ) ) @ B ),
    inference(pattern_uni,[status(thm)],[3033:[bind(A,$thf( sk1 @ ( sum @ F @ ( bang @ H ) ) )),bind(B,$thf( H )),bind(C,$thf( F )),bind(D,$thf( bang @ H ))]]) ).

thf(3084,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ A @ ( bang @ B ) ) ) @ B ),
    inference(simp,[status(thm)],[3034]) ).

thf(46,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( output @ A @ B @ C )
     != ( input @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_pi_Odistinct_I21_J) ).

thf(416,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( output @ A @ B @ C )
     != ( input @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(4370,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3335,334]) ).

thf(4371,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4370:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4383,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4371]) ).

thf(56,axiom,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( match @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_pi_Ofresh_I5_J) ).

thf(446,plain,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( match @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(447,plain,
    ! [D: pi,C: name,B: name,A: name] :
      ( ( fresh_name_pi @ A @ ( match @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    inference(cnf,[status(esa)],[446]) ).

thf(448,plain,
    ! [D: pi,C: name,B: name,A: name] :
      ( ( fresh_name_pi @ A @ ( match @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    inference(lifteq,[status(thm)],[447]) ).

thf(240,axiom,
    ! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Late__Semantics_OInput) ).

thf(1489,plain,
    ! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(189,axiom,
    ! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_Tau) ).

thf(1149,plain,
    ! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(1150,plain,
    ! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
    inference(cnf,[status(esa)],[1149]) ).

thf(3410,plain,
    ! [D: late_residual,C: pi,B: name,A: pi] :
      ( ~ $true
      | ( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) )
       != ( late_transitions @ ( mismatch @ B @ B @ C ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1150,1259]) ).

thf(3411,plain,
    ! [D: late_residual,C: pi,B: name,A: pi] :
      ( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) )
     != ( late_transitions @ ( mismatch @ B @ B @ C ) @ D ) ),
    inference(simp,[status(thm)],[3410]) ).

thf(3427,plain,
    ! [D: late_residual,C: pi,B: name,A: pi] :
      ( ( ( tau @ A )
       != ( mismatch @ B @ B @ C ) )
      | ( ( late_FreeR @ late_TauR @ A )
       != D ) ),
    inference(simp,[status(thm)],[3411]) ).

thf(3431,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( tau @ A )
     != ( mismatch @ B @ B @ C ) ),
    inference(simp,[status(thm)],[3427]) ).

thf(101,axiom,
    ! [A: product_prod_pi_pi,B: product_prod_pi_pi > $o] :
      ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_mem__Collect__eq) ).

thf(591,plain,
    ! [A: product_prod_pi_pi,B: product_prod_pi_pi > $o] :
      ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(55,axiom,
    ! [A: name,B: late_subject,C: pi] :
      ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_fresh__prod) ).

thf(443,plain,
    ! [A: name,B: late_subject,C: pi] :
      ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(34,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( match @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_pi_Odistinct_I61_J) ).

thf(373,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( match @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(374,plain,
    ~ ? [A: name,B: name,C: pi,D: name,E: name,F: pi] :
        ( ( match @ A @ B @ C )
        = ( mismatch @ D @ E @ F ) ),
    inference(miniscope,[status(thm)],[373]) ).

thf(375,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( match @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    inference(cnf,[status(esa)],[374]) ).

thf(376,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( match @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    inference(lifteq,[status(thm)],[375]) ).

thf(108,axiom,
    ! [A: pi,B: late_residual,C: pi] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( sum @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_Sum1) ).

thf(623,plain,
    ! [A: pi,B: late_residual,C: pi] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( sum @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(28,axiom,
    ! [A: late_subject] :
      ( ! [B: name] :
          ( A
         != ( late_InputS @ B ) )
     => ~ ! [B: name] :
            ( A
           != ( late_BoundOutputS @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_subject_Oexhaust) ).

thf(353,plain,
    ! [A: late_subject] :
      ( ! [B: name] :
          ( A
         != ( late_InputS @ B ) )
     => ~ ! [B: name] :
            ( A
           != ( late_BoundOutputS @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(354,plain,
    ! [A: late_subject] :
      ( ~ ? [B: name] :
            ( A
            = ( late_InputS @ B ) )
     => ~ ~ ? [B: name] :
              ( A
              = ( late_BoundOutputS @ B ) ) ),
    inference(miniscope,[status(thm)],[353]) ).

thf(355,plain,
    ! [A: late_subject] :
      ( ( A
        = ( late_InputS @ ( sk4 @ A ) ) )
      | ( A
        = ( late_BoundOutputS @ ( sk5 @ A ) ) ) ),
    inference(cnf,[status(esa)],[354]) ).

thf(356,plain,
    ! [A: late_subject] :
      ( ( ( late_InputS @ ( sk4 @ A ) )
        = A )
      | ( ( late_BoundOutputS @ ( sk5 @ A ) )
        = A ) ),
    inference(lifteq,[status(thm)],[355]) ).

thf(41,axiom,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Late__Semantics_Osubject_Odistinct_I1_J) ).

thf(398,plain,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(399,plain,
    ~ ? [A: name,B: name] :
        ( ( late_InputS @ A )
        = ( late_BoundOutputS @ B ) ),
    inference(miniscope,[status(thm)],[398]) ).

thf(400,plain,
    ! [B: name,A: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(cnf,[status(esa)],[399]) ).

thf(401,plain,
    ! [B: name,A: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(lifteq,[status(thm)],[400]) ).

thf(3504,plain,
    ! [C: name,B: name,A: late_subject] :
      ( ( ( late_BoundOutputS @ ( sk5 @ A ) )
        = A )
      | ( A
       != ( late_BoundOutputS @ C ) )
      | ( ( late_InputS @ ( sk4 @ A ) )
       != ( late_InputS @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[356,401]) ).

thf(3505,plain,
    ! [B: late_subject,A: name] :
      ( ( ( late_BoundOutputS @ ( sk5 @ B ) )
        = B )
      | ( B
       != ( late_BoundOutputS @ A ) ) ),
    inference(pattern_uni,[status(thm)],[3504:[bind(A,$thf( D )),bind(B,$thf( sk4 @ D ))]]) ).

thf(3527,plain,
    ! [A: name] :
      ( ( late_BoundOutputS @ ( sk5 @ ( late_BoundOutputS @ A ) ) )
      = ( late_BoundOutputS @ A ) ),
    inference(simp,[status(thm)],[3505]) ).

thf(190,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Par2F) ).

thf(1151,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(3446,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3197,334]) ).

thf(3447,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3446:[bind(A,$thf( bang @ H )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(3461,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3447]) ).

thf(4863,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3461,334]) ).

thf(4864,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4863:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4871,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4864]) ).

thf(8499,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
       != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1625,603]) ).

thf(8500,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
     != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ),
    inference(simp,[status(thm)],[8499]) ).

thf(8505,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( output @ A @ B @ C ) )
       != q )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 )
       != D ) ),
    inference(simp,[status(thm)],[8500]) ).

thf(8511,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( output @ A @ B @ C ) )
     != q ),
    inference(simp,[status(thm)],[8505]) ).

thf(172,axiom,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).

thf(1051,plain,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(66,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
      = ( ( A = B )
        | ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_name__fresh__abs) ).

thf(480,plain,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
      = ( ( A = B )
        | ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(64,axiom,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_fresh__prod) ).

thf(473,plain,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(474,plain,
    ! [C: pi,B: late_freeRes,A: name] :
      ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(cnf,[status(esa)],[473]) ).

thf(475,plain,
    ! [C: pi,B: late_freeRes,A: name] :
      ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[474]) ).

thf(149,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( match @ A @ B @ C ) @ D )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_matchTrans) ).

thf(924,plain,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( match @ A @ B @ C ) @ D )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(69,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( output @ A @ B @ C )
     != ( tau @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_pi_Odistinct_I19_J) ).

thf(489,plain,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( output @ A @ B @ C )
     != ( tau @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(490,plain,
    ~ ? [A: name,B: name,C: pi,D: pi] :
        ( ( output @ A @ B @ C )
        = ( tau @ D ) ),
    inference(miniscope,[status(thm)],[489]) ).

thf(491,plain,
    ! [D: pi,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( tau @ D ) ),
    inference(cnf,[status(esa)],[490]) ).

thf(492,plain,
    ! [D: pi,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( tau @ D ) ),
    inference(lifteq,[status(thm)],[491]) ).

thf(235,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_inputBoundOutputTrans) ).

thf(1465,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(131,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( match @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_pi_Odistinct_I67_J) ).

thf(763,plain,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( match @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(764,plain,
    ~ ? [A: name,B: name,C: pi,D: name,E: pi] :
        ( ( match @ A @ B @ C )
        = ( res @ D @ E ) ),
    inference(miniscope,[status(thm)],[763]) ).

thf(765,plain,
    ! [E: pi,D: name,C: pi,B: name,A: name] :
      ( ( match @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(cnf,[status(esa)],[764]) ).

thf(766,plain,
    ! [E: pi,D: name,C: pi,B: name,A: name] :
      ( ( match @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(lifteq,[status(thm)],[765]) ).

thf(2379,plain,
    ! [D: pi,C: pi,B: pi,A: name] :
      ( ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) )
      | ( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ D ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[307,1732]) ).

thf(2380,plain,
    ! [B: pi,A: pi] :
      ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( sum @ A @ B ) ) ) @ A )
      & ( fresh_name_pi @ ( sk1 @ ( tau @ ( sum @ A @ B ) ) ) @ B ) ),
    inference(pattern_uni,[status(thm)],[2379:[bind(A,$thf( sk1 @ ( tau @ ( sum @ G @ H ) ) )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( sum @ G @ H ))]]) ).

thf(2433,plain,
    ! [B: pi,A: pi] :
      ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( sum @ A @ B ) ) ) @ A )
      & ( fresh_name_pi @ ( sk1 @ ( tau @ ( sum @ A @ B ) ) ) @ B ) ),
    inference(cnf,[status(esa)],[2380]) ).

thf(2435,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( sum @ A @ B ) ) ) @ B ),
    inference(cnfConj,[status(thm)],[2433]) ).

thf(2437,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( sum @ A @ B ) ) ) @ B ),
    inference(simp,[status(thm)],[2435]) ).

thf(5,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( match @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_pi_Odistinct_I37_J) ).

thf(277,plain,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( match @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(278,plain,
    ~ ? [A: pi,B: name,C: name,D: pi] :
        ( ( tau @ A )
        = ( match @ B @ C @ D ) ),
    inference(miniscope,[status(thm)],[277]) ).

thf(279,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( tau @ A )
     != ( match @ B @ C @ D ) ),
    inference(cnf,[status(esa)],[278]) ).

thf(280,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( tau @ A )
     != ( match @ B @ C @ D ) ),
    inference(lifteq,[status(thm)],[279]) ).

thf(123,axiom,
    ! [A: pi > late_residual > $o,B: pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: pi] :
          ( ( fresh_name_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_residual_Ostrong__induct) ).

thf(734,plain,
    ! [A: pi > late_residual > $o,B: pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: pi] :
          ( ( fresh_name_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(267,axiom,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( ( fresh_name_pi @ C @ A )
       => ( fresh_81631222sidual @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_freshResidual) ).

thf(1622,plain,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( ( fresh_name_pi @ C @ A )
       => ( fresh_81631222sidual @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(166,axiom,
    ! [A: product_prod_pi_pi] :
    ? [B: pi,C: pi] :
      ( A
      = ( product_Pair_pi_pi @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_surj__pair) ).

thf(1030,plain,
    ! [A: product_prod_pi_pi] :
    ? [B: pi,C: pi] :
      ( A
      = ( product_Pair_pi_pi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(1031,plain,
    ! [A: product_prod_pi_pi] :
      ( A
      = ( product_Pair_pi_pi @ ( sk208 @ A ) @ ( sk209 @ A ) ) ),
    inference(cnf,[status(esa)],[1030]) ).

thf(1032,plain,
    ! [A: product_prod_pi_pi] :
      ( ( product_Pair_pi_pi @ ( sk208 @ A ) @ ( sk209 @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[1031]) ).

thf(2752,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ ( par @ p @ q ) @ r )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( ( product_Pair_pi_pi @ ( sk208 @ A ) @ ( sk209 @ A ) )
       != ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1032,1746]) ).

thf(2772,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ ( par @ p @ q ) @ r )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( ( sk208 @ A )
       != pqr )
      | ( ( sk209 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[2752]) ).

thf(246,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( fresh_1641682979reeRes @ D @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_freshFreeDerivative_I1_J) ).

thf(1526,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( fresh_1641682979reeRes @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(224,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: late_freeRes > pi > $o] :
      ( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ B @ C ) )
     => ( ( ( B = late_TauR )
         => ( ( A = C )
           => ( D @ late_TauR @ A ) ) )
       => ( D @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_tauCases) ).

thf(1351,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: late_freeRes > pi > $o] :
      ( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ B @ C ) )
     => ( ( ( B = late_TauR )
         => ( ( A = C )
           => ( D @ late_TauR @ A ) ) )
       => ( D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(44,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( ( output @ A @ B @ C )
        = ( output @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_pi_Oinject_I1_J) ).

thf(409,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( ( output @ A @ B @ C )
        = ( output @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(410,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( ( output @ A @ B @ C )
        = ( output @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(cnf,[status(esa)],[409]) ).

thf(411,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( ( output @ A @ B @ C )
        = ( output @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(lifteq,[status(thm)],[410]) ).

thf(49,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( ( match @ A @ B @ C )
        = ( match @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_pi_Oinject_I4_J) ).

thf(426,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( ( match @ A @ B @ C )
        = ( match @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(427,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( ( match @ A @ B @ C )
        = ( match @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(cnf,[status(esa)],[426]) ).

thf(428,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( ( match @ A @ B @ C )
        = ( match @ D @ E @ F ) )
      = ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(lifteq,[status(thm)],[427]) ).

thf(177,axiom,
    ! [A: pi,B: pi] :
      ( piNil
     != ( par @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_pi_Odistinct_I13_J) ).

thf(1104,plain,
    ! [A: pi,B: pi] :
      ( piNil
     != ( par @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(80,axiom,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Late__Semantics1_Osubject_Odistinct_I1_J) ).

thf(527,plain,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(195,axiom,
    ! [A: pi,B: pi,C: late_residual] :
      ( ( late_transitions @ ( sum @ A @ B ) @ C )
     => ( ~ ( late_transitions @ A @ C )
       => ( late_transitions @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_sumCases_H) ).

thf(1169,plain,
    ! [A: pi,B: pi,C: late_residual] :
      ( ( late_transitions @ ( sum @ A @ B ) @ C )
     => ( ~ ( late_transitions @ A @ C )
       => ( late_transitions @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(40,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( output @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_pi_Odistinct_I23_J) ).

thf(394,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( output @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(395,plain,
    ~ ? [A: name,B: name,C: pi,D: name,E: name,F: pi] :
        ( ( output @ A @ B @ C )
        = ( match @ D @ E @ F ) ),
    inference(miniscope,[status(thm)],[394]) ).

thf(396,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    inference(cnf,[status(esa)],[395]) ).

thf(397,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    inference(lifteq,[status(thm)],[396]) ).

thf(58,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Late__Semantics_OfreeRes_Oinject) ).

thf(452,plain,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(35,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( output @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_pi_Odistinct_I25_J) ).

thf(377,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( output @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(378,plain,
    ~ ? [A: name,B: name,C: pi,D: name,E: name,F: pi] :
        ( ( output @ A @ B @ C )
        = ( mismatch @ D @ E @ F ) ),
    inference(miniscope,[status(thm)],[377]) ).

thf(379,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    inference(cnf,[status(esa)],[378]) ).

thf(380,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    inference(lifteq,[status(thm)],[379]) ).

thf(221,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi] :
      ~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_tauBoundTrans) ).

thf(1336,plain,
    ! [A: pi,B: late_subject,C: name,D: pi] :
      ~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(1337,plain,
    ~ ? [A: pi,B: late_subject,C: name,D: pi] : ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
    inference(miniscope,[status(thm)],[1336]) ).

thf(1338,plain,
    ! [D: pi,C: name,B: late_subject,A: pi] :
      ~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
    inference(cnf,[status(esa)],[1337]) ).

thf(36,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: name,C: pi] : ( strong743114133lation @ piNil @ A @ ( mismatch @ B @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_mismatchNilLeft) ).

thf(381,plain,
    ! [A: set_Pr1834926343_pi_pi,B: name,C: pi] : ( strong743114133lation @ piNil @ A @ ( mismatch @ B @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(3506,plain,
    ! [C: name,B: name,A: late_subject] :
      ( ( ( late_InputS @ ( sk4 @ A ) )
        = A )
      | ( A
       != ( late_InputS @ B ) )
      | ( ( late_BoundOutputS @ ( sk5 @ A ) )
       != ( late_BoundOutputS @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[356,401]) ).

thf(3507,plain,
    ! [B: late_subject,A: name] :
      ( ( ( late_InputS @ ( sk4 @ B ) )
        = B )
      | ( B
       != ( late_InputS @ A ) ) ),
    inference(pattern_uni,[status(thm)],[3506:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( sk5 @ D ))]]) ).

thf(3528,plain,
    ! [A: name] :
      ( ( late_InputS @ ( sk4 @ ( late_InputS @ A ) ) )
      = ( late_InputS @ A ) ),
    inference(simp,[status(thm)],[3507]) ).

thf(17,axiom,
    ! [A: late_subject] :
      ~ ! [B: name] :
          ~ ( fresh_717452603ubject @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_name__exists__fresh) ).

thf(317,plain,
    ! [A: late_subject] :
      ~ ! [B: name] :
          ~ ( fresh_717452603ubject @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(318,plain,
    ~ ~ ! [A: late_subject] :
        ? [B: name] : ( fresh_717452603ubject @ B @ A ),
    inference(miniscope,[status(thm)],[317]) ).

thf(319,plain,
    ! [A: late_subject] : ( fresh_717452603ubject @ ( sk2 @ A ) @ A ),
    inference(cnf,[status(esa)],[318]) ).

thf(6363,plain,
    ! [C: late_subject,B: name,A: name] :
      ( ( fresh_name_name @ A @ B )
      | ( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
       != ( fresh_717452603ubject @ ( sk2 @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[404,319]) ).

thf(6364,plain,
    ! [A: name] : ( fresh_name_name @ ( sk2 @ ( late_InputS @ A ) ) @ A ),
    inference(pattern_uni,[status(thm)],[6363:[bind(A,$thf( sk2 @ ( late_InputS @ E ) )),bind(B,$thf( E )),bind(C,$thf( late_InputS @ E ))]]) ).

thf(6371,plain,
    ! [A: name] : ( fresh_name_name @ ( sk2 @ ( late_InputS @ A ) ) @ A ),
    inference(simp,[status(thm)],[6364]) ).

thf(6382,plain,
    ! [B: name,A: name] :
      ( ( fresh_name_name @ ( sk2 @ ( late_InputS @ A ) ) @ B )
      | ( ( late_InputS @ ( sk4 @ ( late_InputS @ A ) ) )
       != ( late_InputS @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3528,6371]) ).

thf(6383,plain,
    ! [A: name] : ( fresh_name_name @ ( sk2 @ ( late_InputS @ A ) ) @ ( sk4 @ ( late_InputS @ A ) ) ),
    inference(pattern_uni,[status(thm)],[6382:[bind(A,$thf( D )),bind(B,$thf( sk4 @ ( late_InputS @ D ) ))]]) ).

thf(6388,plain,
    ! [A: name] : ( fresh_name_name @ ( sk2 @ ( late_InputS @ A ) ) @ ( sk4 @ ( late_InputS @ A ) ) ),
    inference(simp,[status(thm)],[6383]) ).

thf(31,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( output @ A @ B @ C )
     != ( bang @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_pi_Odistinct_I33_J) ).

thf(363,plain,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( output @ A @ B @ C )
     != ( bang @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(364,plain,
    ~ ? [A: name,B: name,C: pi,D: pi] :
        ( ( output @ A @ B @ C )
        = ( bang @ D ) ),
    inference(miniscope,[status(thm)],[363]) ).

thf(365,plain,
    ! [D: pi,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( bang @ D ) ),
    inference(cnf,[status(esa)],[364]) ).

thf(366,plain,
    ! [D: pi,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( bang @ D ) ),
    inference(lifteq,[status(thm)],[365]) ).

thf(2754,plain,
    ! [B: pi,A: product_prod_pi_pi] :
      ( ~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ B ) )
      | ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( product_Pair_pi_pi @ ( sk208 @ A ) @ ( sk209 @ A ) )
       != ( product_Pair_pi_pi @ B @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1032,270]) ).

thf(2776,plain,
    ! [B: pi,A: product_prod_pi_pi] :
      ( ~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ B ) )
      | ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( sk208 @ A )
       != B )
      | ( ( sk209 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[2754]) ).

thf(2790,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( sk208 @ A ) ) )
      | ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( sk209 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[2776]) ).

thf(2773,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( sk208 @ A )
       != pqr )
      | ( ( sk209 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[2752]) ).

thf(53,axiom,
    ! [A: name,B: late_subject,C: name,D: pi] :
      ( ( fresh_81631222sidual @ A @ ( late_BoundR @ B @ C @ D ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_residual_Ofresh_I1_J) ).

thf(437,plain,
    ! [A: name,B: late_subject,C: name,D: pi] :
      ( ( fresh_81631222sidual @ A @ ( late_BoundR @ B @ C @ D ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(438,plain,
    ! [D: pi,C: name,B: late_subject,A: name] :
      ( ( fresh_81631222sidual @ A @ ( late_BoundR @ B @ C @ D ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    inference(cnf,[status(esa)],[437]) ).

thf(439,plain,
    ! [D: pi,C: name,B: late_subject,A: name] :
      ( ( fresh_81631222sidual @ A @ ( late_BoundR @ B @ C @ D ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
    inference(lifteq,[status(thm)],[438]) ).

thf(207,axiom,
    late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_092_060close_062) ).

thf(1229,plain,
    late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(8497,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
       != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1229,603]) ).

thf(8498,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
     != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ),
    inference(simp,[status(thm)],[8497]) ).

thf(8507,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( output @ A @ B @ C ) )
       != ( par @ p @ q ) )
      | ( ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) )
       != D ) ),
    inference(simp,[status(thm)],[8498]) ).

thf(8513,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( output @ A @ B @ C ) )
     != ( par @ p @ q ) ),
    inference(simp,[status(thm)],[8507]) ).

thf(1955,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: name,A: name] :
      ( ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) )
      | ( B != x )
      | ( A != y ) ),
    inference(paramod_ordered,[status(thm)],[301,1366]) ).

thf(1956,plain,
    ! [C: pi,B: set_Pr1834926343_pi_pi,A: name] :
      ( ( strong743114133lation @ piNil @ B @ ( match @ y @ A @ C ) )
      | ( A != x ) ),
    inference(pattern_uni,[status(thm)],[1955:[bind(A,$thf( y ))]]) ).

thf(2194,plain,
    ! [B: pi,A: set_Pr1834926343_pi_pi] : ( strong743114133lation @ piNil @ A @ ( match @ y @ x @ B ) ),
    inference(simp,[status(thm)],[1956]) ).

thf(2259,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ y @ x @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2194,349]) ).

thf(2260,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ y @ x @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2259]) ).

thf(2261,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ y @ x @ B )
       != ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2260]) ).

thf(2264,plain,
    ! [B: pi,A: pi] :
      ( ( match @ y @ x @ A )
     != ( tau @ B ) ),
    inference(simp,[status(thm)],[2261]) ).

thf(126,axiom,
    ! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
      ~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_BoundR @ ( late_InputS @ E ) @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_resOutputInputTrans) ).

thf(746,plain,
    ! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
      ~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_BoundR @ ( late_InputS @ E ) @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(12,axiom,
    ! [A: name,B: late_freeRes,C: name] :
      ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_fresh__prod) ).

thf(302,plain,
    ! [A: name,B: late_freeRes,C: name] :
      ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(103,axiom,
    ! [A: pi,B: late_residual,C: pi] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( sum @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_Sum2) ).

thf(598,plain,
    ! [A: pi,B: late_residual,C: pi] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( sum @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(10,axiom,
    ! [A: late_subject,B: name,C: pi,D: late_subject,E: name,F: pi] :
      ( ( ( late_BoundR @ A @ B @ C )
        = ( late_BoundR @ D @ E @ F ) )
      = ( ( A = D )
        & ( ( abs_fun_name_pi @ B @ C )
          = ( abs_fun_name_pi @ E @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_residual_Oinject_I1_J) ).

thf(295,plain,
    ! [A: late_subject,B: name,C: pi,D: late_subject,E: name,F: pi] :
      ( ( ( late_BoundR @ A @ B @ C )
        = ( late_BoundR @ D @ E @ F ) )
      = ( ( A = D )
        & ( ( abs_fun_name_pi @ B @ C )
          = ( abs_fun_name_pi @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(296,plain,
    ! [F: pi,E: name,D: late_subject,C: pi,B: name,A: late_subject] :
      ( ( ( late_BoundR @ A @ B @ C )
        = ( late_BoundR @ D @ E @ F ) )
      = ( ( A = D )
        & ( ( abs_fun_name_pi @ B @ C )
          = ( abs_fun_name_pi @ E @ F ) ) ) ),
    inference(cnf,[status(esa)],[295]) ).

thf(297,plain,
    ! [F: pi,E: name,D: late_subject,C: pi,B: name,A: late_subject] :
      ( ( ( late_BoundR @ A @ B @ C )
        = ( late_BoundR @ D @ E @ F ) )
      = ( ( A = D )
        & ( ( abs_fun_name_pi @ B @ C )
          = ( abs_fun_name_pi @ E @ F ) ) ) ),
    inference(lifteq,[status(thm)],[296]) ).

thf(50,axiom,
    ( fresh_name_name
    = ( != @ name ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_name__fresh) ).

thf(429,plain,
    ( fresh_name_name
    = ( ^ [A: name,B: name] : ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(135,axiom,
    fresh_name_pi @ y @ qr,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_cClose2_Ohyps_I11_J) ).

thf(815,plain,
    fresh_name_pi @ y @ qr,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(120,axiom,
    ! [A: pi,B: name,C: pi] :
      ( ( tau @ A )
     != ( res @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_pi_Odistinct_I45_J) ).

thf(726,plain,
    ! [A: pi,B: name,C: pi] :
      ( ( tau @ A )
     != ( res @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(727,plain,
    ~ ? [A: pi,B: name,C: pi] :
        ( ( tau @ A )
        = ( res @ B @ C ) ),
    inference(miniscope,[status(thm)],[726]) ).

thf(728,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( tau @ A )
     != ( res @ B @ C ) ),
    inference(cnf,[status(esa)],[727]) ).

thf(729,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( tau @ A )
     != ( res @ B @ C ) ),
    inference(lifteq,[status(thm)],[728]) ).

thf(252,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( sum @ A @ B )
     != ( par @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_pi_Odistinct_I79_J) ).

thf(1557,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( sum @ A @ B )
     != ( par @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(1558,plain,
    ~ ? [A: pi,B: pi,C: pi,D: pi] :
        ( ( sum @ A @ B )
        = ( par @ C @ D ) ),
    inference(miniscope,[status(thm)],[1557]) ).

thf(1559,plain,
    ! [D: pi,C: pi,B: pi,A: pi] :
      ( ( sum @ A @ B )
     != ( par @ C @ D ) ),
    inference(cnf,[status(esa)],[1558]) ).

thf(1560,plain,
    ! [D: pi,C: pi,B: pi,A: pi] :
      ( ( sum @ A @ B )
     != ( par @ C @ D ) ),
    inference(lifteq,[status(thm)],[1559]) ).

thf(3378,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3178,276]) ).

thf(3379,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3378:[bind(A,$thf( tau @ H )),bind(B,$thf( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(3395,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3379]) ).

thf(4767,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( tau @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ C ) ) ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[276,3395]) ).

thf(4768,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4767:[bind(A,$thf( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ ( tau @ I ) ) ) ) ) )),bind(B,$thf( I )),bind(C,$thf( tau @ I ))]]) ).

thf(4785,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4768]) ).

thf(2599,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ y @ a @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2220,349]) ).

thf(2600,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ y @ a @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2599]) ).

thf(2601,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ y @ a @ B )
       != ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2600]) ).

thf(2606,plain,
    ! [B: pi,A: pi] :
      ( ( match @ y @ a @ A )
     != ( tau @ B ) ),
    inference(simp,[status(thm)],[2601]) ).

thf(4358,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3335,276]) ).

thf(4359,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4358:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4385,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4359]) ).

thf(141,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_717452603ubject @ C @ B )
           => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_transitions_OPar2B) ).

thf(889,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_717452603ubject @ C @ B )
           => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(70,axiom,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( output @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_pi_Ofresh_I2_J) ).

thf(493,plain,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh_name_pi @ A @ ( output @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(185,axiom,
    ! [A: name,B: name,C: name,D: name,E: pi] :
      ( ( A != B )
     => ( ( A != C )
       => ( ( A != D )
         => ( ( subs @ ( input @ B @ A @ E ) @ C @ D )
            = ( input @ ( subst_name @ B @ C @ D ) @ A @ ( subs @ E @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_simps_I4_J) ).

thf(1128,plain,
    ! [A: name,B: name,C: name,D: name,E: pi] :
      ( ( A != B )
     => ( ( A != C )
       => ( ( A != D )
         => ( ( subs @ ( input @ B @ A @ E ) @ C @ D )
            = ( input @ ( subst_name @ B @ C @ D ) @ A @ ( subs @ E @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(19,axiom,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( output @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_pi_Odistinct_I1_J) ).

thf(324,plain,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( output @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(7,axiom,
    ! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_nilSimRight) ).

thf(285,plain,
    ! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(3267,plain,
    ! [B: name,A: name] : ( fresh_name_name @ ( sk3 @ ( late_OutputR @ A @ B ) ) @ B ),
    inference(cnfConj,[status(thm)],[3265]) ).

thf(3269,plain,
    ! [B: name,A: name] : ( fresh_name_name @ ( sk3 @ ( late_OutputR @ A @ B ) ) @ B ),
    inference(simp,[status(thm)],[3267]) ).

thf(10759,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
       != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1154,1259]) ).

thf(10760,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
     != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ),
    inference(simp,[status(thm)],[10759]) ).

thf(10780,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( ( mismatch @ A @ A @ B )
       != ( par @ ( par @ p @ q ) @ r ) )
      | ( ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) )
       != C ) ),
    inference(simp,[status(thm)],[10760]) ).

thf(10794,plain,
    ! [B: pi,A: name] :
      ( ( mismatch @ A @ A @ B )
     != ( par @ ( par @ p @ q ) @ r ) ),
    inference(simp,[status(thm)],[10780]) ).

thf(193,axiom,
    ! [A: late_freeRes > $o,B: late_freeRes] :
      ( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
     => ( ( A @ late_TauR )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_freeRes_Oinducts) ).

thf(1159,plain,
    ! [A: late_freeRes > $o,B: late_freeRes] :
      ( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
     => ( ( A @ late_TauR )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(60,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( sum @ A @ B )
        = ( sum @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_pi_Oinject_I6_J) ).

thf(459,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( sum @ A @ B )
        = ( sum @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(460,plain,
    ! [D: pi,C: pi,B: pi,A: pi] :
      ( ( ( sum @ A @ B )
        = ( sum @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(cnf,[status(esa)],[459]) ).

thf(461,plain,
    ! [D: pi,C: pi,B: pi,A: pi] :
      ( ( ( sum @ A @ B )
        = ( sum @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(lifteq,[status(thm)],[460]) ).

thf(209,axiom,
    ! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_resInputFreeTrans) ).

thf(1234,plain,
    ! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(219,axiom,
    ! [A: pi > pi > $o,B: pi,C: pi] :
      ( ! [D: pi] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: pi] :
            ( ! [H: pi] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: pi] :
              ( ! [F: pi] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: pi] :
                ( ( fresh_name_pi @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: pi] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: pi] :
                  ( ! [H: pi] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: pi] :
                    ( ! [H: pi] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: pi] :
                      ( ! [G: pi] : ( A @ G @ D )
                     => ( ! [G: pi] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: pi] :
                        ( ! [G: pi] : ( A @ G @ D )
                       => ( ! [G: pi] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: pi] :
                          ( ( fresh_name_pi @ D @ F )
                         => ( ! [G: pi] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: pi] :
                            ( ! [F: pi] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_pi_Ostrong__induct) ).

thf(1328,plain,
    ! [A: pi > pi > $o,B: pi,C: pi] :
      ( ! [D: pi] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: pi] :
            ( ! [H: pi] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: pi] :
              ( ! [F: pi] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: pi] :
                ( ( fresh_name_pi @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: pi] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: pi] :
                  ( ! [H: pi] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: pi] :
                    ( ! [H: pi] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: pi] :
                      ( ! [G: pi] : ( A @ G @ D )
                     => ( ! [G: pi] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: pi] :
                        ( ! [G: pi] : ( A @ G @ D )
                       => ( ! [G: pi] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: pi] :
                          ( ( fresh_name_pi @ D @ F )
                         => ( ! [G: pi] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: pi] :
                            ( ! [F: pi] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(179,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi] :
      ( ! [C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ C @ piNil ) @ C ) @ A )
     => ( strong743114133lation @ ( par @ B @ piNil ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_parZeroLeft) ).

thf(1111,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi] :
      ( ! [C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ C @ piNil ) @ C ) @ A )
     => ( strong743114133lation @ ( par @ B @ piNil ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(10555,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
       != ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1625,940]) ).

thf(10556,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
     != ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ) ),
    inference(simp,[status(thm)],[10555]) ).

thf(10561,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( input @ A @ B @ C ) )
       != q )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 )
       != D ) ),
    inference(simp,[status(thm)],[10556]) ).

thf(10566,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( input @ A @ B @ C ) )
     != q ),
    inference(simp,[status(thm)],[10561]) ).

thf(1963,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: name,A: name] :
      ( ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) )
      | ( B != a )
      | ( A != x ) ),
    inference(paramod_ordered,[status(thm)],[301,587]) ).

thf(1964,plain,
    ! [C: pi,B: set_Pr1834926343_pi_pi,A: name] :
      ( ( strong743114133lation @ piNil @ B @ ( match @ x @ A @ C ) )
      | ( A != a ) ),
    inference(pattern_uni,[status(thm)],[1963:[bind(A,$thf( x ))]]) ).

thf(2198,plain,
    ! [B: pi,A: set_Pr1834926343_pi_pi] : ( strong743114133lation @ piNil @ A @ ( match @ x @ a @ B ) ),
    inference(simp,[status(thm)],[1964]) ).

thf(4623,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ x @ a @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2198,442]) ).

thf(4624,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ x @ a @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4623]) ).

thf(4628,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ x @ a @ B )
       != ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4624]) ).

thf(4636,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ x @ a @ A )
     != ( input @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4628]) ).

thf(174,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_prod_Oinject) ).

thf(1096,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(47,axiom,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi > $o] :
      ( ! [C: product_prod_pi_pi] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collec1051790738_pi_pi @ A )
        = ( collec1051790738_pi_pi @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Collect__cong) ).

thf(420,plain,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi > $o] :
      ( ! [C: product_prod_pi_pi] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collec1051790738_pi_pi @ A )
        = ( collec1051790738_pi_pi @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(1847,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ A ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1816,276]) ).

thf(1848,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ A ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[1847:[bind(A,$thf( tau @ G )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( tau @ G ) ) ) )),bind(C,$thf( G ))]]) ).

thf(1851,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ A ) ) ) ) @ A ),
    inference(simp,[status(thm)],[1848]) ).

thf(1763,plain,
    ! [B: late_residual,A: name] :
      ( ~ $true
      | ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
       != ( late_transitions @ ( res @ A @ piNil ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1625,751]) ).

thf(1764,plain,
    ! [B: late_residual,A: name] :
      ( ( late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) )
     != ( late_transitions @ ( res @ A @ piNil ) @ B ) ),
    inference(simp,[status(thm)],[1763]) ).

thf(1768,plain,
    ! [B: late_residual,A: name] :
      ( ( ( res @ A @ piNil )
       != q )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 )
       != B ) ),
    inference(simp,[status(thm)],[1764]) ).

thf(1772,plain,
    ! [A: name] :
      ( ( res @ A @ piNil )
     != q ),
    inference(simp,[status(thm)],[1768]) ).

thf(156,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( input @ A @ B @ C ) @ D )
     => ~ ! [E: name,F: name,G: pi] :
            ( ( ( A = F )
              & ( ( abs_fun_name_pi @ B @ C )
                = ( abs_fun_name_pi @ E @ G ) ) )
           => ( ( D
                = ( late_BoundR @ ( late_InputS @ F ) @ E @ G ) )
             => ( E = F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_inputCases_H) ).

thf(948,plain,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( input @ A @ B @ C ) @ D )
     => ~ ! [E: name,F: name,G: pi] :
            ( ( ( A = F )
              & ( ( abs_fun_name_pi @ B @ C )
                = ( abs_fun_name_pi @ E @ G ) ) )
           => ( ( D
                = ( late_BoundR @ ( late_InputS @ F ) @ E @ G ) )
             => ( E = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(4643,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ x @ y @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2195,514]) ).

thf(4644,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ x @ y @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4643]) ).

thf(4660,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ x @ y @ B )
       != ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4644]) ).

thf(4668,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ x @ y @ A )
     != ( output @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4660]) ).

thf(20,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( input @ A @ B @ C )
     != ( bang @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_pi_Odistinct_I59_J) ).

thf(328,plain,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( input @ A @ B @ C )
     != ( bang @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(23,axiom,
    ! [A: name] : ( fresh_name_pi @ A @ piNil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_pi_Ofresh_I1_J) ).

thf(338,plain,
    ! [A: name] : ( fresh_name_pi @ A @ piNil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(339,plain,
    ! [A: name] : ( fresh_name_pi @ A @ piNil ),
    inference(cnf,[status(esa)],[338]) ).

thf(261,axiom,
    ! [A: pi > late_residual > $o,B: pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: pi] :
          ( ( fresh_name_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_residual_Ostrong__inducts) ).

thf(1584,plain,
    ! [A: pi > late_residual > $o,B: pi,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: pi] :
          ( ( fresh_name_pi @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(145,axiom,
    late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_cClose2_Ohyps_I2_J) ).

thf(907,plain,
    late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(3412,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
       != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[907,1259]) ).

thf(3413,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
     != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ),
    inference(simp,[status(thm)],[3412]) ).

thf(3424,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( ( mismatch @ A @ A @ B )
       != ( par @ q @ r ) )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ qr )
       != C ) ),
    inference(simp,[status(thm)],[3413]) ).

thf(3428,plain,
    ! [B: pi,A: name] :
      ( ( mismatch @ A @ A @ B )
     != ( par @ q @ r ) ),
    inference(simp,[status(thm)],[3424]) ).

thf(114,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: pi] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_name_pi @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_resSimCases) ).

thf(686,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: pi] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_name_pi @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(3275,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ A ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3146,276]) ).

thf(3276,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ A ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3275:[bind(A,$thf( tau @ G )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( tau @ G ) ) ) )),bind(C,$thf( G ))]]) ).

thf(3305,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ A ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3276]) ).

thf(4242,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3305,334]) ).

thf(4243,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4242:[bind(A,$thf( bang @ H )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(4255,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4243]) ).

thf(5901,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4255,334]) ).

thf(5902,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5901:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(5932,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5902]) ).

thf(620,plain,
    ~ ? [A: pi,B: pi,C: name,D: pi] :
        ( ( par @ A @ B )
        = ( res @ C @ D ) ),
    inference(miniscope,[status(thm)],[619]) ).

thf(621,plain,
    ! [D: pi,C: name,B: pi,A: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    inference(cnf,[status(esa)],[620]) ).

thf(622,plain,
    ! [D: pi,C: name,B: pi,A: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    inference(lifteq,[status(thm)],[621]) ).

thf(229,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_1641682979reeRes @ D @ B )
       => ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_ResF) ).

thf(1382,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh_1641682979reeRes @ D @ B )
       => ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(4230,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3305,276]) ).

thf(4231,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4230:[bind(A,$thf( tau @ H )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(4257,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4231]) ).

thf(5951,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( tau @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ C ) ) ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[276,4257]) ).

thf(5952,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5951:[bind(A,$thf( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ ( tau @ I ) ) ) ) ) )),bind(B,$thf( I )),bind(C,$thf( tau @ I ))]]) ).

thf(5973,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5952]) ).

thf(93,axiom,
    ( strong743114133lation
    = ( ^ [A: pi,B: set_Pr1834926343_pi_pi,C: pi] :
          ( ! [D: late_subject,E: name,F: pi] :
              ( ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
                & ( fresh_name_pi @ E @ A ) )
             => ? [G: pi] :
                  ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
                  & ( strong2129052853vative @ G @ F @ D @ E @ B ) ) )
          & ! [D: late_freeRes,E: pi] :
              ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
             => ? [F: pi] :
                  ( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_simulation__def) ).

thf(569,plain,
    ( strong743114133lation
    = ( ^ [A: pi,B: set_Pr1834926343_pi_pi,C: pi] :
          ( ! [D: late_subject,E: name,F: pi] :
              ( ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
                & ( fresh_name_pi @ E @ A ) )
             => ? [G: pi] :
                  ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
                  & ( strong2129052853vative @ G @ F @ D @ E @ B ) ) )
          & ! [D: late_freeRes,E: pi] :
              ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
             => ? [F: pi] :
                  ( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(3001,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ C ) ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[334,1851]) ).

thf(3002,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3001:[bind(A,$thf( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ H ) ) ) ) )),bind(B,$thf( H )),bind(C,$thf( bang @ H ))]]) ).

thf(3109,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3002]) ).

thf(39,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( sum @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_pi_Odistinct_I71_J) ).

thf(390,plain,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(391,plain,
    ~ ? [A: name,B: name,C: pi,D: pi,E: pi] :
        ( ( mismatch @ A @ B @ C )
        = ( sum @ D @ E ) ),
    inference(miniscope,[status(thm)],[390]) ).

thf(392,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( mismatch @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(cnf,[status(esa)],[391]) ).

thf(393,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( mismatch @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(lifteq,[status(thm)],[392]) ).

thf(180,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Par1F) ).

thf(1114,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(76,axiom,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_Late__Semantics_Osubject_Oinject_I2_J) ).

thf(515,plain,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(237,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ C @ E )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Late__Semantics_OClose2) ).

thf(1478,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ C @ E )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(220,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_name_pi @ A @ ( res @ B @ C ) )
      = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_pi_Ofresh_I9_J) ).

thf(1333,plain,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_name_pi @ A @ ( res @ B @ C ) )
      = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(25,axiom,
    ! [A: pi] :
      ( piNil
     != ( tau @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_pi_Odistinct_I3_J) ).

thf(343,plain,
    ! [A: pi] :
      ( piNil
     != ( tau @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(211,axiom,
    ! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
      ( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
     => ~ ( fresh_717452603ubject @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_inputIneqTrans) ).

thf(1241,plain,
    ! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
      ( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
     => ~ ( fresh_717452603ubject @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(30,axiom,
    ! [A: name,B: late_subject,C: name] :
      ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_fresh__prod) ).

thf(360,plain,
    ! [A: name,B: late_subject,C: name] :
      ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(8493,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
       != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[907,603]) ).

thf(8494,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
     != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ),
    inference(simp,[status(thm)],[8493]) ).

thf(8506,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( output @ A @ B @ C ) )
       != ( par @ q @ r ) )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ qr )
       != D ) ),
    inference(simp,[status(thm)],[8494]) ).

thf(8512,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( output @ A @ B @ C ) )
     != ( par @ q @ r ) ),
    inference(simp,[status(thm)],[8506]) ).

thf(73,axiom,
    ! [A: pi,B: pi] :
      ( ( tau @ A )
     != ( bang @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_pi_Odistinct_I47_J) ).

thf(505,plain,
    ! [A: pi,B: pi] :
      ( ( tau @ A )
     != ( bang @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(506,plain,
    ~ ? [A: pi,B: pi] :
        ( ( tau @ A )
        = ( bang @ B ) ),
    inference(miniscope,[status(thm)],[505]) ).

thf(507,plain,
    ! [B: pi,A: pi] :
      ( ( tau @ A )
     != ( bang @ B ) ),
    inference(cnf,[status(esa)],[506]) ).

thf(508,plain,
    ! [B: pi,A: pi] :
      ( ( tau @ A )
     != ( bang @ B ) ),
    inference(lifteq,[status(thm)],[507]) ).

thf(147,axiom,
    fresh_name_pi @ y @ ( par @ q @ r ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_cClose2_Ohyps_I9_J) ).

thf(921,plain,
    fresh_name_pi @ y @ ( par @ q @ r ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(2444,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ A ),
    inference(cnfConj,[status(thm)],[2443]) ).

thf(2446,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ A ),
    inference(simp,[status(thm)],[2444]) ).

thf(2891,plain,
    ! [D: pi,C: name,B: pi,A: pi] :
      ( ( fresh_name_pi @ C @ D )
      | ( ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ A )
       != ( fresh_name_pi @ C @ ( tau @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2446,276]) ).

thf(2892,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ ( tau @ B ) @ A ) ) @ B ),
    inference(pattern_uni,[status(thm)],[2891:[bind(A,$thf( tau @ H )),bind(B,$thf( G )),bind(C,$thf( sk1 @ ( sum @ ( tau @ H ) @ G ) )),bind(D,$thf( H ))]]) ).

thf(2915,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ ( tau @ B ) @ A ) ) @ B ),
    inference(simp,[status(thm)],[2892]) ).

thf(2011,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: name,A: name] :
      ( ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) )
      | ( A != a )
      | ( B != y ) ),
    inference(paramod_ordered,[status(thm)],[301,754]) ).

thf(2012,plain,
    ! [C: pi,B: set_Pr1834926343_pi_pi,A: name] :
      ( ( strong743114133lation @ piNil @ B @ ( match @ A @ y @ C ) )
      | ( A != a ) ),
    inference(pattern_uni,[status(thm)],[2011:[bind(A,$thf( A )),bind(B,$thf( y ))]]) ).

thf(2221,plain,
    ! [B: pi,A: set_Pr1834926343_pi_pi] : ( strong743114133lation @ piNil @ A @ ( match @ a @ y @ B ) ),
    inference(simp,[status(thm)],[2012]) ).

thf(5887,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( tau @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ C ) ) ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[276,4255]) ).

thf(5888,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5887:[bind(A,$thf( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ ( tau @ I ) ) ) ) ) )),bind(B,$thf( I )),bind(C,$thf( tau @ I ))]]) ).

thf(5909,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5888]) ).

thf(45,axiom,
    ! [A: pi,B: pi,C: pi] :
      ( ( sum @ A @ B )
     != ( bang @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_pi_Odistinct_I83_J) ).

thf(412,plain,
    ! [A: pi,B: pi,C: pi] :
      ( ( sum @ A @ B )
     != ( bang @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(159,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( input @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_pi_Odistinct_I55_J) ).

thf(965,plain,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( input @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(5965,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4257,334]) ).

thf(5966,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5965:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(5996,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5966]) ).

thf(48,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Late__Semantics1_OfreeRes_Oinject) ).

thf(423,plain,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(424,plain,
    ! [D: name,C: name,B: name,A: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(cnf,[status(esa)],[423]) ).

thf(425,plain,
    ! [D: name,C: name,B: name,A: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(lifteq,[status(thm)],[424]) ).

thf(188,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
     => ( fresh_name_pi @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_fresh__prodD_I1_J) ).

thf(1146,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
     => ( fresh_name_pi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(1101,plain,
    ~ ? [A: name,B: name,C: pi,D: name,E: pi] :
        ( ( output @ A @ B @ C )
        = ( res @ D @ E ) ),
    inference(miniscope,[status(thm)],[1100]) ).

thf(1102,plain,
    ! [E: pi,D: name,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(cnf,[status(esa)],[1101]) ).

thf(1103,plain,
    ! [E: pi,D: name,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(lifteq,[status(thm)],[1102]) ).

thf(4420,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3337,334]) ).

thf(4421,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4420:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4438,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4421]) ).

thf(95,axiom,
    ! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
      ( ( ( late_FreeR @ A @ B )
        = ( late_FreeR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_residual_Oinject_I2_J) ).

thf(573,plain,
    ! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
      ( ( ( late_FreeR @ A @ B )
        = ( late_FreeR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(137,axiom,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Late__Semantics_OfreeRes_Odistinct_I1_J) ).

thf(819,plain,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(144,axiom,
    ! [A: pi,B: pi,C: name] :
      ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ rel )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ C @ A ) @ ( res @ C @ B ) ) @ rel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Res) ).

thf(904,plain,
    ! [A: pi,B: pi,C: name] :
      ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ rel )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ C @ A ) @ ( res @ C @ B ) ) @ rel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(265,axiom,
    ! [A: pi,B: name] :
      ( ( subs @ A @ B @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_subst__identity) ).

thf(1615,plain,
    ! [A: pi,B: name] :
      ( ( subs @ A @ B @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(125,axiom,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( match @ C @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_Match) ).

thf(743,plain,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( match @ C @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(9,axiom,
    ! [A: pi,B: pi,C: pi] :
      ( ( tau @ A )
     != ( sum @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_pi_Odistinct_I41_J) ).

thf(291,plain,
    ! [A: pi,B: pi,C: pi] :
      ( ( tau @ A )
     != ( sum @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(157,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_tauOutputTrans) ).

thf(958,plain,
    ! [A: pi,B: name,C: name,D: pi] :
      ~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(4320,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3109,334]) ).

thf(4321,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4320:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4328,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4321]) ).

thf(2239,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ A ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1851,276]) ).

thf(2240,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[2239:[bind(A,$thf( tau @ H )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ H ) ) ) ) )),bind(C,$thf( H ))]]) ).

thf(2247,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[2240]) ).

thf(2647,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2247,276]) ).

thf(2648,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[2647:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(2669,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[2648]) ).

thf(2794,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2669,276]) ).

thf(2795,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[2794:[bind(A,$thf( tau @ J )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ J ) ) ) ) ) ) )),bind(C,$thf( J ))]]) ).

thf(2817,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[2795]) ).

thf(213,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( output @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_pi_Odistinct_I29_J) ).

thf(1253,plain,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( output @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(1254,plain,
    ~ ? [A: name,B: name,C: pi,D: pi,E: pi] :
        ( ( output @ A @ B @ C )
        = ( par @ D @ E ) ),
    inference(miniscope,[status(thm)],[1253]) ).

thf(1255,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(cnf,[status(esa)],[1254]) ).

thf(1256,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(lifteq,[status(thm)],[1255]) ).

thf(286,plain,
    ! [B: set_Pr1834926343_pi_pi,A: pi] : ( strong743114133lation @ A @ B @ piNil ),
    inference(cnf,[status(esa)],[285]) ).

thf(183,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Late__Semantics_OPar2B) ).

thf(1124,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ E )
       => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(444,plain,
    ! [C: pi,B: late_subject,A: name] :
      ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(cnf,[status(esa)],[443]) ).

thf(445,plain,
    ! [C: pi,B: late_subject,A: name] :
      ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[444]) ).

thf(228,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
     => ~ ! [E: pi,F: name,G: name] :
            ( ( ( A = F )
              & ( B = G )
              & ( C = E ) )
           => ( ( late_transitions @ E @ D )
             => ( F = G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_mismatchCases_H) ).

thf(1371,plain,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
     => ~ ! [E: pi,F: name,G: name] :
            ( ( ( A = F )
              & ( B = G )
              & ( C = E ) )
           => ( ( late_transitions @ E @ D )
             => ( F = G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(1105,plain,
    ~ ? [A: pi,B: pi] :
        ( piNil
        = ( par @ A @ B ) ),
    inference(miniscope,[status(thm)],[1104]) ).

thf(1106,plain,
    ! [B: pi,A: pi] :
      ( piNil
     != ( par @ A @ B ) ),
    inference(cnf,[status(esa)],[1105]) ).

thf(1107,plain,
    ! [B: pi,A: pi] :
      ( ( par @ A @ B )
     != piNil ),
    inference(lifteq,[status(thm)],[1106]) ).

thf(62,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( input @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_pi_Odistinct_I35_J) ).

thf(466,plain,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( input @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(4615,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ a @ y @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2221,442]) ).

thf(4616,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ a @ y @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4615]) ).

thf(4632,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ a @ y @ B )
       != ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4616]) ).

thf(4640,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ a @ y @ A )
     != ( input @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4632]) ).

thf(382,plain,
    ! [C: pi,B: name,A: set_Pr1834926343_pi_pi] : ( strong743114133lation @ piNil @ A @ ( mismatch @ B @ B @ C ) ),
    inference(cnf,[status(esa)],[381]) ).

thf(117,axiom,
    ! [A: pi,B: pi,C: name,D: name] :
      ( ( subs @ ( par @ A @ B ) @ C @ D )
      = ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_simps_I8_J) ).

thf(713,plain,
    ! [A: pi,B: pi,C: name,D: name] :
      ( ( subs @ ( par @ A @ B ) @ C @ D )
      = ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(1854,plain,
    ! [B: late_residual,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
       != ( late_transitions @ ( res @ A @ piNil ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1229,751]) ).

thf(1855,plain,
    ! [B: late_residual,A: name] :
      ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
     != ( late_transitions @ ( res @ A @ piNil ) @ B ) ),
    inference(simp,[status(thm)],[1854]) ).

thf(1861,plain,
    ! [B: late_residual,A: name] :
      ( ( ( res @ A @ piNil )
       != ( par @ p @ q ) )
      | ( ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) )
       != B ) ),
    inference(simp,[status(thm)],[1855]) ).

thf(1865,plain,
    ! [A: name] :
      ( ( res @ A @ piNil )
     != ( par @ p @ q ) ),
    inference(simp,[status(thm)],[1861]) ).

thf(105,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ A )
       => ( ( fresh_name_pi @ C @ E )
         => ( ( fresh_717452603ubject @ C @ B )
           => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_transitions_OPar1B) ).

thf(604,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ C @ A )
       => ( ( fresh_name_pi @ C @ E )
         => ( ( fresh_717452603ubject @ C @ B )
           => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(203,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: late_freeRes] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_1641682979reeRes @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_simCasesCont) ).

thf(1209,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: late_freeRes] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_1641682979reeRes @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(181,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ~ ( late_transitions @ ( res @ A @ ( output @ B @ A @ C ) ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_resOutputOutputTrans) ).

thf(1117,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ~ ( late_transitions @ ( res @ A @ ( output @ B @ A @ C ) ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(417,plain,
    ~ ? [A: name,B: name,C: pi,D: name,E: name,F: pi] :
        ( ( output @ A @ B @ C )
        = ( input @ D @ E @ F ) ),
    inference(miniscope,[status(thm)],[416]) ).

thf(418,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( input @ D @ E @ F ) ),
    inference(cnf,[status(esa)],[417]) ).

thf(419,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( input @ D @ E @ F ) ),
    inference(lifteq,[status(thm)],[418]) ).

thf(171,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_old_Oprod_Oinject) ).

thf(1048,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(2293,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ x @ y @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2195,349]) ).

thf(2294,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ x @ y @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2293]) ).

thf(2295,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ x @ y @ B )
       != ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2294]) ).

thf(2299,plain,
    ! [B: pi,A: pi] :
      ( ( match @ x @ y @ A )
     != ( tau @ B ) ),
    inference(simp,[status(thm)],[2295]) ).

thf(1761,plain,
    ! [B: late_residual,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
       != ( late_transitions @ ( res @ A @ piNil ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[907,751]) ).

thf(1762,plain,
    ! [B: late_residual,A: name] :
      ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
     != ( late_transitions @ ( res @ A @ piNil ) @ B ) ),
    inference(simp,[status(thm)],[1761]) ).

thf(1767,plain,
    ! [B: late_residual,A: name] :
      ( ( ( res @ A @ piNil )
       != ( par @ q @ r ) )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ qr )
       != B ) ),
    inference(simp,[status(thm)],[1762]) ).

thf(1771,plain,
    ! [A: name] :
      ( ( res @ A @ piNil )
     != ( par @ q @ r ) ),
    inference(simp,[status(thm)],[1767]) ).

thf(4647,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ a @ y @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2221,514]) ).

thf(4648,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ a @ y @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4647]) ).

thf(4659,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ a @ y @ B )
       != ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4648]) ).

thf(4667,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ a @ y @ A )
     != ( output @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4659]) ).

thf(3,axiom,
    ! [A: pi,B: pi] :
      ( ( ( tau @ A )
        = ( tau @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_pi_Oinject_I2_J) ).

thf(271,plain,
    ! [A: pi,B: pi] :
      ( ( ( tau @ A )
        = ( tau @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(257,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_717452603ubject @ E @ B )
       => ( ( E != C )
         => ( ( fresh_name_pi @ C @ A )
           => ( ( fresh_717452603ubject @ C @ B )
             => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_transitions_OResB) ).

thf(1571,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_717452603ubject @ E @ B )
       => ( ( E != C )
         => ( ( fresh_name_pi @ C @ A )
           => ( ( fresh_717452603ubject @ C @ B )
             => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(200,axiom,
    ! [A: late_residual] :
      ~ ( late_transitions @ piNil @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_zeroTrans) ).

thf(1194,plain,
    ! [A: late_residual] :
      ~ ( late_transitions @ piNil @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(10549,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
       != ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[907,940]) ).

thf(10550,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
     != ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ) ),
    inference(simp,[status(thm)],[10549]) ).

thf(10560,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( input @ A @ B @ C ) )
       != ( par @ q @ r ) )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ qr )
       != D ) ),
    inference(simp,[status(thm)],[10550]) ).

thf(10565,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( input @ A @ B @ C ) )
     != ( par @ q @ r ) ),
    inference(simp,[status(thm)],[10560]) ).

thf(5192,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4202,334]) ).

thf(5193,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5192:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(5212,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( bang @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5193]) ).

thf(4902,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3463,276]) ).

thf(4903,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4902:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4929,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4903]) ).

thf(361,plain,
    ! [C: name,B: late_subject,A: name] :
      ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(cnf,[status(esa)],[360]) ).

thf(362,plain,
    ! [C: name,B: late_subject,A: name] :
      ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[361]) ).

thf(450,plain,
    ! [B: pi,A: pi] :
      ( ( ( bang @ A )
        = ( bang @ B ) )
      = ( A = B ) ),
    inference(cnf,[status(esa)],[449]) ).

thf(451,plain,
    ! [B: pi,A: pi] :
      ( ( ( bang @ A )
        = ( bang @ B ) )
      = ( A = B ) ),
    inference(lifteq,[status(thm)],[450]) ).

thf(4777,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3395,334]) ).

thf(4778,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4777:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4805,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4778]) ).

thf(74,axiom,
    ! [A: name,B: late_subject,C: late_subject] :
      ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_fresh__prod) ).

thf(509,plain,
    ! [A: name,B: late_subject,C: late_subject] :
      ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(2627,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ a @ y @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2221,349]) ).

thf(2628,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ a @ y @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2627]) ).

thf(2629,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ a @ y @ B )
       != ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2628]) ).

thf(2632,plain,
    ! [B: pi,A: pi] :
      ( ( match @ a @ y @ A )
     != ( tau @ B ) ),
    inference(simp,[status(thm)],[2629]) ).

thf(83,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_Late__Semantics_OClose1) ).

thf(535,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh_name_pi @ F @ A )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(321,plain,
    ~ ? [A: pi,B: name,C: name,D: pi] :
        ( ( tau @ A )
        = ( mismatch @ B @ C @ D ) ),
    inference(miniscope,[status(thm)],[320]) ).

thf(322,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( tau @ A )
     != ( mismatch @ B @ C @ D ) ),
    inference(cnf,[status(esa)],[321]) ).

thf(323,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( tau @ A )
     != ( mismatch @ B @ C @ D ) ),
    inference(lifteq,[status(thm)],[322]) ).

thf(102,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ B @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_forget) ).

thf(594,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ B @ A @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(218,axiom,
    ! [A: name,B: pi,C: pi,D: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( par @ ( par @ B @ C ) @ D ) ) @ ( par @ B @ ( res @ A @ ( par @ C @ D ) ) ) ) @ rel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_FreshExt) ).

thf(1325,plain,
    ! [A: name,B: pi,C: pi,D: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( par @ ( par @ B @ C ) @ D ) ) @ ( par @ B @ ( res @ A @ ( par @ C @ D ) ) ) ) @ rel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(109,axiom,
    ! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_subject] :
          ( ( fresh_717452603ubject @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_residual_Ostrong__inducts) ).

thf(626,plain,
    ! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_subject] :
          ( ( fresh_717452603ubject @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(251,axiom,
    fresh_name_pi @ x @ r,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25__092_060open_062x_A_092_060sharp_062_AR_092_060close_062) ).

thf(1556,plain,
    fresh_name_pi @ x @ r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(165,axiom,
    ! [A: name,B: pi,C: late_freeRes,D: pi] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
     => ~ ! [E: pi,F: late_freeRes,G: pi,H: name] :
            ( ( ( res @ A @ B )
              = ( res @ H @ E ) )
           => ( ( ( late_FreeR @ C @ D )
                = ( late_FreeR @ F @ ( res @ H @ G ) ) )
             => ( ( late_transitions @ E @ ( late_FreeR @ F @ G ) )
               => ~ ( fresh_1641682979reeRes @ H @ F ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_resCasesF_H) ).

thf(1022,plain,
    ! [A: name,B: pi,C: late_freeRes,D: pi] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
     => ~ ! [E: pi,F: late_freeRes,G: pi,H: name] :
            ( ( ( res @ A @ B )
              = ( res @ H @ E ) )
           => ( ( ( late_FreeR @ C @ D )
                = ( late_FreeR @ F @ ( res @ H @ G ) ) )
             => ( ( late_transitions @ E @ ( late_FreeR @ F @ G ) )
               => ~ ( fresh_1641682979reeRes @ H @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(4611,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ x @ y @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2195,442]) ).

thf(4612,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ x @ y @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4611]) ).

thf(4627,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ x @ y @ B )
       != ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4612]) ).

thf(4635,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ x @ y @ A )
     != ( input @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4627]) ).

thf(133,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_pi_Odistinct_I73_J) ).

thf(808,plain,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(809,plain,
    ~ ? [A: name,B: name,C: pi,D: pi,E: pi] :
        ( ( mismatch @ A @ B @ C )
        = ( par @ D @ E ) ),
    inference(miniscope,[status(thm)],[808]) ).

thf(810,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( mismatch @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(cnf,[status(esa)],[809]) ).

thf(811,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( mismatch @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(lifteq,[status(thm)],[810]) ).

thf(129,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( match @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_pi_Odistinct_I65_J) ).

thf(755,plain,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( match @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(756,plain,
    ~ ? [A: name,B: name,C: pi,D: pi,E: pi] :
        ( ( match @ A @ B @ C )
        = ( par @ D @ E ) ),
    inference(miniscope,[status(thm)],[755]) ).

thf(757,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( match @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(cnf,[status(esa)],[756]) ).

thf(758,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( match @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(lifteq,[status(thm)],[757]) ).

thf(222,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( par @ A @ B )
        = ( par @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_pi_Oinject_I7_J) ).

thf(1339,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( par @ A @ B )
        = ( par @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(88,axiom,
    fresh_name_pi @ x @ q,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_cClose2_Ohyps_I12_J) ).

thf(552,plain,
    fresh_name_pi @ x @ q,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(32,axiom,
    ! [A: name] :
      ~ ! [B: name] :
          ~ ( fresh_name_name @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_name__exists__fresh) ).

thf(367,plain,
    ! [A: name] :
      ~ ! [B: name] :
          ~ ( fresh_name_name @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(136,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_outputTauTrans) ).

thf(816,plain,
    ! [A: name,B: name,C: pi,D: pi] :
      ~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(1786,plain,
    ! [C: pi,B: name,A: name] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ ( res @ y @ ( par @ p2 @ piNil ) ) ) @ rel )
      | ( ( par @ ( par @ p @ q ) @ r )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( late_TauR != late_TauR )
      | ( C != pqr )
      | ( ( subs @ piNil @ A @ B )
       != ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ),
    inference(simp,[status(thm)],[1773]) ).

thf(1800,plain,
    ! [B: name,A: name] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ piNil ) ) ) @ rel )
      | ( ( par @ ( par @ p @ q ) @ r )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( ( subs @ piNil @ A @ B )
       != ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ),
    inference(simp,[status(thm)],[1786]) ).

thf(5082,plain,
    ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ piNil ) ) ) @ rel )
    | ( ( par @ ( par @ p @ q ) @ r )
     != ( par @ p @ ( par @ q @ r ) ) )
    | ( ( subs @ ( par @ q2 @ r ) @ x @ y )
     != piNil ) ),
    inference(rewrite,[status(thm)],[1800,1496]) ).

thf(67,axiom,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_fresh__prod) ).

thf(483,plain,
    ! [A: name,B: name,C: late_freeRes] :
      ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ B @ C ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(158,axiom,
    ! [A: pi,B: pi,C: pi] :
      ( ( tau @ A )
     != ( par @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_pi_Odistinct_I43_J) ).

thf(961,plain,
    ! [A: pi,B: pi,C: pi] :
      ( ( tau @ A )
     != ( par @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(962,plain,
    ~ ? [A: pi,B: pi,C: pi] :
        ( ( tau @ A )
        = ( par @ B @ C ) ),
    inference(miniscope,[status(thm)],[961]) ).

thf(963,plain,
    ! [C: pi,B: pi,A: pi] :
      ( ( tau @ A )
     != ( par @ B @ C ) ),
    inference(cnf,[status(esa)],[962]) ).

thf(964,plain,
    ! [C: pi,B: pi,A: pi] :
      ( ( tau @ A )
     != ( par @ B @ C ) ),
    inference(lifteq,[status(thm)],[963]) ).

thf(61,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( output @ A @ B @ C )
     != ( sum @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_pi_Odistinct_I27_J) ).

thf(462,plain,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( output @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(151,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name] :
      ( ( subs @ ( output @ A @ B @ C ) @ D @ E )
      = ( output @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_simps_I3_J) ).

thf(932,plain,
    ! [A: name,B: name,C: pi,D: name,E: name] :
      ( ( subs @ ( output @ A @ B @ C ) @ D @ E )
      = ( output @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(59,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( input @ A @ B @ C )
     != ( sum @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_pi_Odistinct_I53_J) ).

thf(455,plain,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( input @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(197,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( res @ C @ B )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_substRes2) ).

thf(1176,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( res @ C @ B )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(51,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( ( input @ A @ B @ C )
        = ( input @ D @ E @ F ) )
      = ( ( A = D )
        & ( ( abs_fun_name_pi @ B @ C )
          = ( abs_fun_name_pi @ E @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_pi_Oinject_I3_J) ).

thf(431,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( ( input @ A @ B @ C )
        = ( input @ D @ E @ F ) )
      = ( ( A = D )
        & ( ( abs_fun_name_pi @ B @ C )
          = ( abs_fun_name_pi @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(148,axiom,
    ! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_freshRes) ).

thf(922,plain,
    ! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(254,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( input @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_pi_Odistinct_I57_J) ).

thf(1562,plain,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( input @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(78,axiom,
    ! [A: name,B: late_freeRes,C: late_freeRes] :
      ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_fresh__prod) ).

thf(521,plain,
    ! [A: name,B: late_freeRes,C: late_freeRes] :
      ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(196,axiom,
    ! [A: late_residual > $o,B: late_residual] :
      ( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_residual_Oinducts) ).

thf(1171,plain,
    ! [A: late_residual > $o,B: late_residual] :
      ( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(430,plain,
    ( fresh_name_name
    = ( ^ [A: name,B: name] : ( A != B ) ) ),
    inference(lifteq,[status(thm)],[429]) ).

thf(1626,plain,
    ! [A: name] :
      ( ( fresh_name_name @ A )
      = ( ^ [B: name] : ( A != B ) ) ),
    inference(func_ext,[status(esa)],[430]) ).

thf(260,axiom,
    fresh_name_pi @ y @ q,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_cClose2_Ohyps_I13_J) ).

thf(1583,plain,
    fresh_name_pi @ y @ q,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(1206,plain,
    ~ ? [A: name,B: pi] :
        ( piNil
        = ( res @ A @ B ) ),
    inference(miniscope,[status(thm)],[1205]) ).

thf(1207,plain,
    ! [B: pi,A: name] :
      ( piNil
     != ( res @ A @ B ) ),
    inference(cnf,[status(esa)],[1206]) ).

thf(1208,plain,
    ! [B: pi,A: name] :
      ( ( res @ A @ B )
     != piNil ),
    inference(lifteq,[status(thm)],[1207]) ).

thf(10752,plain,
    ! [A: pi] :
      ( ~ $true
      | ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
       != ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1154,270]) ).

thf(10753,plain,
    ! [A: pi] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
       != ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ A ) ) ) ),
    inference(simp,[status(thm)],[10752]) ).

thf(10754,plain,
    ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ),
    inference(pattern_uni,[status(thm)],[10753:[bind(A,$thf( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ))]]) ).

thf(10826,plain,
    ! [B: name,A: name] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ piNil ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( ( subs @ piNil @ A @ B )
       != ( subs @ q2 @ x @ y ) ) ),
    inference(paramod_ordered,[status(thm)],[1496,10754]) ).

thf(10829,plain,
    ! [B: name,A: name] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ piNil ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( q2 != piNil )
      | ( A != x )
      | ( B != y ) ),
    inference(simp,[status(thm)],[10826]) ).

thf(10836,plain,
    ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ piNil ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
    | ( q2 != piNil ) ),
    inference(simp,[status(thm)],[10829]) ).

thf(10865,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( q2 != piNil )
      | ( ( product_Pair_pi_pi @ ( sk19 @ A ) @ ( sk20 @ A ) )
       != ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ piNil ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[580,10836]) ).

thf(10867,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( q2 != piNil )
      | ( ( sk19 @ A )
       != ( par @ ( res @ y @ ( par @ p2 @ piNil ) ) @ r ) )
      | ( ( sk20 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[10865]) ).

thf(3360,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ C ) ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[334,3165]) ).

thf(3361,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3360:[bind(A,$thf( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ H ) ) ) ) )),bind(B,$thf( H )),bind(C,$thf( bang @ H ))]]) ).

thf(3362,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3361]) ).

thf(4511,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( tau @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ C ) ) ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[276,3362]) ).

thf(4512,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4511:[bind(A,$thf( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ ( tau @ I ) ) ) ) ) )),bind(B,$thf( I )),bind(C,$thf( tau @ I ))]]) ).

thf(4529,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4512]) ).

thf(134,axiom,
    ! [A: name,B: pi,C: name,D: pi] :
      ( ( ( res @ A @ B )
        = ( res @ C @ D ) )
      = ( ( abs_fun_name_pi @ A @ B )
        = ( abs_fun_name_pi @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_pi_Oinject_I8_J) ).

thf(812,plain,
    ! [A: name,B: pi,C: name,D: pi] :
      ( ( ( res @ A @ B )
        = ( res @ C @ D ) )
      = ( ( abs_fun_name_pi @ A @ B )
        = ( abs_fun_name_pi @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(341,plain,
    ! [C: late_subject,B: late_freeRes,A: name] :
      ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(cnf,[status(esa)],[340]) ).

thf(342,plain,
    ! [C: late_subject,B: late_freeRes,A: name] :
      ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_717452603ubject @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[341]) ).

thf(164,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_name_pi @ C @ E )
           => ( ( C != B )
             => ( ( C != F )
               => ( ( fresh_name_pi @ C @ G )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_transitions_OComm1) ).

thf(1018,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( ( fresh_name_pi @ C @ A )
         => ( ( fresh_name_pi @ C @ E )
           => ( ( C != B )
             => ( ( C != F )
               => ( ( fresh_name_pi @ C @ G )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(10750,plain,
    ! [B: late_residual,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
       != ( late_transitions @ ( res @ A @ piNil ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1154,751]) ).

thf(10751,plain,
    ! [B: late_residual,A: name] :
      ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
     != ( late_transitions @ ( res @ A @ piNil ) @ B ) ),
    inference(simp,[status(thm)],[10750]) ).

thf(10774,plain,
    ! [B: late_residual,A: name] :
      ( ( ( res @ A @ piNil )
       != ( par @ ( par @ p @ q ) @ r ) )
      | ( ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) )
       != B ) ),
    inference(simp,[status(thm)],[10751]) ).

thf(10788,plain,
    ! [A: name] :
      ( ( res @ A @ piNil )
     != ( par @ ( par @ p @ q ) @ r ) ),
    inference(simp,[status(thm)],[10774]) ).

thf(89,axiom,
    ! [A: pi,B: name,C: name] :
      ( ( subs @ ( bang @ A ) @ B @ C )
      = ( bang @ ( subs @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_simps_I10_J) ).

thf(553,plain,
    ! [A: pi,B: name,C: name] :
      ( ( subs @ ( bang @ A ) @ B @ C )
      = ( bang @ ( subs @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(966,plain,
    ~ ? [A: name,B: name,C: pi,D: pi,E: pi] :
        ( ( input @ A @ B @ C )
        = ( par @ D @ E ) ),
    inference(miniscope,[status(thm)],[965]) ).

thf(967,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(cnf,[status(esa)],[966]) ).

thf(968,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( par @ D @ E ) ),
    inference(lifteq,[status(thm)],[967]) ).

thf(456,plain,
    ~ ? [A: name,B: name,C: pi,D: pi,E: pi] :
        ( ( input @ A @ B @ C )
        = ( sum @ D @ E ) ),
    inference(miniscope,[status(thm)],[455]) ).

thf(457,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(cnf,[status(esa)],[456]) ).

thf(458,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(lifteq,[status(thm)],[457]) ).

thf(138,axiom,
    ! [A: name > late_residual > $o,B: name,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: name] :
          ( ( fresh_name_name @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_residual_Ostrong__induct) ).

thf(823,plain,
    ! [A: name > late_residual > $o,B: name,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: name] :
          ( ( fresh_name_name @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(3029,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ C ) ) ) ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[334,2247]) ).

thf(3030,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[3029:[bind(A,$thf( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( bang @ I ) ) ) ) ) )),bind(B,$thf( I )),bind(C,$thf( bang @ I ))]]) ).

thf(3082,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[3030]) ).

thf(255,axiom,
    ! [A: name,B: pi,C: name,D: name,E: pi] :
      ~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_resTauOutputTrans) ).

thf(1566,plain,
    ! [A: name,B: pi,C: name,D: name,E: pi] :
      ~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(325,plain,
    ~ ? [A: name,B: name,C: pi] :
        ( piNil
        = ( output @ A @ B @ C ) ),
    inference(miniscope,[status(thm)],[324]) ).

thf(326,plain,
    ! [C: pi,B: name,A: name] :
      ( piNil
     != ( output @ A @ B @ C ) ),
    inference(cnf,[status(esa)],[325]) ).

thf(327,plain,
    ! [C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != piNil ),
    inference(lifteq,[status(thm)],[326]) ).

thf(309,plain,
    ! [B: name,A: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(cnf,[status(esa)],[308]) ).

thf(310,plain,
    ! [B: name,A: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(lifteq,[status(thm)],[309]) ).

thf(1836,plain,
    ! [C: late_residual,B: name,A: pi] :
      ( ~ $true
      | ( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) )
       != ( late_transitions @ ( res @ B @ piNil ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1150,751]) ).

thf(1837,plain,
    ! [C: late_residual,B: name,A: pi] :
      ( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) )
     != ( late_transitions @ ( res @ B @ piNil ) @ C ) ),
    inference(simp,[status(thm)],[1836]) ).

thf(1842,plain,
    ! [C: late_residual,B: name,A: pi] :
      ( ( ( tau @ A )
       != ( res @ B @ piNil ) )
      | ( ( late_FreeR @ late_TauR @ A )
       != C ) ),
    inference(simp,[status(thm)],[1837]) ).

thf(1845,plain,
    ! [B: name,A: pi] :
      ( ( tau @ A )
     != ( res @ B @ piNil ) ),
    inference(simp,[status(thm)],[1842]) ).

thf(4715,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3394,276]) ).

thf(4716,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4715:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4749,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( bang @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4716]) ).

thf(1759,plain,
    ! [B: late_residual,A: name] :
      ( ~ $true
      | ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
       != ( late_transitions @ ( res @ A @ piNil ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[543,751]) ).

thf(1760,plain,
    ! [B: late_residual,A: name] :
      ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
     != ( late_transitions @ ( res @ A @ piNil ) @ B ) ),
    inference(simp,[status(thm)],[1759]) ).

thf(1766,plain,
    ! [B: late_residual,A: name] :
      ( ( ( res @ A @ piNil )
       != p )
      | ( ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 )
       != B ) ),
    inference(simp,[status(thm)],[1760]) ).

thf(1770,plain,
    ! [A: name] :
      ( ( res @ A @ piNil )
     != p ),
    inference(simp,[status(thm)],[1766]) ).

thf(208,axiom,
    ! [A: name,B: name,C: name,D: name,E: pi] :
      ( ( A != B )
     => ( ( A != C )
       => ( ( subs @ ( input @ D @ A @ E ) @ B @ C )
          = ( input @ ( subst_name @ D @ B @ C ) @ A @ ( subs @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_substInput) ).

thf(1230,plain,
    ! [A: name,B: name,C: name,D: name,E: pi] :
      ( ( A != B )
     => ( ( A != C )
       => ( ( subs @ ( input @ D @ A @ E ) @ B @ C )
          = ( input @ ( subst_name @ D @ B @ C ) @ A @ ( subs @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(111,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_transitions_OInput) ).

thf(673,plain,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(329,plain,
    ~ ? [A: name,B: name,C: pi,D: pi] :
        ( ( input @ A @ B @ C )
        = ( bang @ D ) ),
    inference(miniscope,[status(thm)],[328]) ).

thf(330,plain,
    ! [D: pi,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( bang @ D ) ),
    inference(cnf,[status(esa)],[329]) ).

thf(331,plain,
    ! [D: pi,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( bang @ D ) ),
    inference(lifteq,[status(thm)],[330]) ).

thf(4521,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3362,334]) ).

thf(4522,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4521:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4549,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4522]) ).

thf(4964,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3617,334]) ).

thf(4965,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4964:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4982,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( bang @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4965]) ).

thf(358,plain,
    ! [D: pi,C: name,B: name,A: name] :
      ( ( fresh_name_pi @ A @ ( mismatch @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    inference(cnf,[status(esa)],[357]) ).

thf(359,plain,
    ! [D: pi,C: name,B: name,A: name] :
      ( ( fresh_name_pi @ A @ ( mismatch @ B @ C @ D ) )
      = ( ( fresh_name_name @ A @ B )
        & ( fresh_name_name @ A @ C )
        & ( fresh_name_pi @ A @ D ) ) ),
    inference(lifteq,[status(thm)],[358]) ).

thf(204,axiom,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_inputFreeTrans) ).

thf(1218,plain,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(5044,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3618,334]) ).

thf(5045,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[5044:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(5062,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( bang @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[5045]) ).

thf(1705,plain,
    ! [A: late_residual] :
      ( ~ $true
      | ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
       != ( late_transitions @ piNil @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[543,712]) ).

thf(1706,plain,
    ! [A: late_residual] :
      ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
     != ( late_transitions @ piNil @ A ) ),
    inference(simp,[status(thm)],[1705]) ).

thf(1709,plain,
    ! [A: late_residual] :
      ( ( p != piNil )
      | ( ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 )
       != A ) ),
    inference(simp,[status(thm)],[1706]) ).

thf(1711,plain,
    p != piNil,
    inference(simp,[status(thm)],[1709]) ).

thf(3021,plain,
    ! [D: pi,C: pi,B: pi,A: name] :
      ( ( fresh_name_pi @ A @ B )
      | ( ( fresh_name_pi @ A @ ( bang @ B ) )
       != ( fresh_name_pi @ ( sk1 @ ( sum @ C @ D ) ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[334,2446]) ).

thf(3022,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ ( bang @ B ) @ A ) ) @ B ),
    inference(pattern_uni,[status(thm)],[3021:[bind(A,$thf( sk1 @ ( sum @ ( bang @ H ) @ G ) )),bind(B,$thf( H )),bind(C,$thf( bang @ H )),bind(D,$thf( G ))]]) ).

thf(3080,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ ( bang @ B ) @ A ) ) @ B ),
    inference(simp,[status(thm)],[3022]) ).

thf(96,axiom,
    member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062) ).

thf(576,plain,
    member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(250,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: late_freeRes] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_1641682979reeRes @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_resSimCases) ).

thf(1538,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: late_freeRes] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_1641682979reeRes @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(86,axiom,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
     => ~ ( ( fresh_1641682979reeRes @ A @ D )
          | ( fresh_1641682979reeRes @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_outputFreshTrans) ).

thf(544,plain,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
     => ~ ( ( fresh_1641682979reeRes @ A @ D )
          | ( fresh_1641682979reeRes @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(249,axiom,
    ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_freeRes_Ofresh_I2_J) ).

thf(1536,plain,
    ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(205,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( match @ A @ B @ C ) @ D )
     => ~ ! [E: pi] :
            ( ( ( B = A )
              & ( C = E ) )
           => ~ ( late_transitions @ E @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_matchCases_H) ).

thf(1221,plain,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( match @ A @ B @ C ) @ D )
     => ~ ! [E: pi] :
            ( ( ( B = A )
              & ( C = E ) )
           => ~ ( late_transitions @ E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(10553,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
       != ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1229,940]) ).

thf(10554,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
     != ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ) ),
    inference(simp,[status(thm)],[10553]) ).

thf(10563,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( input @ A @ B @ C ) )
       != ( par @ p @ q ) )
      | ( ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) )
       != D ) ),
    inference(simp,[status(thm)],[10554]) ).

thf(10568,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( input @ A @ B @ C ) )
     != ( par @ p @ q ) ),
    inference(simp,[status(thm)],[10563]) ).

thf(1744,plain,
    ! [A: pi] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( late_TauR != late_TauR )
      | ( A != pqr ) ),
    inference(simp,[status(thm)],[1740]) ).

thf(1745,plain,
    ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
    | ( ( par @ p @ q )
     != p )
    | ( ( par @ q @ r )
     != r ) ),
    inference(simp,[status(thm)],[1744]) ).

thf(2718,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( product_Pair_pi_pi @ ( sk19 @ A ) @ ( sk20 @ A ) )
       != ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[580,1745]) ).

thf(2728,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( sk19 @ A )
       != pqr )
      | ( ( sk20 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[2718]) ).

thf(1238,plain,
    ~ ? [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
        ( ( late_BoundR @ A @ B @ C )
        = ( late_FreeR @ D @ E ) ),
    inference(miniscope,[status(thm)],[1237]) ).

thf(1239,plain,
    ! [E: pi,D: late_freeRes,C: pi,B: name,A: late_subject] :
      ( ( late_BoundR @ A @ B @ C )
     != ( late_FreeR @ D @ E ) ),
    inference(cnf,[status(esa)],[1238]) ).

thf(1240,plain,
    ! [E: pi,D: late_freeRes,C: pi,B: name,A: late_subject] :
      ( ( late_BoundR @ A @ B @ C )
     != ( late_FreeR @ D @ E ) ),
    inference(lifteq,[status(thm)],[1239]) ).

thf(37,axiom,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( input @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_pi_Odistinct_I5_J) ).

thf(383,plain,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( input @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(384,plain,
    ~ ? [A: name,B: name,C: pi] :
        ( piNil
        = ( input @ A @ B @ C ) ),
    inference(miniscope,[status(thm)],[383]) ).

thf(385,plain,
    ! [C: pi,B: name,A: name] :
      ( piNil
     != ( input @ A @ B @ C ) ),
    inference(cnf,[status(esa)],[384]) ).

thf(386,plain,
    ! [C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != piNil ),
    inference(lifteq,[status(thm)],[385]) ).

thf(4621,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ y @ x @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2194,442]) ).

thf(4622,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ y @ x @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4621]) ).

thf(4626,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ y @ x @ B )
       != ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4622]) ).

thf(4634,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ y @ x @ A )
     != ( input @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4626]) ).

thf(94,axiom,
    ! [A: pi,B: pi,C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ A @ B ) @ C ) @ ( par @ A @ ( par @ B @ C ) ) ) @ rel ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Ass) ).

thf(571,plain,
    ! [A: pi,B: pi,C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ A @ B ) @ C ) @ ( par @ A @ ( par @ B @ C ) ) ) @ rel ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(4655,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ x @ a @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2198,514]) ).

thf(4656,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ x @ a @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4655]) ).

thf(4663,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ x @ a @ B )
       != ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4656]) ).

thf(4671,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ x @ a @ A )
     != ( output @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4663]) ).

thf(4619,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ y @ a @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2220,442]) ).

thf(4620,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ y @ a @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4619]) ).

thf(4631,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ y @ a @ B )
       != ( input @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4620]) ).

thf(4639,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ y @ a @ A )
     != ( input @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4631]) ).

thf(463,plain,
    ~ ? [A: name,B: name,C: pi,D: pi,E: pi] :
        ( ( output @ A @ B @ C )
        = ( sum @ D @ E ) ),
    inference(miniscope,[status(thm)],[462]) ).

thf(464,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(cnf,[status(esa)],[463]) ).

thf(465,plain,
    ! [E: pi,D: pi,C: pi,B: name,A: name] :
      ( ( output @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(lifteq,[status(thm)],[464]) ).

thf(3420,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ~ $true
      | ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
       != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[543,1259]) ).

thf(3421,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
     != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ),
    inference(simp,[status(thm)],[3420]) ).

thf(3423,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( ( mismatch @ A @ A @ B )
       != p )
      | ( ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 )
       != C ) ),
    inference(simp,[status(thm)],[3421]) ).

thf(3433,plain,
    ! [B: pi,A: name] :
      ( ( mismatch @ A @ A @ B )
     != p ),
    inference(simp,[status(thm)],[3423]) ).

thf(198,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ E @ A )
       => ( ( E != C )
         => ( fresh_name_pi @ E @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_freshBoundDerivative_I2_J) ).

thf(1180,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_name_pi @ E @ A )
       => ( ( E != C )
         => ( fresh_name_pi @ E @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(4851,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3461,276]) ).

thf(4852,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4851:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4873,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4852]) ).

thf(162,axiom,
    member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( par @ ( subs @ q2 @ x @ y ) @ r ) ) ) ) @ rel,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_A_092_060parallel_062_AR_J_J_A_092_060in_062_ARel_092_060close_062) ).

thf(976,plain,
    member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( par @ ( subs @ q2 @ x @ y ) @ r ) ) ) ) @ rel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(258,axiom,
    ! [A: name,B: name,C: name,D: pi,E: pi] :
      ~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_FreeR @ late_TauR @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_resOutputTauTrans) ).

thf(1575,plain,
    ! [A: name,B: name,C: name,D: pi,E: pi] :
      ~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_FreeR @ late_TauR @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1858,plain,
    ! [A: late_residual] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
       != ( late_transitions @ piNil @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1229,712]) ).

thf(1859,plain,
    ! [A: late_residual] :
      ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
     != ( late_transitions @ piNil @ A ) ),
    inference(simp,[status(thm)],[1858]) ).

thf(1863,plain,
    ! [A: late_residual] :
      ( ( ( par @ p @ q )
       != piNil )
      | ( ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) )
       != A ) ),
    inference(simp,[status(thm)],[1859]) ).

thf(1866,plain,
    ( ( par @ p @ q )
   != piNil ),
    inference(simp,[status(thm)],[1863]) ).

thf(3572,plain,
    ! [C: name,B: name,A: name] :
      ( ( ( late_InputS @ A )
       != ( late_BoundOutputS @ C ) )
      | ( ( late_InputS @ ( sk4 @ ( late_InputS @ A ) ) )
       != ( late_InputS @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3528,401]) ).

thf(3573,plain,
    ! [B: name,A: name] :
      ( ( late_InputS @ B )
     != ( late_BoundOutputS @ A ) ),
    inference(pattern_uni,[status(thm)],[3572:[bind(A,$thf( E )),bind(B,$thf( sk4 @ ( late_InputS @ E ) )),bind(C,$thf( C ))]]) ).

thf(3584,plain,
    ! [B: name,A: name] :
      ( ( late_InputS @ B )
     != ( late_BoundOutputS @ A ) ),
    inference(simp,[status(thm)],[3573]) ).

thf(90,axiom,
    ! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
      ~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_outputBoundTrans) ).

thf(556,plain,
    ! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
      ~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(79,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
      = ( ( A = B )
        | ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_abs__fresh_I1_J) ).

thf(524,plain,
    ! [A: name,B: name,C: pi] :
      ( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
      = ( ( A = B )
        | ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(10766,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
       != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[1154,603]) ).

thf(10767,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
     != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ),
    inference(simp,[status(thm)],[10766]) ).

thf(10781,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( output @ A @ B @ C ) )
       != ( par @ ( par @ p @ q ) @ r ) )
      | ( ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) )
       != D ) ),
    inference(simp,[status(thm)],[10767]) ).

thf(10796,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( output @ A @ B @ C ) )
     != ( par @ ( par @ p @ q ) @ r ) ),
    inference(simp,[status(thm)],[10781]) ).

thf(98,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_717452603ubject @ E @ B )
       => ( ( E != C )
         => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Late__Semantics_OResB) ).

thf(581,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh_717452603ubject @ E @ B )
       => ( ( E != C )
         => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(2321,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ x @ a @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2198,349]) ).

thf(2322,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ x @ a @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2321]) ).

thf(2323,plain,
    ! [D: pi,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ x @ a @ B )
       != ( tau @ D ) ) ),
    inference(simp,[status(thm)],[2322]) ).

thf(2325,plain,
    ! [B: pi,A: pi] :
      ( ( match @ x @ a @ A )
     != ( tau @ B ) ),
    inference(simp,[status(thm)],[2323]) ).

thf(130,axiom,
    ! [A: pi,B: late_residual,C: name,D: name] :
      ( ( late_transitions @ A @ B )
     => ( ( C != D )
       => ( late_transitions @ ( mismatch @ C @ D @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_Mismatch) ).

thf(759,plain,
    ! [A: pi,B: late_residual,C: name,D: name] :
      ( ( late_transitions @ A @ B )
     => ( ( C != D )
       => ( late_transitions @ ( mismatch @ C @ D @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(262,axiom,
    ! [A: pi,B: late_residual] :
      ( ( late_transitions @ ( tau @ A ) @ B )
     => ~ ! [C: pi] :
            ( ( ( tau @ A )
              = ( tau @ C ) )
           => ( B
             != ( late_FreeR @ late_TauR @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_tauCases_H) ).

thf(1590,plain,
    ! [A: pi,B: late_residual] :
      ( ( late_transitions @ ( tau @ A ) @ B )
     => ~ ! [C: pi] :
            ( ( ( tau @ A )
              = ( tau @ C ) )
           => ( B
             != ( late_FreeR @ late_TauR @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(4653,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ y @ x @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2194,514]) ).

thf(4654,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ y @ x @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4653]) ).

thf(4658,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ y @ x @ B )
       != ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4654]) ).

thf(4666,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ y @ x @ A )
     != ( output @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4658]) ).

thf(303,plain,
    ! [C: name,B: late_freeRes,A: name] :
      ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(cnf,[status(esa)],[302]) ).

thf(304,plain,
    ! [C: name,B: late_freeRes,A: name] :
      ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_name @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[303]) ).

thf(245,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: late_subject] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_717452603ubject @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_resSimCases) ).

thf(1508,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: late_subject] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_717452603ubject @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(238,axiom,
    ! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_freeRes,E: pi] :
      ( ( strong743114133lation @ A @ B @ C )
     => ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
       => ? [F: pi] :
            ( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
            & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_simE_I2_J) ).

thf(1481,plain,
    ! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_freeRes,E: pi] :
      ( ( strong743114133lation @ A @ B @ C )
     => ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
       => ? [F: pi] :
            ( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
            & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(110,axiom,
    ! [A: late_subject > pi > $o,B: late_subject,C: pi] :
      ( ! [D: late_subject] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: late_subject] :
            ( ! [H: late_subject] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: late_subject] :
              ( ! [F: late_subject] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: late_subject] :
                ( ( fresh_717452603ubject @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: late_subject] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: late_subject] :
                  ( ! [H: late_subject] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: late_subject] :
                    ( ! [H: late_subject] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: late_subject] :
                      ( ! [G: late_subject] : ( A @ G @ D )
                     => ( ! [G: late_subject] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: late_subject] :
                        ( ! [G: late_subject] : ( A @ G @ D )
                       => ( ! [G: late_subject] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: late_subject] :
                          ( ( fresh_717452603ubject @ D @ F )
                         => ( ! [G: late_subject] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: late_subject] :
                            ( ! [F: late_subject] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_pi_Ostrong__inducts) ).

thf(632,plain,
    ! [A: late_subject > pi > $o,B: late_subject,C: pi] :
      ( ! [D: late_subject] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: late_subject] :
            ( ! [H: late_subject] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: late_subject] :
              ( ! [F: late_subject] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: late_subject] :
                ( ( fresh_717452603ubject @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: late_subject] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: late_subject] :
                  ( ! [H: late_subject] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: late_subject] :
                    ( ! [H: late_subject] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: late_subject] :
                      ( ! [G: late_subject] : ( A @ G @ D )
                     => ( ! [G: late_subject] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: late_subject] :
                        ( ! [G: late_subject] : ( A @ G @ D )
                       => ( ! [G: late_subject] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: late_subject] :
                          ( ( fresh_717452603ubject @ D @ F )
                         => ( ! [G: late_subject] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: late_subject] :
                            ( ! [F: late_subject] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(212,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_name_pi @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_simCasesCont) ).

thf(1244,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_name_pi @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(122,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Late__Semantics_OComm1) ).

thf(731,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(2917,plain,
    ! [D: pi,C: name,B: pi,A: pi] :
      ( ( fresh_name_pi @ C @ D )
      | ( ( fresh_name_pi @ ( sk1 @ ( sum @ A @ B ) ) @ B )
       != ( fresh_name_pi @ C @ ( tau @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2447,276]) ).

thf(2918,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ A @ ( tau @ B ) ) ) @ B ),
    inference(pattern_uni,[status(thm)],[2917:[bind(A,$thf( F )),bind(B,$thf( tau @ H )),bind(C,$thf( sk1 @ ( sum @ F @ ( tau @ H ) ) )),bind(D,$thf( H ))]]) ).

thf(2934,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( sum @ A @ ( tau @ B ) ) ) @ B ),
    inference(simp,[status(thm)],[2918]) ).

thf(100,axiom,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh_81631222sidual @ A @ ( late_FreeR @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_residual_Ofresh_I2_J) ).

thf(588,plain,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh_81631222sidual @ A @ ( late_FreeR @ B @ C ) )
      = ( ( fresh_1641682979reeRes @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(230,axiom,
    ! [A: pi,B: pi,C: late_subject,D: name,E: pi] :
      ( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
            ( ( ( par @ A @ B )
              = ( par @ F @ J ) )
           => ( ( ( late_BoundR @ C @ D @ E )
                = ( late_BoundR @ G @ H @ ( par @ I @ J ) ) )
             => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
               => ( ( fresh_name_pi @ H @ F )
                 => ( ( fresh_name_pi @ H @ J )
                   => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) )
       => ~ ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
              ( ( ( par @ A @ B )
                = ( par @ J @ F ) )
             => ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ G @ H @ ( par @ J @ I ) ) )
               => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
                 => ( ( fresh_name_pi @ H @ J )
                   => ( ( fresh_name_pi @ H @ F )
                     => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_parCasesB_H) ).

thf(1385,plain,
    ! [A: pi,B: pi,C: late_subject,D: name,E: pi] :
      ( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
            ( ( ( par @ A @ B )
              = ( par @ F @ J ) )
           => ( ( ( late_BoundR @ C @ D @ E )
                = ( late_BoundR @ G @ H @ ( par @ I @ J ) ) )
             => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
               => ( ( fresh_name_pi @ H @ F )
                 => ( ( fresh_name_pi @ H @ J )
                   => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) )
       => ~ ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
              ( ( ( par @ A @ B )
                = ( par @ J @ F ) )
             => ( ( ( late_BoundR @ C @ D @ E )
                  = ( late_BoundR @ G @ H @ ( par @ J @ I ) ) )
               => ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
                 => ( ( fresh_name_pi @ H @ J )
                   => ( ( fresh_name_pi @ H @ F )
                     => ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(566,plain,
    ~ ? [A: name,B: name,C: pi,D: name,E: pi] :
        ( ( mismatch @ A @ B @ C )
        = ( res @ D @ E ) ),
    inference(miniscope,[status(thm)],[565]) ).

thf(567,plain,
    ! [E: pi,D: name,C: pi,B: name,A: name] :
      ( ( mismatch @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(cnf,[status(esa)],[566]) ).

thf(568,plain,
    ! [E: pi,D: name,C: pi,B: name,A: name] :
      ( ( mismatch @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(lifteq,[status(thm)],[567]) ).

thf(8,axiom,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( match @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_pi_Odistinct_I7_J) ).

thf(287,plain,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( match @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(288,plain,
    ~ ? [A: name,B: name,C: pi] :
        ( piNil
        = ( match @ A @ B @ C ) ),
    inference(miniscope,[status(thm)],[287]) ).

thf(289,plain,
    ! [C: pi,B: name,A: name] :
      ( piNil
     != ( match @ A @ B @ C ) ),
    inference(cnf,[status(esa)],[288]) ).

thf(290,plain,
    ! [C: pi,B: name,A: name] :
      ( ( match @ A @ B @ C )
     != piNil ),
    inference(lifteq,[status(thm)],[289]) ).

thf(432,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( ( input @ A @ B @ C )
        = ( input @ D @ E @ F ) )
      = ( ( A = D )
        & ( ( abs_fun_name_pi @ B @ C )
          = ( abs_fun_name_pi @ E @ F ) ) ) ),
    inference(cnf,[status(esa)],[431]) ).

thf(433,plain,
    ! [F: pi,E: name,D: name,C: pi,B: name,A: name] :
      ( ( ( input @ A @ B @ C )
        = ( input @ D @ E @ F ) )
      = ( ( A = D )
        & ( ( abs_fun_name_pi @ B @ C )
          = ( abs_fun_name_pi @ E @ F ) ) ) ),
    inference(lifteq,[status(thm)],[432]) ).

thf(3414,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( mismatch @ A @ A @ B ) @ C )
       != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1734,1259]) ).

thf(3415,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( late_transitions @ ( mismatch @ A @ A @ B ) @ C )
     != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[3414]) ).

thf(3426,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( ( mismatch @ A @ A @ B )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( C
       != ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[3415]) ).

thf(3430,plain,
    ! [B: pi,A: name] :
      ( ( mismatch @ A @ A @ B )
     != ( par @ p @ ( par @ q @ r ) ) ),
    inference(simp,[status(thm)],[3426]) ).

thf(143,axiom,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
      ( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_old_Oprod_Oinducts) ).

thf(899,plain,
    ! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
      ( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(344,plain,
    ~ ? [A: pi] :
        ( piNil
        = ( tau @ A ) ),
    inference(miniscope,[status(thm)],[343]) ).

thf(345,plain,
    ! [A: pi] :
      ( piNil
     != ( tau @ A ) ),
    inference(cnf,[status(esa)],[344]) ).

thf(346,plain,
    ! [A: pi] :
      ( ( tau @ A )
     != piNil ),
    inference(lifteq,[status(thm)],[345]) ).

thf(5120,plain,
    ! [E: pi,D: set_Pr1834926343_pi_pi,C: pi,B: name,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( mismatch @ B @ B @ C ) )
       != ( strong743114133lation @ piNil @ D @ ( tau @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[382,349]) ).

thf(5121,plain,
    ! [E: pi,D: set_Pr1834926343_pi_pi,C: pi,B: name,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( mismatch @ B @ B @ C ) )
     != ( strong743114133lation @ piNil @ D @ ( tau @ E ) ) ),
    inference(simp,[status(thm)],[5120]) ).

thf(5125,plain,
    ! [E: pi,D: set_Pr1834926343_pi_pi,C: pi,B: name,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != D )
      | ( ( mismatch @ B @ B @ C )
       != ( tau @ E ) ) ),
    inference(simp,[status(thm)],[5121]) ).

thf(5128,plain,
    ! [C: pi,B: pi,A: name] :
      ( ( mismatch @ A @ A @ B )
     != ( tau @ C ) ),
    inference(simp,[status(thm)],[5125]) ).

thf(87,axiom,
    ! [A: pi,B: name,C: name] :
      ( ( subs @ ( tau @ A ) @ B @ C )
      = ( tau @ ( subs @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_simps_I2_J) ).

thf(549,plain,
    ! [A: pi,B: name,C: name] :
      ( ( subs @ ( tau @ A ) @ B @ C )
      = ( tau @ ( subs @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(4914,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( bang @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3463,334]) ).

thf(4915,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4914:[bind(A,$thf( bang @ I )),bind(B,$thf( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ ( bang @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4927,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( bang @ ( tau @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4915]) ).

thf(241,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name] :
      ( ( subs @ ( mismatch @ A @ B @ C ) @ D @ E )
      = ( mismatch @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_simps_I6_J) ).

thf(1491,plain,
    ! [A: name,B: name,C: pi,D: name,E: name] :
      ( ( subs @ ( mismatch @ A @ B @ C ) @ D @ E )
      = ( mismatch @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(1719,plain,
    ! [A: late_residual] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
       != ( late_transitions @ piNil @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[907,712]) ).

thf(1720,plain,
    ! [A: late_residual] :
      ( ( late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) )
     != ( late_transitions @ piNil @ A ) ),
    inference(simp,[status(thm)],[1719]) ).

thf(1723,plain,
    ! [A: late_residual] :
      ( ( ( par @ q @ r )
       != piNil )
      | ( ( late_BoundR @ ( late_InputS @ a ) @ x @ qr )
       != A ) ),
    inference(simp,[status(thm)],[1720]) ).

thf(1725,plain,
    ( ( par @ q @ r )
   != piNil ),
    inference(simp,[status(thm)],[1723]) ).

thf(259,axiom,
    ! [A: name > pi > $o,B: name,C: pi] :
      ( ! [D: name] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: name] :
            ( ! [H: name] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: name] :
              ( ! [F: name] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: name] :
                ( ( fresh_name_name @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: name] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: name] :
                  ( ! [H: name] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: name] :
                    ( ! [H: name] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: name] :
                      ( ! [G: name] : ( A @ G @ D )
                     => ( ! [G: name] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: name] :
                        ( ! [G: name] : ( A @ G @ D )
                       => ( ! [G: name] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: name] :
                          ( ( fresh_name_name @ D @ F )
                         => ( ! [G: name] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: name] :
                            ( ! [F: name] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_pi_Ostrong__induct) ).

thf(1578,plain,
    ! [A: name > pi > $o,B: name,C: pi] :
      ( ! [D: name] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: name] :
            ( ! [H: name] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: name] :
              ( ! [F: name] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: name] :
                ( ( fresh_name_name @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: name] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: name] :
                  ( ! [H: name] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: name] :
                    ( ! [H: name] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: name] :
                      ( ! [G: name] : ( A @ G @ D )
                     => ( ! [G: name] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: name] :
                        ( ! [G: name] : ( A @ G @ D )
                       => ( ! [G: name] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: name] :
                          ( ( fresh_name_name @ D @ F )
                         => ( ! [G: name] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: name] :
                            ( ! [F: name] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(4641,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ~ $true
      | ( ( strong743114133lation @ piNil @ A @ ( match @ a @ x @ B ) )
       != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2199,514]) ).

thf(4642,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( strong743114133lation @ piNil @ A @ ( match @ a @ x @ B ) )
     != ( strong743114133lation @ piNil @ C @ ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4641]) ).

thf(4662,plain,
    ! [F: pi,E: name,D: name,C: set_Pr1834926343_pi_pi,B: pi,A: set_Pr1834926343_pi_pi] :
      ( ( piNil != piNil )
      | ( A != C )
      | ( ( match @ a @ x @ B )
       != ( output @ D @ E @ F ) ) ),
    inference(simp,[status(thm)],[4642]) ).

thf(4670,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( match @ a @ x @ A )
     != ( output @ B @ C @ D ) ),
    inference(simp,[status(thm)],[4662]) ).

thf(3229,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( subs @ ( par @ q2 @ r ) @ x @ y )
       != piNil )
      | ( ( product_Pair_pi_pi @ ( sk208 @ A ) @ ( sk209 @ A ) )
       != ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ piNil ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1032,3213]) ).

thf(3232,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( subs @ ( par @ q2 @ r ) @ x @ y )
       != piNil )
      | ( ( sk208 @ A )
       != pqr )
      | ( ( sk209 @ A )
       != ( res @ y @ ( par @ p2 @ piNil ) ) ) ),
    inference(simp,[status(thm)],[3229]) ).

thf(817,plain,
    ~ ? [A: name,B: name,C: pi,D: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
    inference(miniscope,[status(thm)],[816]) ).

thf(818,plain,
    ! [D: pi,C: pi,B: name,A: name] :
      ~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
    inference(cnf,[status(esa)],[817]) ).

thf(2714,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ ( par @ p @ q ) @ r )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( ( product_Pair_pi_pi @ ( sk19 @ A ) @ ( sk20 @ A ) )
       != ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[580,1746]) ).

thf(2736,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ ( par @ p @ q ) @ r )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( ( sk19 @ A )
       != pqr )
      | ( ( sk20 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[2714]) ).

thf(421,plain,
    ! [B: product_prod_pi_pi > $o,A: product_prod_pi_pi > $o] :
      ( ( ( A @ ( sk7 @ B @ A ) )
       != ( B @ ( sk7 @ B @ A ) ) )
      | ( ( collec1051790738_pi_pi @ A )
        = ( collec1051790738_pi_pi @ B ) ) ),
    inference(cnf,[status(esa)],[420]) ).

thf(422,plain,
    ! [B: product_prod_pi_pi > $o,A: product_prod_pi_pi > $o] :
      ( ( ( A @ ( sk7 @ B @ A ) )
       != ( B @ ( sk7 @ B @ A ) ) )
      | ( ( collec1051790738_pi_pi @ A )
        = ( collec1051790738_pi_pi @ B ) ) ),
    inference(lifteq,[status(thm)],[421]) ).

thf(272,plain,
    ! [B: pi,A: pi] :
      ( ( ( tau @ A )
        = ( tau @ B ) )
      = ( A = B ) ),
    inference(cnf,[status(esa)],[271]) ).

thf(273,plain,
    ! [B: pi,A: pi] :
      ( ( ( tau @ A )
        = ( tau @ B ) )
      = ( A = B ) ),
    inference(lifteq,[status(thm)],[272]) ).

thf(4559,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3363,276]) ).

thf(4560,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4559:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4579,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( bang @ ( tau @ ( tau @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4560]) ).

thf(10863,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( q2 != piNil )
      | ( ( product_Pair_pi_pi @ ( sk208 @ A ) @ ( sk209 @ A ) )
       != ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ piNil ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1032,10836]) ).

thf(10868,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( q2 != piNil )
      | ( ( sk208 @ A )
       != ( par @ ( res @ y @ ( par @ p2 @ piNil ) ) @ r ) )
      | ( ( sk209 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[10863]) ).

thf(10551,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D )
       != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1734,940]) ).

thf(10552,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D )
     != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[10551]) ).

thf(10564,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( input @ A @ B @ C ) )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( D
       != ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[10552]) ).

thf(10569,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( input @ A @ B @ C ) )
     != ( par @ p @ ( par @ q @ r ) ) ),
    inference(simp,[status(thm)],[10564]) ).

thf(292,plain,
    ~ ? [A: pi,B: pi,C: pi] :
        ( ( tau @ A )
        = ( sum @ B @ C ) ),
    inference(miniscope,[status(thm)],[291]) ).

thf(293,plain,
    ! [C: pi,B: pi,A: pi] :
      ( ( tau @ A )
     != ( sum @ B @ C ) ),
    inference(cnf,[status(esa)],[292]) ).

thf(294,plain,
    ! [C: pi,B: pi,A: pi] :
      ( ( tau @ A )
     != ( sum @ B @ C ) ),
    inference(lifteq,[status(thm)],[293]) ).

thf(216,axiom,
    ! [A: name,B: pi,C: late_freeRes,D: pi,E: pi > $o] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
     => ( ! [F: pi] :
            ( ( late_transitions @ B @ ( late_FreeR @ C @ F ) )
           => ( ( fresh_1641682979reeRes @ A @ C )
             => ( E @ ( res @ A @ F ) ) ) )
       => ( E @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_resCasesF) ).

thf(1314,plain,
    ! [A: name,B: pi,C: late_freeRes,D: pi,E: pi > $o] :
      ( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
     => ( ! [F: pi] :
            ( ( late_transitions @ B @ ( late_FreeR @ C @ F ) )
           => ( ( fresh_1641682979reeRes @ A @ C )
             => ( E @ ( res @ A @ F ) ) ) )
       => ( E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(8501,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ~ $true
      | ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
       != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[543,603]) ).

thf(8502,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) )
     != ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ) ),
    inference(simp,[status(thm)],[8501]) ).

thf(8504,plain,
    ! [D: late_residual,C: pi,B: name,A: name] :
      ( ( ( res @ A @ ( output @ A @ B @ C ) )
       != p )
      | ( ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 )
       != D ) ),
    inference(simp,[status(thm)],[8502]) ).

thf(8510,plain,
    ! [C: pi,B: name,A: name] :
      ( ( res @ A @ ( output @ A @ B @ C ) )
     != p ),
    inference(simp,[status(thm)],[8504]) ).

thf(2716,plain,
    ! [B: pi,A: product_prod_pi_pi] :
      ( ~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ B ) )
      | ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( product_Pair_pi_pi @ ( sk19 @ A ) @ ( sk20 @ A ) )
       != ( product_Pair_pi_pi @ B @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[580,270]) ).

thf(2730,plain,
    ! [B: pi,A: product_prod_pi_pi] :
      ( ~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ B ) )
      | ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( sk19 @ A )
       != B )
      | ( ( sk20 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[2716]) ).

thf(2746,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( sk19 @ A ) ) )
      | ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( sk20 @ A )
       != ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ),
    inference(simp,[status(thm)],[2730]) ).

thf(253,axiom,
    fresh_name_pi @ x @ p2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_cClose2_Ohyps_I7_J) ).

thf(1561,plain,
    fresh_name_pi @ x @ p2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(132,axiom,
    ! [A: pi > pi > $o,B: pi,C: pi] :
      ( ! [D: pi] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: pi] :
            ( ! [H: pi] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: pi] :
              ( ! [F: pi] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: pi] :
                ( ( fresh_name_pi @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: pi] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: pi] :
                  ( ! [H: pi] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: pi] :
                    ( ! [H: pi] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: pi] :
                      ( ! [G: pi] : ( A @ G @ D )
                     => ( ! [G: pi] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: pi] :
                        ( ! [G: pi] : ( A @ G @ D )
                       => ( ! [G: pi] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: pi] :
                          ( ( fresh_name_pi @ D @ F )
                         => ( ! [G: pi] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: pi] :
                            ( ! [F: pi] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_pi_Ostrong__inducts) ).

thf(767,plain,
    ! [A: pi > pi > $o,B: pi,C: pi] :
      ( ! [D: pi] : ( A @ D @ piNil )
     => ( ! [D: name,E: name,F: pi,G: pi] :
            ( ! [H: pi] : ( A @ H @ F )
           => ( A @ G @ ( output @ D @ E @ F ) ) )
       => ( ! [D: pi,E: pi] :
              ( ! [F: pi] : ( A @ F @ D )
             => ( A @ E @ ( tau @ D ) ) )
         => ( ! [D: name,E: name,F: pi,G: pi] :
                ( ( fresh_name_pi @ E @ G )
               => ( ( fresh_name_name @ E @ D )
                 => ( ! [H: pi] : ( A @ H @ F )
                   => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
           => ( ! [D: name,E: name,F: pi,G: pi] :
                  ( ! [H: pi] : ( A @ H @ F )
                 => ( A @ G @ ( match @ D @ E @ F ) ) )
             => ( ! [D: name,E: name,F: pi,G: pi] :
                    ( ! [H: pi] : ( A @ H @ F )
                   => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
               => ( ! [D: pi,E: pi,F: pi] :
                      ( ! [G: pi] : ( A @ G @ D )
                     => ( ! [G: pi] : ( A @ G @ E )
                       => ( A @ F @ ( sum @ D @ E ) ) ) )
                 => ( ! [D: pi,E: pi,F: pi] :
                        ( ! [G: pi] : ( A @ G @ D )
                       => ( ! [G: pi] : ( A @ G @ E )
                         => ( A @ F @ ( par @ D @ E ) ) ) )
                   => ( ! [D: name,E: pi,F: pi] :
                          ( ( fresh_name_pi @ D @ F )
                         => ( ! [G: pi] : ( A @ G @ E )
                           => ( A @ F @ ( res @ D @ E ) ) ) )
                     => ( ! [D: pi,E: pi] :
                            ( ! [F: pi] : ( A @ F @ D )
                           => ( A @ E @ ( bang @ D ) ) )
                       => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(959,plain,
    ~ ? [A: pi,B: name,C: name,D: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
    inference(miniscope,[status(thm)],[958]) ).

thf(960,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
    inference(cnf,[status(esa)],[959]) ).

thf(167,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ ( par @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_pi_Ofresh_I8_J) ).

thf(1033,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh_name_pi @ A @ ( par @ B @ C ) )
      = ( ( fresh_name_pi @ A @ B )
        & ( fresh_name_pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(201,axiom,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi,F: late_freeRes > pi > $o] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
     => ( ( ( D
            = ( late_OutputR @ A @ B ) )
         => ( ( C = E )
           => ( F @ ( late_OutputR @ A @ B ) @ C ) ) )
       => ( F @ D @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_outputCases) ).

thf(1197,plain,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi,F: late_freeRes > pi > $o] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
     => ( ( ( D
            = ( late_OutputR @ A @ B ) )
         => ( ( C = E )
           => ( F @ ( late_OutputR @ A @ B ) @ C ) ) )
       => ( F @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(119,axiom,
    ! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_subject] :
          ( ( fresh_717452603ubject @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_residual_Ostrong__induct) ).

thf(720,plain,
    ! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
      ( ! [D: late_subject,E: name,F: pi,G: late_subject] :
          ( ( fresh_717452603ubject @ E @ G )
         => ( ( fresh_717452603ubject @ E @ D )
           => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
     => ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(194,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_fresh__fact2) ).

thf(1165,plain,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(140,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Late__Semantics_OComm2) ).

thf(886,plain,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(1742,plain,
    ! [A: pi] :
      ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( late_FreeR @ late_TauR @ A )
       != ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[1740]) ).

thf(150,axiom,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( A != B )
     => ( ( A != C )
       => ( ( subs @ ( res @ A @ D ) @ B @ C )
          = ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_simps_I9_J) ).

thf(928,plain,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( A != B )
     => ( ( A != C )
       => ( ( subs @ ( res @ A @ D ) @ B @ C )
          = ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(413,plain,
    ~ ? [A: pi,B: pi,C: pi] :
        ( ( sum @ A @ B )
        = ( bang @ C ) ),
    inference(miniscope,[status(thm)],[412]) ).

thf(414,plain,
    ! [C: pi,B: pi,A: pi] :
      ( ( sum @ A @ B )
     != ( bang @ C ) ),
    inference(cnf,[status(esa)],[413]) ).

thf(415,plain,
    ! [C: pi,B: pi,A: pi] :
      ( ( sum @ A @ B )
     != ( bang @ C ) ),
    inference(lifteq,[status(thm)],[414]) ).

thf(124,axiom,
    ! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_resInputBoundOutputTrans) ).

thf(740,plain,
    ! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(1537,plain,
    ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
    inference(cnf,[status(esa)],[1536]) ).

thf(146,axiom,
    ! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
      ( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( ( fresh_name_pi @ D @ B )
         => ( ! [G: pi] :
                ( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
               => ( F @ ( par @ G @ B ) ) )
           => ( ! [G: pi] :
                  ( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
                 => ( F @ ( par @ A @ G ) ) )
             => ( F @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_parCasesB) ).

thf(908,plain,
    ! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
      ( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ( fresh_name_pi @ D @ A )
       => ( ( fresh_name_pi @ D @ B )
         => ( ! [G: pi] :
                ( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
               => ( F @ ( par @ G @ B ) ) )
           => ( ! [G: pi] :
                  ( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
                 => ( F @ ( par @ A @ G ) ) )
             => ( F @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(820,plain,
    ~ ? [A: name,B: name] :
        ( ( late_OutputR @ A @ B )
        = late_TauR ),
    inference(miniscope,[status(thm)],[819]) ).

thf(821,plain,
    ! [B: name,A: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(cnf,[status(esa)],[820]) ).

thf(822,plain,
    ! [B: name,A: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(lifteq,[status(thm)],[821]) ).

thf(4308,plain,
    ! [C: pi,B: name,A: pi] :
      ( ( fresh_name_pi @ B @ C )
      | ( ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ A ) ) ) ) ) @ A )
       != ( fresh_name_pi @ B @ ( tau @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3109,276]) ).

thf(4309,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(pattern_uni,[status(thm)],[4308:[bind(A,$thf( tau @ I )),bind(B,$thf( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ ( tau @ I ) ) ) ) ) )),bind(C,$thf( I ))]]) ).

thf(4330,plain,
    ! [A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( tau @ ( tau @ ( bang @ ( tau @ A ) ) ) ) ) ) @ A ),
    inference(simp,[status(thm)],[4309]) ).

thf(264,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: name] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_name_name @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_resSimCases) ).

thf(1597,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: name] :
      ( ( eqvt_pi @ A )
     => ( ! [F: pi,G: name] :
            ( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
           => ( ( G != C )
             => ? [H: pi] :
                  ( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
       => ( ! [F: pi,G: late_subject,H: name] :
              ( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
             => ( ( fresh_717452603ubject @ C @ G )
               => ( ( C != H )
                 => ( ( fresh_name_name @ H @ E )
                   => ? [I: pi] :
                        ( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
                        & ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
         => ( ! [F: pi,G: late_freeRes] :
                ( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
               => ( ( fresh_1641682979reeRes @ C @ G )
                 => ? [H: pi] :
                      ( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
                      & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
           => ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(244,axiom,
    ! [A: name,B: pi,C: pi,D: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ A @ ( par @ C @ D ) ) @ B ) @ ( res @ A @ ( par @ C @ ( par @ D @ B ) ) ) ) @ rel ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_FreshExt_H) ).

thf(1505,plain,
    ! [A: name,B: pi,C: pi,D: pi] :
      ( ( fresh_name_pi @ A @ B )
     => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ A @ ( par @ C @ D ) ) @ B ) @ ( res @ A @ ( par @ C @ ( par @ D @ B ) ) ) ) @ rel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(182,axiom,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
        = ( subs @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_substTrans) ).

thf(1120,plain,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
        = ( subs @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(72,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( input @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_pi_Odistinct_I51_J) ).

thf(501,plain,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( input @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(368,plain,
    ~ ~ ! [A: name] :
        ? [B: name] : ( fresh_name_name @ B @ A ),
    inference(miniscope,[status(thm)],[367]) ).

thf(369,plain,
    ! [A: name] : ( fresh_name_name @ ( sk6 @ A ) @ A ),
    inference(cnf,[status(esa)],[368]) ).

thf(106,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: name] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_name_name @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_simCasesCont) ).

thf(607,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: name] :
      ( ( eqvt_pi @ A )
     => ( ! [E: late_subject,F: name,G: pi] :
            ( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
           => ( ( fresh_name_pi @ F @ C )
             => ( ( fresh_name_pi @ F @ B )
               => ( ( fresh_717452603ubject @ F @ E )
                 => ( ( fresh_name_name @ F @ D )
                   => ? [H: pi] :
                        ( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
                        & ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
       => ( ! [E: late_freeRes,F: pi] :
              ( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
             => ? [G: pi] :
                  ( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
                  & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
         => ( strong743114133lation @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(68,axiom,
    ! [A: name,B: late_subject,C: late_freeRes] :
      ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_fresh__prod) ).

thf(486,plain,
    ! [A: name,B: late_subject,C: late_freeRes] :
      ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
      = ( ( fresh_717452603ubject @ A @ B )
        & ( fresh_1641682979reeRes @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(152,axiom,
    ! [A: set_Pr1834926343_pi_pi,B: pi] :
      ( ! [C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ ( par @ C @ piNil ) ) @ A )
     => ( strong743114133lation @ B @ A @ ( par @ B @ piNil ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_parZeroRight) ).

thf(935,plain,
    ! [A: set_Pr1834926343_pi_pi,B: pi] :
      ( ! [C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ ( par @ C @ piNil ) ) @ A )
     => ( strong743114133lation @ B @ A @ ( par @ B @ piNil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(923,plain,
    ! [B: pi,A: name] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
    inference(cnf,[status(esa)],[922]) ).

thf(199,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pair__inject) ).

thf(1184,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( product_Pair_pi_pi @ A @ B )
        = ( product_Pair_pi_pi @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(2434,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( sum @ A @ B ) ) ) @ A ),
    inference(cnfConj,[status(thm)],[2433]) ).

thf(2436,plain,
    ! [B: pi,A: pi] : ( fresh_name_pi @ ( sk1 @ ( tau @ ( sum @ A @ B ) ) ) @ A ),
    inference(simp,[status(thm)],[2434]) ).

thf(3416,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
       != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1229,1259]) ).

thf(3417,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) )
     != ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ) ),
    inference(simp,[status(thm)],[3416]) ).

thf(3422,plain,
    ! [C: late_residual,B: pi,A: name] :
      ( ( ( mismatch @ A @ A @ B )
       != ( par @ p @ q ) )
      | ( ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) )
       != C ) ),
    inference(simp,[status(thm)],[3417]) ).

thf(3432,plain,
    ! [B: pi,A: name] :
      ( ( mismatch @ A @ A @ B )
     != ( par @ p @ q ) ),
    inference(simp,[status(thm)],[3422]) ).

thf(232,axiom,
    ! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_subject,E: name,F: pi] :
      ( ( strong743114133lation @ A @ B @ C )
     => ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
       => ( ( fresh_name_pi @ E @ A )
         => ? [G: pi] :
              ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
              & ( strong2129052853vative @ G @ F @ D @ E @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_simE_I1_J) ).

thf(1449,plain,
    ! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_subject,E: name,F: pi] :
      ( ( strong743114133lation @ A @ B @ C )
     => ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
       => ( ( fresh_name_pi @ E @ A )
         => ? [G: pi] :
              ( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
              & ( strong2129052853vative @ G @ F @ D @ E @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(236,axiom,
    ! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
      ( ( late_transitions @ ( match @ A @ B @ C ) @ D )
     => ( ( ( late_transitions @ C @ D )
         => ( ( A = B )
           => ( E @ A @ A ) ) )
       => ( E @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_matchCases) ).

thf(1468,plain,
    ! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
      ( ( late_transitions @ ( match @ A @ B @ C ) @ D )
     => ( ( ( late_transitions @ C @ D )
         => ( ( A = B )
           => ( E @ A @ A ) ) )
       => ( E @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(71,axiom,
    ! [A: late_subject > $o,B: late_subject] :
      ( ! [C: name] : ( A @ ( late_InputS @ C ) )
     => ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_subject_Oinducts) ).

thf(496,plain,
    ! [A: late_subject > $o,B: late_subject] :
      ( ! [C: name] : ( A @ ( late_InputS @ C ) )
     => ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(115,axiom,
    ! [A: pi,B: pi,C: late_residual] :
      ( ( late_transitions @ ( sum @ A @ B ) @ C )
     => ( ~ ( late_transitions @ A @ C )
       => ( late_transitions @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_sumCases) ).

thf(708,plain,
    ! [A: pi,B: pi,C: late_residual] :
      ( ( late_transitions @ ( sum @ A @ B ) @ C )
     => ( ~ ( late_transitions @ A @ C )
       => ( late_transitions @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(467,plain,
    ~ ? [A: pi,B: name,C: name,D: pi] :
        ( ( tau @ A )
        = ( input @ B @ C @ D ) ),
    inference(miniscope,[status(thm)],[466]) ).

thf(468,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( tau @ A )
     != ( input @ B @ C @ D ) ),
    inference(cnf,[status(esa)],[467]) ).

thf(469,plain,
    ! [D: pi,C: name,B: name,A: pi] :
      ( ( tau @ A )
     != ( input @ B @ C @ D ) ),
    inference(lifteq,[status(thm)],[468]) ).

thf(227,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ ( res @ C @ B ) @ C @ A )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_substRes3) ).

thf(1367,plain,
    ! [A: name,B: pi,C: name] :
      ( ( fresh_name_pi @ A @ B )
     => ( ( subs @ ( res @ C @ B ) @ C @ A )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(2735,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( ( product_Pair_pi_pi @ ( sk19 @ A ) @ ( sk20 @ A ) )
       != ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ) ),
    inference(simp,[status(thm)],[2714]) ).

thf(6145,plain,
    ! [A: product_prod_pi_pi] :
      ( ~ ( member558706512_pi_pi @ A @ rel )
      | ( ( par @ p @ q )
       != p )
      | ( ( par @ q @ r )
       != r )
      | ( A
       != ( product_Pair_pi_pi @ pqr @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[2735,580]) ).

thf(1563,plain,
    ~ ? [A: name,B: name,C: pi,D: name,E: pi] :
        ( ( input @ A @ B @ C )
        = ( res @ D @ E ) ),
    inference(miniscope,[status(thm)],[1562]) ).

thf(1564,plain,
    ! [E: pi,D: name,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(cnf,[status(esa)],[1563]) ).

thf(1565,plain,
    ! [E: pi,D: name,C: pi,B: name,A: name] :
      ( ( input @ A @ B @ C )
     != ( res @ D @ E ) ),
    inference(lifteq,[status(thm)],[1564]) ).

thf(1757,plain,
    ! [B: late_residual,A: name] :
      ( ~ $true
      | ( ( late_transitions @ ( res @ A @ piNil ) @ B )
       != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1734,751]) ).

thf(1758,plain,
    ! [B: late_residual,A: name] :
      ( ( late_transitions @ ( res @ A @ piNil ) @ B )
     != ( late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[1757]) ).

thf(1765,plain,
    ! [B: late_residual,A: name] :
      ( ( ( res @ A @ piNil )
       != ( par @ p @ ( par @ q @ r ) ) )
      | ( B
       != ( late_FreeR @ late_TauR @ pqr ) ) ),
    inference(simp,[status(thm)],[1758]) ).

thf(1769,plain,
    ! [A: name] :
      ( ( res @ A @ piNil )
     != ( par @ p @ ( par @ q @ r ) ) ),
    inference(simp,[status(thm)],[1765]) ).

thf(18327,plain,
    $false,
    inference(e,[status(thm)],[892,1036,1718,10785,1454,479,347,8514,1237,518,941,1110,352,2199,1322,1158,1596,683,1443,1142,440,1533,4747,1041,1486,408,977,730,276,1618,10567,308,1569,1205,449,269,677,3429,533,4440,945,340,538,1497,2195,4638,472,5163,1260,1342,5161,3335,1746,1127,1359,301,1529,436,1228,829,404,973,1046,320,565,4607,1366,1055,719,372,5064,3617,751,357,4984,2356,389,1628,587,619,1462,1132,559,3463,5214,969,284,316,3231,1100,3268,4669,1741,3084,416,4383,448,1494,1489,3431,591,443,376,623,3527,514,1151,4871,8511,353,1051,480,475,924,492,1465,766,2437,280,734,1622,2772,1526,1351,411,428,1104,527,1169,397,307,452,380,3303,270,1338,381,6388,366,2790,2773,1047,512,439,8513,334,2264,746,302,598,297,429,815,729,1560,6371,349,4785,2606,4385,889,493,1128,710,1740,324,285,1032,3269,3618,10794,1159,461,1234,1328,1111,10566,4636,1096,356,420,1851,1772,1259,317,948,4668,328,339,3210,1584,3428,1155,686,476,489,5932,622,1099,1382,5973,569,3109,393,1114,515,1150,1478,1333,343,938,1241,360,8512,508,311,921,398,2915,2221,5909,1732,298,412,965,5996,425,1146,1103,4438,573,601,1154,819,904,423,402,1615,743,577,291,958,4328,2817,1256,3213,3086,286,1124,281,445,313,1371,1107,466,335,4640,350,382,2220,713,1865,604,1209,274,1117,419,1048,377,2299,1771,4667,271,1571,1194,10565,5212,4929,362,451,4805,2669,509,3197,434,2632,535,3073,323,594,726,2446,1325,626,1556,1022,4635,811,387,758,1339,3133,552,367,1557,816,5082,3165,483,1149,964,462,932,455,1176,394,3363,1364,1496,3178,505,431,922,1562,521,1171,473,1626,1583,426,1208,531,3395,10867,4529,3146,812,749,342,1018,10788,754,553,968,458,823,580,295,3082,1566,327,4200,310,1845,4749,4255,712,1770,409,1230,673,3305,331,4549,338,4982,359,1218,1336,5062,1711,3080,585,370,470,576,1538,808,544,907,2247,1257,1536,1221,10568,2728,314,1240,4202,386,4634,446,571,4257,4671,4639,465,3433,1180,4873,976,1575,1866,1734,1108,3584,10754,363,556,524,10796,2194,581,2325,759,1590,319,4666,304,1508,1481,390,1745,632,401,1244,731,2934,588,1253,961,1385,2447,568,290,433,3430,2198,763,383,899,346,5128,549,4927,1030,1491,716,287,1725,1578,4670,3232,1229,1625,818,405,2736,3337,422,273,4579,10868,10569,752,373,603,305,294,1314,1816,8510,2746,437,1561,767,960,532,1033,1197,720,1165,886,1742,928,415,740,3362,332,10836,1537,459,908,822,4330,1597,442,1505,1120,501,3076,277,3394,369,607,3528,486,3461,337,935,923,1184,543,2436,3432,1449,1468,496,708,469,1367,940,6145,1565,1769,755]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ITP187^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.19  % Computer : n019.cluster.edu
% 0.10/0.19  % Model    : x86_64 x86_64
% 0.10/0.19  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19  % Memory   : 8046.5625MB
% 0.10/0.19  % OS       : Linux 6.8.0-71-generic
% 0.10/0.19  % CPULimit : 300
% 0.10/0.19  % WCLimit  : 300
% 0.10/0.19  % DateTime : Tue Sep 29 20:08:48 UTC 2026
% 0.10/0.20  % CPUTime  : 
% 0.10/0.20  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/0.78  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.50/1.23  % [INFO] 	 Parsing done (443ms). 
% 2.50/1.24  % [INFO] 	 Running in sequential loop mode. 
% 3.66/1.64  % [INFO] 	 eprover registered as external prover. 
% 3.66/1.65  % [INFO] 	 Scanning for conjecture ... 
% 4.11/1.83  % [INFO] 	 Found a conjecture (or negated_conjecture) and 323 axioms. Running axiom selection ... 
% 4.38/2.00  % [INFO] 	 Axiom selection finished. Selected 266 axioms (removed 57 axioms). 
% 5.81/2.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 6.25/2.40  % [INFO] 	 Type checking passed. 
% 6.25/2.41  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 129.52/39.00  % External prover 'e' found a proof!
% 129.52/39.00  % [INFO] 	 Killing All external provers ... 
% 129.52/39.00  % Time passed: 38668ms (effective reasoning time: 37753ms)
% 129.52/39.00  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 129.52/39.01  % Axioms used in derivation (266): fact_280_pi_Odistinct_I39_J, fact_176_outputIneqTrans, fact_288_pi_Odistinct_I51_J, fact_293_pi_Ostrong__induct, fact_119_residual_Ofresh_I2_J, fact_254_pi_Odistinct_I5_J, fact_133_parCasesB_H, fact_121_pi_Oinject_I1_J, fact_143_residual_Ostrong__induct, fact_237_simE_I1_J, fact_255_matchCases, fact_272_nilSim_I2_J, fact_232_resSimCases, fact_19_simps_I8_J, fact_160_transitions_OComm1, fact_151_transitions_OClose2, fact_199_resInputFreeTrans, fact_98_fresh__prod, fact_100_cClose2_Ohyps_I1_J, fact_66_Collect__mem__eq, fact_126_Late__Semantics_OResB, fact_8_Free_Ohyps, fact_277_pi_Odistinct_I9_J, fact_245_parZeroRight, fact_279_pi_Odistinct_I25_J, fact_172_freeRes_Oexhaust, fact_312_pi_Oinject_I6_J, fact_165_Late__Semantics_OComm2, fact_299_pi_Ofresh_I7_J, fact_214_pi_Ofresh_I4_J, fact_266_pi_Oinject_I4_J, fact_148_Late__Semantics_OClose1, fact_233_resSimCases, fact_89_cClose2_Ohyps_I2_J, fact_180_Open, fact_209_residual_Ofresh_I1_J, fact_20_FreshExt, fact_190_pi_Odistinct_I55_J, fact_128_outputFreshTrans, fact_152_resCasesF, fact_296_pi_Ostrong__inducts, fact_249_simps_I1_J, fact_132_pi_Odistinct_I31_J, fact_158_freshFreeDerivative_I1_J, fact_292_pi_Ostrong__induct, fact_248_pi_Ofresh_I1_J, fact_203_resTauBoundTrans, fact_39_cClose2_Ohyps_I11_J, fact_45_name__exists__fresh, fact_21_FreshExt_H, fact_168_Late__Semantics_OfreeRes_Oinject, fact_135_transitions_OPar2B, fact_161_transitions_OComm2, fact_142_residual_Ostrong__inducts, fact_52_substRes2, fact_18_simps_I9_J, fact_115_subject_Ofresh_I1_J, fact_32_prod_Oinject, fact_96_fresh__prod, fact_308_pi_Odistinct_I79_J, fact_155_Late__Semantics_OPar1B, fact_114_resOutputTauTrans, fact_46_freshRes, fact_204_inputIneqTrans, fact_146_residual_Ostrong__induct, fact_297_pi_Ostrong__inducts, fact_153_resCasesF_H, fact_311_pi_Odistinct_I83_J, fact_149_Late__Semantics_OClose2, fact_213_pi_Ofresh_I9_J, fact_12_cClose2_Ohyps_I12_J, fact_195_pi_Odistinct_I19_J, fact_309_pi_Odistinct_I81_J, fact_167_Late__Semantics1_OfreeRes_Oinject, fact_267_pi_Odistinct_I3_J, fact_10__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_092_060close_062, fact_268_pi_Odistinct_I37_J, fact_88_pi_Odistinct_I85_J, fact_210_simps_I3_J, fact_281_pi_Oinject_I5_J, fact_118_freeRes_Ofresh_I2_J, fact_205_tauOutputTrans, fact_162_Late__Semantics1_Osubject_Oinject_I2_J, fact_244_simulation__def, fact_113_fresh__prodD_I1_J, fact_239_simCasesCont, fact_1_cClose2_Ohyps_I6_J, fact_192_pi_Odistinct_I43_J, fact_26__092_060open_062y_A_092_060sharp_062_AR_092_060close_062, fact_85_surj__pair, fact_219_abs__fun__eq1, fact_163_Late__Semantics1_Osubject_Oinject_I1_J, fact_184_resTauOutputTrans, fact_150_transitions_OClose1, fact_145_residual_Ostrong__induct, fact_270_pi_Odistinct_I23_J, fact_23_Par2F, fact_263_pi_Odistinct_I13_J, fact_285_mismatchCases_H, fact_169_name__fresh, fact_310_pi_Odistinct_I27_J, fact_294_pi_Ostrong__inducts, fact_177_outputCases_H, fact_154_ResF, fact_117_Late__Semantics_Osubject_Oinject_I2_J, fact_241_simCasesCont, fact_242_simCasesCont, fact_171_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_99_fresh__prod, fact_236_parSym, fact_183_Late__Semantics1_Osubject_Odistinct_I1_J, fact_9__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_A_092_060parallel_062_AR_J_J_A_092_060in_062_ARel_092_060close_062, fact_47_fresh__fact2, fact_200_Late__Semantics_OInput, fact_295_pi_Ostrong__inducts, fact_5_Res, fact_2_cClose2_Ohyps_I10_J, fact_273_nilSim_I3_J, fact_182_resCases_H, fact_179_resOutputOutputTrans, fact_197_inputFreeTrans, fact_166_subject_Oexhaust, fact_134_transitions_OPar1B, fact_240_simCasesCont, fact_173_freeRes_Oinducts, fact_140_residual_Ostrong__inducts, fact_224_name__fresh__abs, fact_58_old_Oprod_Oinducts, fact_41_substTrans, fact_93_fresh__prod, fact_259_nilCases_H, fact_220_subst__name__def, fact_24_subst__identity, fact_300_simps_I10_J, fact_207_tauCases_H, fact_276_pi_Ofresh_I6_J, fact_136_transitions_OResB, fact_314_sumCases, fact_4_Ass, fact_170_freeRes_Ofresh_I1_J, fact_129_residual_Odistinct_I1_J, fact_316_Sum1, fact_208_Tau, fact_175_Output, fact_243_simCases, fact_317_Sum2, fact_94_fresh__prod, fact_14_cClose2_Ohyps_I8_J, fact_307_pi_Odistinct_I41_J, fact_315_sumCases_H, fact_15_cClose2_Ohyps_I3_J, fact_92_fresh__prod, fact_49_forget, fact_125_resOutputInputTrans, fact_13_cClose2_Ohyps_I7_J, fact_188_pi_Oinject_I2_J, fact_319_pi_Odistinct_I89_J, fact_286_mismatchTrans, fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062, fact_90_fresh__prod, fact_156_Late__Semantics_OPar2B, fact_42_name__exists__fresh, fact_298_pi_Ofresh_I10_J, fact_22_Par1F, fact_64_old_Oprod_Oexhaust, fact_185_resInputBoundOutputTrans, fact_253_pi_Odistinct_I49_J, fact_278_pi_Odistinct_I61_J, fact_265_pi_Odistinct_I7_J, fact_238_simE_I2_J, fact_304_pi_Odistinct_I59_J, fact_247_simps_I5_J, fact_235_resSimCases, fact_107_fresh__prodD_I2_J, fact_229_residual_Oinject_I1_J, fact_116_subject_Ofresh_I2_J, fact_305_pi_Odistinct_I53_J, fact_215_pi_Oinject_I3_J, fact_261_pi_Odistinct_I65_J, fact_187_simps_I2_J, fact_251_matchNilLeft, fact_123_subject_Oinducts, fact_318_pi_Odistinct_I33_J, fact_43_name__exists__fresh, fact_48_fresh__fact1, fact_306_pi_Odistinct_I47_J, fact_157_parCasesB, fact_11_cClose2_Ohyps_I13_J, fact_191_pi_Odistinct_I57_J, fact_87_residual_Oinject_I2_J, fact_127_freshBoundDerivative_I1_J, fact_260_zeroTrans, fact_3_cClose2_Ohyps_I5_J, fact_291_pi_Ostrong__induct, fact_284_Mismatch, fact_252_nilSimRight, fact_212_simps_I4_J, fact_141_residual_Ostrong__inducts, fact_130_residual_Oinducts, fact_258_Match, fact_282_pi_Odistinct_I75_J, fact_137_freshResidual, fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062, fact_230_pi_Oinject_I8_J, fact_138_freshBoundDerivative_I2_J, fact_174_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_16_cClose2_Ohyps_I9_J, fact_290_pi_Ostrong__induct, fact_95_fresh__prod, fact_40_pi_Ofresh_I8_J, fact_228_abs__fresh_I1_J, fact_189_pi_Odistinct_I35_J, fact_51_substRes3, fact_246_parZeroLeft, fact_193_pi_Odistinct_I45_J, fact_283_pi_Odistinct_I73_J, fact_262_pi_Odistinct_I67_J, fact_196_resTrans_I2_J, fact_131_pi_Odistinct_I29_J, fact_139_residual_Ostrong__inducts, fact_101_cPar1_Ohyps, fact_313_pi_Oinject_I9_J, fact_144_residual_Ostrong__induct, fact_198_tauBoundTrans, fact_257_matchCases_H, fact_50_freshFreeDerivative_I2_J, fact_274_nilSim_I1_J, fact_231_inputCases_H, fact_159_outputTauTrans, fact_65_mem__Collect__eq, fact_287_mismatchCases, fact_73_Pair__inject, fact_86_pi_Oinject_I7_J, fact_256_matchTrans, fact_120_pi_Ofresh_I2_J, fact_38_old_Oprod_Oinject, fact_289_mismatchNilLeft, fact_271_resZeroTrans, fact_269_pi_Odistinct_I1_J, fact_303_pi_Odistinct_I71_J, fact_211_substInput, fact_178_outputCases, fact_264_pi_Odistinct_I15_J, fact_206_tauCases, fact_124_outputBoundTrans, fact_0_cClose2_Ohyps_I14_J, fact_79_prod__cases, fact_194_pi_Odistinct_I21_J, fact_91_fresh__prod, fact_201_transitions_OInput, fact_301_simps_I7_J, fact_147_resTrans_I1_J, fact_181_resCasesB_H, fact_44_name__exists__fresh, fact_234_resSimCases, fact_17_cClose2_Ohyps_I4_J, fact_275_simps_I6_J, fact_25__092_060open_062x_A_092_060sharp_062_AR_092_060close_062, fact_186_pi_Ofresh_I3_J, fact_250_pi_Ofresh_I5_J, fact_164_Late__Semantics_OComm1, fact_97_fresh__prod, fact_202_inputBoundOutputTrans, fact_122_Late__Semantics_Osubject_Odistinct_I1_J, fact_302_pi_Odistinct_I77_J, fact_67_Collect__cong
% 129.52/39.01  % No. of inferences in proof: 1281
% 129.52/39.01  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 38668 ms resp. 37753 ms w/o parsing
% 132.39/39.47  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 132.39/39.48  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------