TSTP Solution File: ITP186^2 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP186^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:23:50 EDT 2024

% Result   : Theorem 232.46s 171.38s
% Output   : Refutation 233.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  326
% Syntax   : Number of formulae    :  599 ( 354 unt;  55 typ;   0 def)
%            Number of atoms       : 1350 ( 547 equ;   0 cnn)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives : 7505 ( 285   ~;  12   |;  70   &;6314   @)
%                                         (   0 <=>; 824  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   8 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  601 ( 601   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   55 (  52 usr;  17 con; 0-13 aty)
%            Number of variables   : 2535 (  76   ^2428   !;   8   ?;2535   :)
%                                         (  23  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
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(fs_name_type,type,
    fs_name: 
      !>[TA: $tType] : $o ).

thf(pt_name_type,type,
    pt_name: 
      !>[TA: $tType] : $o ).

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

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

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

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

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

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

thf(piNil_type,type,
    piNil: pi ).

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

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

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

thf(pi_rec_type,type,
    pi_rec: 
      !>[TA: $tType] : ( TA > ( name > name > pi > TA > TA ) > ( pi > TA > TA ) > ( name > name > pi > TA > TA ) > ( name > name > pi > TA > TA ) > ( name > name > pi > TA > TA ) > ( pi > pi > TA > TA > TA ) > ( pi > pi > TA > TA > TA ) > ( name > pi > TA > TA ) > ( pi > TA > TA ) > pi > TA ) ).

thf(pi_rec_set_type,type,
    pi_rec_set: 
      !>[TA: $tType] : ( TA > ( name > name > pi > TA > TA ) > ( pi > TA > TA ) > ( name > name > pi > TA > TA ) > ( name > name > pi > TA > TA ) > ( name > name > pi > TA > TA ) > ( pi > pi > TA > TA > TA ) > ( pi > pi > TA > TA > TA ) > ( name > pi > TA > TA ) > ( pi > TA > TA ) > pi > TA > $o ) ).

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

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

thf(finite_finite_type,type,
    finite_finite: 
      !>[TA: $tType] : ( ( set @ TA ) > $o ) ).

thf(if_type,type,
    if: 
      !>[TA: $tType] : ( $o > TA > TA > TA ) ).

thf(late_case_freeRes_type,type,
    late_case_freeRes: 
      !>[TA: $tType] : ( ( name > name > TA ) > TA > late_freeRes > TA ) ).

thf(late_case_subject_type,type,
    late_case_subject: 
      !>[TA: $tType] : ( ( name > TA ) > ( name > TA ) > late_subject > TA ) ).

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

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

thf(late_TauR_type,type,
    late_TauR: late_freeRes ).

thf(late_freeRes_rec_type,type,
    late_freeRes_rec: 
      !>[TA: $tType] : ( ( name > name > TA ) > TA > late_freeRes > TA ) ).

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

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

thf(late_residual_rec_type,type,
    late_residual_rec: 
      !>[TA: $tType] : ( ( late_subject > name > pi > TA ) > ( late_freeRes > pi > TA ) > late_residual > TA ) ).

thf(late_r582136743ec_set_type,type,
    late_r582136743ec_set: 
      !>[TA: $tType] : ( ( late_subject > name > pi > TA ) > ( late_freeRes > pi > TA ) > late_residual > TA > $o ) ).

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

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

thf(late_subject_rec_type,type,
    late_subject_rec: 
      !>[TA: $tType] : ( ( name > TA ) > ( name > TA ) > late_subject > TA ) ).

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

thf(sup_sup_type,type,
    sup_sup: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(abs_fun_type,type,
    abs_fun: 
      !>[TA: $tType,TB: $tType] : ( TB > TA > TB > ( noption @ TA ) ) ).

thf(fresh_type,type,
    fresh: 
      !>[TA: $tType,TB: $tType] : ( TB > TA > $o ) ).

thf(supp_type,type,
    supp: 
      !>[TA: $tType,TB: $tType] : ( TB > ( set @ TA ) ) ).

thf(supports_type,type,
    supports: 
      !>[TA: $tType,TB: $tType] : ( ( set @ TB ) > TA > $o ) ).

thf(collect_type,type,
    collect: 
      !>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).

thf(member_type,type,
    member: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).

thf(p_type,type,
    p: pi ).

thf(pqr_type,type,
    pqr: pi ).

thf(p2_type,type,
    p2: pi ).

thf(q_type,type,
    q: pi ).

thf(qr_type,type,
    qr: pi ).

thf(q2_type,type,
    q2: pi ).

thf(r_type,type,
    r: pi ).

thf(alpha_type,type,
    alpha: late_freeRes ).

thf(a_type,type,
    a: name ).

thf(b_type,type,
    b: name ).

thf(x_type,type,
    x: name ).

thf(123,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( fresh @ name @ pi @ A @ ( res @ B @ C ) )
      = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_pi_Ofresh_I9_J) ).

thf(645,plain,
    ! [A: name,B: name,C: pi] :
      ( ( fresh @ name @ pi @ A @ ( res @ B @ C ) )
      = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(193,axiom,
    fresh @ name @ pi @ x @ p2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_cComm2_Ohyps_I7_J) ).

thf(1036,plain,
    fresh @ name @ pi @ x @ p2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(247,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/sandbox/benchmark/theBenchmark.p',fact_151_matchCases_H) ).

thf(1337,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)],[247]) ).

thf(214,axiom,
    ! [TA: $tType,A: name > name > TA,B: TA] :
      ( ( late_case_freeRes @ TA @ A @ B @ late_TauR )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_freeRes_Ocase_I2_J) ).

thf(1168,plain,
    ! [TA: $tType,A: name > name > TA,B: TA] :
      ( ( late_case_freeRes @ TA @ A @ B @ late_TauR )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(164,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi] :
      ~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_tauBoundTrans) ).

thf(846,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)],[164]) ).

thf(117,axiom,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Late__Semantics_Osubject_Oinject_I2_J) ).

thf(628,plain,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(205,axiom,
    late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Free_Ohyps) ).

thf(1083,plain,
    late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(178,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( B != C )
       => ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Open) ).

thf(941,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)],[178]) ).

thf(153,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/sandbox/benchmark/theBenchmark.p',fact_97_resTauBoundTrans) ).

thf(777,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)],[153]) ).

thf(34,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/sandbox/benchmark/theBenchmark.p',fact_148_pi_Ofresh_I6_J) ).

thf(365,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)],[34]) ).

thf(255,axiom,
    fresh @ name @ pi @ x @ q,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_cComm2_Ohyps_I8_J) ).

thf(1369,plain,
    fresh @ name @ pi @ x @ q,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(224,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 @ name @ late_subject @ H @ E )
                   => ( ( H != F )
                     => ( ( fresh @ name @ pi @ F @ D )
                       => ~ ( fresh @ name @ late_subject @ 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 @ name @ late_freeRes @ G @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_resCases_H) ).

thf(1200,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 @ name @ late_subject @ H @ E )
                   => ( ( H != F )
                     => ( ( fresh @ name @ pi @ F @ D )
                       => ~ ( fresh @ name @ late_subject @ 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 @ name @ late_freeRes @ G @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(232,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/sandbox/benchmark/theBenchmark.p',fact_104_resOutputInputTrans) ).

thf(1290,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)],[232]) ).

thf(264,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh @ name @ pi @ D @ A )
       => ( fresh @ name @ pi @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_freshFreeDerivative_I2_J) ).

thf(1401,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)],[264]) ).

thf(15,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/sandbox/benchmark/theBenchmark.p',fact_113_pi_Oinject_I1_J) ).

thf(308,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)],[15]) ).

thf(204,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/sandbox/benchmark/theBenchmark.p',fact_154_mismatchCases_H) ).

thf(1073,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)],[204]) ).

thf(173,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 @ name @ late_subject @ J @ G )
                   => ( ( J != H )
                     => ( ( fresh @ name @ pi @ H @ F )
                       => ~ ( fresh @ name @ late_subject @ H @ G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_resCasesB_H) ).

thf(873,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 @ name @ late_subject @ J @ G )
                   => ( ( J != H )
                     => ( ( fresh @ name @ pi @ H @ F )
                       => ~ ( fresh @ name @ late_subject @ H @ G ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(113,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( input @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_pi_Odistinct_I57_J) ).

thf(614,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)],[113]) ).

thf(272,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 @ name @ late_subject @ C @ B )
           => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_transitions_OPar1B) ).

thf(1426,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 @ name @ late_subject @ C @ B )
           => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(41,axiom,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( mismatch @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_pi_Odistinct_I9_J) ).

thf(384,plain,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( mismatch @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(79,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( bang @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_pi_Odistinct_I77_J) ).

thf(500,plain,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( bang @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(213,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( fresh @ name @ pi @ A @ ( subs @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_fresh__fact2) ).

thf(1164,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)],[213]) ).

thf(243,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 @ name @ late_subject @ E @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_freshBoundDerivative_I1_J) ).

thf(1327,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 @ name @ late_subject @ E @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(26,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Late__Semantics1_OfreeRes_Oinject) ).

thf(340,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)],[26]) ).

thf(175,axiom,
    ! [TA: $tType,A: TA > ( set @ name ),B: TA > late_residual > $o,C: TA,D: late_residual] :
      ( ! [E: TA] : ( finite_finite @ name @ ( A @ E ) )
     => ( ! [E: late_subject,F: name,G: pi,H: TA] :
            ( ~ ( member @ name @ F @ ( A @ H ) )
           => ( ( fresh @ name @ late_subject @ F @ E )
             => ( B @ H @ ( late_BoundR @ E @ F @ G ) ) ) )
       => ( ! [E: late_freeRes,F: pi,G: TA] : ( B @ G @ ( late_FreeR @ E @ F ) )
         => ( B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_residual_Ostrong__induct_H) ).

thf(930,plain,
    ! [TA: $tType,A: TA > ( set @ name ),B: TA > late_residual > $o,C: TA,D: late_residual] :
      ( ! [E: TA] : ( finite_finite @ name @ ( A @ E ) )
     => ( ! [E: late_subject,F: name,G: pi,H: TA] :
            ( ~ ( member @ name @ F @ ( A @ H ) )
           => ( ( fresh @ name @ late_subject @ F @ E )
             => ( B @ H @ ( late_BoundR @ E @ F @ G ) ) ) )
       => ( ! [E: late_freeRes,F: pi,G: TA] : ( B @ G @ ( late_FreeR @ E @ F ) )
         => ( B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(159,axiom,
    ! [A: pi,B: late_residual] :
      ( ( late_transitions @ ( par @ A @ ( bang @ A ) ) @ B )
     => ( late_transitions @ ( bang @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_Bang) ).

thf(829,plain,
    ! [A: pi,B: late_residual] :
      ( ( late_transitions @ ( par @ A @ ( bang @ A ) ) @ B )
     => ( late_transitions @ ( bang @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(141,axiom,
    ! [A: pi > $o,B: pi] :
      ( ( A @ piNil )
     => ( ! [C: name,D: name,E: pi] :
            ( ( A @ E )
           => ( A @ ( output @ C @ D @ E ) ) )
       => ( ! [C: pi] :
              ( ( A @ C )
             => ( A @ ( tau @ C ) ) )
         => ( ! [C: name,D: name,E: pi] :
                ( ( A @ E )
               => ( A @ ( input @ C @ D @ E ) ) )
           => ( ! [C: name,D: name,E: pi] :
                  ( ( A @ E )
                 => ( A @ ( match @ C @ D @ E ) ) )
             => ( ! [C: name,D: name,E: pi] :
                    ( ( A @ E )
                   => ( A @ ( mismatch @ C @ D @ E ) ) )
               => ( ! [C: pi,D: pi] :
                      ( ( A @ C )
                     => ( ( A @ D )
                       => ( A @ ( sum @ C @ D ) ) ) )
                 => ( ! [C: pi,D: pi] :
                        ( ( A @ C )
                       => ( ( A @ D )
                         => ( A @ ( par @ C @ D ) ) ) )
                   => ( ! [C: name,D: pi] :
                          ( ( A @ D )
                         => ( A @ ( res @ C @ D ) ) )
                     => ( ! [C: pi] :
                            ( ( A @ C )
                           => ( A @ ( bang @ C ) ) )
                       => ( A @ B ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_pi_Oinducts) ).

thf(709,plain,
    ! [A: pi > $o,B: pi] :
      ( ( A @ piNil )
     => ( ! [C: name,D: name,E: pi] :
            ( ( A @ E )
           => ( A @ ( output @ C @ D @ E ) ) )
       => ( ! [C: pi] :
              ( ( A @ C )
             => ( A @ ( tau @ C ) ) )
         => ( ! [C: name,D: name,E: pi] :
                ( ( A @ E )
               => ( A @ ( input @ C @ D @ E ) ) )
           => ( ! [C: name,D: name,E: pi] :
                  ( ( A @ E )
                 => ( A @ ( match @ C @ D @ E ) ) )
             => ( ! [C: name,D: name,E: pi] :
                    ( ( A @ E )
                   => ( A @ ( mismatch @ C @ D @ E ) ) )
               => ( ! [C: pi,D: pi] :
                      ( ( A @ C )
                     => ( ( A @ D )
                       => ( A @ ( sum @ C @ D ) ) ) )
                 => ( ! [C: pi,D: pi] :
                        ( ( A @ C )
                       => ( ( A @ D )
                         => ( A @ ( par @ C @ D ) ) ) )
                   => ( ! [C: name,D: pi] :
                          ( ( A @ D )
                         => ( A @ ( res @ C @ D ) ) )
                     => ( ! [C: pi] :
                            ( ( A @ C )
                           => ( A @ ( bang @ C ) ) )
                       => ( A @ B ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(53,axiom,
    ! [TA: $tType,A: TA > late_subject > $o,B: TA,C: late_subject] :
      ( ! [D: name,E: TA] : ( A @ E @ ( late_InputS @ D ) )
     => ( ! [D: name,E: TA] : ( A @ E @ ( late_BoundOutputS @ D ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_subject_Ostrong__induct_H) ).

thf(417,plain,
    ! [TA: $tType,A: TA > late_subject > $o,B: TA,C: late_subject] :
      ( ! [D: name,E: TA] : ( A @ E @ ( late_InputS @ D ) )
     => ( ! [D: name,E: TA] : ( A @ E @ ( late_BoundOutputS @ D ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(8,axiom,
    ! [A: name] : ( fresh @ name @ pi @ A @ piNil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_pi_Ofresh_I1_J) ).

thf(288,plain,
    ! [A: name] : ( fresh @ name @ pi @ A @ piNil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(252,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/sandbox/benchmark/theBenchmark.p',fact_134_substInput) ).

thf(1359,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)],[252]) ).

thf(260,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( A != B )
     => ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_transitions_OInput) ).

thf(1386,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)],[260]) ).

thf(12,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( sum @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_pi_Odistinct_I71_J) ).

thf(301,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)],[12]) ).

thf(19,axiom,
    ( ( fresh @ name @ name )
    = ( != @ name ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_name__fresh) ).

thf(320,plain,
    ( ( fresh @ name @ name )
    = ( ^ [A: name,B: name] : ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(254,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 @ name @ late_subject @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_inputIneqTrans) ).

thf(1366,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 @ name @ late_subject @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(199,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_inputBoundOutputTrans) ).

thf(1055,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)],[199]) ).

thf(99,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/sandbox/benchmark/theBenchmark.p',fact_140_residual_Oinject_I1_J) ).

thf(570,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)],[99]) ).

thf(37,axiom,
    ! [TA: $tType,A: TA > $o,B: name > TA,C: name > TA,D: name] :
      ( ! [E: name] : ( A @ ( B @ E ) )
     => ( ! [E: name] : ( A @ ( C @ E ) )
       => ( ( late_subject_rec @ TA @ B @ C @ ( late_InputS @ D ) )
          = ( B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_subject_Orecs_I1_J) ).

thf(372,plain,
    ! [TA: $tType,A: TA > $o,B: name > TA,C: name > TA,D: name] :
      ( ! [E: name] : ( A @ ( B @ E ) )
     => ( ! [E: name] : ( A @ ( C @ E ) )
       => ( ( late_subject_rec @ TA @ B @ C @ ( late_InputS @ D ) )
          = ( B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(80,axiom,
    ! [TA: $tType,A: TA > $o,B: name > TA,C: name > TA,D: name] :
      ( ! [E: name] : ( A @ ( B @ E ) )
     => ( ! [E: name] : ( A @ ( C @ E ) )
       => ( ( late_subject_rec @ TA @ B @ C @ ( late_BoundOutputS @ D ) )
          = ( C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_subject_Orecs_I2_J) ).

thf(504,plain,
    ! [TA: $tType,A: TA > $o,B: name > TA,C: name > TA,D: name] :
      ( ! [E: name] : ( A @ ( B @ E ) )
     => ( ! [E: name] : ( A @ ( C @ E ) )
       => ( ( late_subject_rec @ TA @ B @ C @ ( late_BoundOutputS @ D ) )
          = ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(244,axiom,
    ! [A: pi] : ( late_bangPred @ A @ ( par @ A @ ( bang @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_aux2) ).

thf(1330,plain,
    ! [A: pi] : ( late_bangPred @ A @ ( par @ A @ ( bang @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(105,axiom,
    ! [A: name,B: pi] :
      ( piNil
     != ( res @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_pi_Odistinct_I15_J) ).

thf(587,plain,
    ! [A: name,B: pi] :
      ( piNil
     != ( res @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(139,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 @ name @ late_freeRes @ A @ C )
             => ( E @ ( res @ A @ F ) ) ) )
       => ( E @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_resCasesF) ).

thf(702,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 @ name @ late_freeRes @ A @ C )
             => ( E @ ( res @ A @ F ) ) ) )
       => ( E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(176,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh @ name @ pi @ F @ A )
         => ( ( fresh @ name @ pi @ F @ E )
           => ( ( F != B )
             => ( ( F != C )
               => ( ( fresh @ name @ pi @ F @ D )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_transitions_OComm2) ).

thf(934,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)],[176]) ).

thf(32,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( output @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_pi_Odistinct_I23_J) ).

thf(357,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)],[32]) ).

thf(221,axiom,
    ! [A: name,B: late_residual] :
      ~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_resZeroTrans) ).

thf(1191,plain,
    ! [A: name,B: late_residual] :
      ~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(263,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Par1F) ).

thf(1398,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)],[263]) ).

thf(21,axiom,
    ! [A: late_subject] :
      ( ! [B: name] :
          ( A
         != ( late_InputS @ B ) )
     => ~ ! [B: name] :
            ( A
           != ( late_BoundOutputS @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_subject_Oexhaust) ).

thf(325,plain,
    ! [A: late_subject] :
      ( ! [B: name] :
          ( A
         != ( late_InputS @ B ) )
     => ~ ! [B: name] :
            ( A
           != ( late_BoundOutputS @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(63,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( match @ A @ B @ C )
     != ( bang @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_pi_Odistinct_I69_J) ).

thf(448,plain,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( match @ A @ B @ C )
     != ( bang @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(269,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/sandbox/benchmark/theBenchmark.p',fact_146_simps_I6_J) ).

thf(1415,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)],[269]) ).

thf(71,axiom,
    ! [A: pi,B: pi] :
      ( ( ( tau @ A )
        = ( tau @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_pi_Oinject_I2_J) ).

thf(475,plain,
    ! [A: pi,B: pi] :
      ( ( ( tau @ A )
        = ( tau @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(76,axiom,
    ! [A: pi] : ( late_bangPred @ A @ ( bang @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_aux1) ).

thf(492,plain,
    ! [A: pi] : ( late_bangPred @ A @ ( bang @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(146,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh @ name @ pi @ C @ E )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Late__Semantics_OPar1B) ).

thf(756,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)],[146]) ).

thf(106,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( input @ A @ B @ C )
     != ( match @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_pi_Odistinct_I49_J) ).

thf(591,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)],[106]) ).

thf(270,axiom,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA > pi > $o,B: TA,C: pi] :
          ( ! [D: TA] : ( A @ D @ piNil )
         => ( ! [D: name,E: name,F: pi,G: TA] :
                ( ! [H: TA] : ( A @ H @ F )
               => ( A @ G @ ( output @ D @ E @ F ) ) )
           => ( ! [D: pi,E: TA] :
                  ( ! [F: TA] : ( A @ F @ D )
                 => ( A @ E @ ( tau @ D ) ) )
             => ( ! [D: name,E: name,F: pi,G: TA] :
                    ( ( fresh @ name @ TA @ E @ G )
                   => ( ( fresh @ name @ name @ E @ D )
                     => ( ! [H: TA] : ( A @ H @ F )
                       => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
               => ( ! [D: name,E: name,F: pi,G: TA] :
                      ( ! [H: TA] : ( A @ H @ F )
                     => ( A @ G @ ( match @ D @ E @ F ) ) )
                 => ( ! [D: name,E: name,F: pi,G: TA] :
                        ( ! [H: TA] : ( A @ H @ F )
                       => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
                   => ( ! [D: pi,E: pi,F: TA] :
                          ( ! [G: TA] : ( A @ G @ D )
                         => ( ! [G: TA] : ( A @ G @ E )
                           => ( A @ F @ ( sum @ D @ E ) ) ) )
                     => ( ! [D: pi,E: pi,F: TA] :
                            ( ! [G: TA] : ( A @ G @ D )
                           => ( ! [G: TA] : ( A @ G @ E )
                             => ( A @ F @ ( par @ D @ E ) ) ) )
                       => ( ! [D: name,E: pi,F: TA] :
                              ( ( fresh @ name @ TA @ D @ F )
                             => ( ! [G: TA] : ( A @ G @ E )
                               => ( A @ F @ ( res @ D @ E ) ) ) )
                         => ( ! [D: pi,E: TA] :
                                ( ! [F: TA] : ( A @ F @ D )
                               => ( A @ E @ ( bang @ D ) ) )
                           => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_pi_Ostrong__induct) ).

thf(1418,plain,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA > pi > $o,B: TA,C: pi] :
          ( ! [D: TA] : ( A @ D @ piNil )
         => ( ! [D: name,E: name,F: pi,G: TA] :
                ( ! [H: TA] : ( A @ H @ F )
               => ( A @ G @ ( output @ D @ E @ F ) ) )
           => ( ! [D: pi,E: TA] :
                  ( ! [F: TA] : ( A @ F @ D )
                 => ( A @ E @ ( tau @ D ) ) )
             => ( ! [D: name,E: name,F: pi,G: TA] :
                    ( ( fresh @ name @ TA @ E @ G )
                   => ( ( fresh @ name @ name @ E @ D )
                     => ( ! [H: TA] : ( A @ H @ F )
                       => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
               => ( ! [D: name,E: name,F: pi,G: TA] :
                      ( ! [H: TA] : ( A @ H @ F )
                     => ( A @ G @ ( match @ D @ E @ F ) ) )
                 => ( ! [D: name,E: name,F: pi,G: TA] :
                        ( ! [H: TA] : ( A @ H @ F )
                       => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
                   => ( ! [D: pi,E: pi,F: TA] :
                          ( ! [G: TA] : ( A @ G @ D )
                         => ( ! [G: TA] : ( A @ G @ E )
                           => ( A @ F @ ( sum @ D @ E ) ) ) )
                     => ( ! [D: pi,E: pi,F: TA] :
                            ( ! [G: TA] : ( A @ G @ D )
                           => ( ! [G: TA] : ( A @ G @ E )
                             => ( A @ F @ ( par @ D @ E ) ) ) )
                       => ( ! [D: name,E: pi,F: TA] :
                              ( ( fresh @ name @ TA @ D @ F )
                             => ( ! [G: TA] : ( A @ G @ E )
                               => ( A @ F @ ( res @ D @ E ) ) ) )
                         => ( ! [D: pi,E: TA] :
                                ( ! [F: TA] : ( A @ F @ D )
                               => ( A @ E @ ( bang @ D ) ) )
                           => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(31,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( output @ A @ B @ C )
     != ( bang @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_pi_Odistinct_I33_J) ).

thf(353,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(156,axiom,
    ! [A: late_residual > $o,B: late_residual] :
      ( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
     => ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_residual_Oinducts) ).

thf(821,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)],[156]) ).

thf(259,axiom,
    ! [A: pi,B: late_residual,C: pi] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( sum @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_Sum2) ).

thf(1383,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)],[259]) ).

thf(29,axiom,
    pt_name @ late_residual,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual___Agent_Opt__name_12) ).

thf(348,plain,
    pt_name @ late_residual,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(119,axiom,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ( pt_name @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Agent_Opt__name_1) ).

thf(634,plain,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ( pt_name @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(136,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/sandbox/benchmark/theBenchmark.p',fact_123_outputBoundTrans) ).

thf(692,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)],[136]) ).

thf(10,axiom,
    ! [A: pi] :
      ( piNil
     != ( tau @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_pi_Odistinct_I3_J) ).

thf(293,plain,
    ! [A: pi] :
      ( piNil
     != ( tau @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(262,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh @ name @ late_subject @ E @ B )
       => ( ( E != C )
         => ( ( fresh @ name @ pi @ C @ A )
           => ( ( fresh @ name @ late_subject @ C @ B )
             => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_transitions_OResB) ).

thf(1394,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh @ name @ late_subject @ E @ B )
       => ( ( E != C )
         => ( ( fresh @ name @ pi @ C @ A )
           => ( ( fresh @ name @ late_subject @ C @ B )
             => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(128,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: TB,D: TA > $o,E: name,F: late_subject,G: pi] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( finite_finite @ name @ ( supp @ TB @ name @ C ) )
             => ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
               => ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
                 => ( ! [H: late_subject,I: name,J: pi] :
                        ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ I @ A )
                       => ( ( fresh @ name @ late_subject @ I @ H )
                         => ( ( fresh @ name @ TB @ I @ C )
                           => ( ( D @ ( A @ H @ I @ J ) )
                             => ( fresh @ name @ TA @ I @ ( A @ H @ I @ J ) ) ) ) ) )
                   => ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ E @ A )
                     => ( ( fresh @ name @ ( late_freeRes > pi > TA ) @ E @ B )
                       => ( ( fresh @ name @ late_subject @ E @ F )
                         => ( ( late_residual_rec @ TA @ A @ B @ ( late_BoundR @ F @ E @ G ) )
                            = ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_residual_Orecs_I1_J) ).

thf(660,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: TB,D: TA > $o,E: name,F: late_subject,G: pi] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( finite_finite @ name @ ( supp @ TB @ name @ C ) )
             => ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
               => ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
                 => ( ! [H: late_subject,I: name,J: pi] :
                        ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ I @ A )
                       => ( ( fresh @ name @ late_subject @ I @ H )
                         => ( ( fresh @ name @ TB @ I @ C )
                           => ( ( D @ ( A @ H @ I @ J ) )
                             => ( fresh @ name @ TA @ I @ ( A @ H @ I @ J ) ) ) ) ) )
                   => ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ E @ A )
                     => ( ( fresh @ name @ ( late_freeRes > pi > TA ) @ E @ B )
                       => ( ( fresh @ name @ late_subject @ E @ F )
                         => ( ( late_residual_rec @ TA @ A @ B @ ( late_BoundR @ F @ E @ G ) )
                            = ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(51,axiom,
    ! [A: pi,B: pi,C: pi] :
      ( ( sum @ A @ B )
     != ( bang @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_pi_Odistinct_I83_J) ).

thf(411,plain,
    ! [A: pi,B: pi,C: pi] :
      ( ( sum @ A @ B )
     != ( bang @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(57,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/sandbox/benchmark/theBenchmark.p',fact_147_pi_Ofresh_I5_J) ).

thf(428,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)],[57]) ).

thf(165,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Late__Semantics_OComm1) ).

thf(849,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)],[165]) ).

thf(81,axiom,
    fs_name @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Agent_Ofs__name_4) ).

thf(507,plain,
    fs_name @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(257,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Late__Semantics_OComm2) ).

thf(1377,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)],[257]) ).

thf(5,axiom,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ( pt_name @ ( noption @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nominal_Onoption___Agent_Opt__name_7) ).

thf(280,plain,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ( pt_name @ ( noption @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(14,axiom,
    fs_name @ late_freeRes,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_9) ).

thf(307,plain,
    fs_name @ late_freeRes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(64,axiom,
    ! [A: name,B: late_subject,C: name,D: pi] :
      ( ( fresh @ name @ late_residual @ A @ ( late_BoundR @ B @ C @ D ) )
      = ( ( fresh @ name @ late_subject @ A @ B )
        & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_residual_Ofresh_I1_J) ).

thf(452,plain,
    ! [A: name,B: late_subject,C: name,D: pi] :
      ( ( fresh @ name @ late_residual @ A @ ( late_BoundR @ B @ C @ D ) )
      = ( ( fresh @ name @ late_subject @ A @ B )
        & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(84,axiom,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: late_residual,D: TA,E: name] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( late_r582136743ec_set @ TA @ A @ B @ C @ D )
             => ( ! [F: TA] :
                    ( ( late_r582136743ec_set @ TA @ A @ B @ C @ F )
                   => ( F = D ) )
               => ( ( fresh @ name @ late_residual @ E @ C )
                 => ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ E @ A )
                   => ( ( fresh @ name @ ( late_freeRes > pi > TA ) @ E @ B )
                     => ( fresh @ name @ TA @ E @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_residual_Orec__fresh) ).

thf(512,plain,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: late_residual,D: TA,E: name] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( late_r582136743ec_set @ TA @ A @ B @ C @ D )
             => ( ! [F: TA] :
                    ( ( late_r582136743ec_set @ TA @ A @ B @ C @ F )
                   => ( F = D ) )
               => ( ( fresh @ name @ late_residual @ E @ C )
                 => ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ E @ A )
                   => ( ( fresh @ name @ ( late_freeRes > pi > TA ) @ E @ B )
                     => ( fresh @ name @ TA @ E @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(91,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/sandbox/benchmark/theBenchmark.p',fact_111_pi_Ofresh_I2_J) ).

thf(546,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)],[91]) ).

thf(237,axiom,
    ! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
      ( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
     => ( ( fresh @ name @ pi @ D @ A )
       => ( ( fresh @ name @ pi @ D @ B )
         => ( ! [G: pi] :
                ( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
               => ( F @ ( par @ G @ B ) ) )
           => ( ! [G: pi] :
                  ( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
                 => ( F @ ( par @ A @ G ) ) )
             => ( F @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_parCasesB) ).

thf(1306,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)],[237]) ).

thf(40,axiom,
    ! [A: name,B: name] :
      ( ( fresh @ name @ late_subject @ A @ ( late_InputS @ B ) )
      = ( fresh @ name @ name @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_subject_Ofresh_I1_J) ).

thf(381,plain,
    ! [A: name,B: name] :
      ( ( fresh @ name @ late_subject @ A @ ( late_InputS @ B ) )
      = ( fresh @ name @ name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(196,axiom,
    ! [A: pi,B: pi] :
      ( ( late_bangPred @ A @ B )
     => ( ( B
         != ( bang @ A ) )
       => ( B
          = ( par @ A @ ( bang @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_bangPred_Ocases) ).

thf(1047,plain,
    ! [A: pi,B: pi] :
      ( ( late_bangPred @ A @ B )
     => ( ( B
         != ( bang @ A ) )
       => ( B
          = ( par @ A @ ( bang @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(211,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/sandbox/benchmark/theBenchmark.p',fact_187_sumCases_H) ).

thf(1153,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)],[211]) ).

thf(148,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh @ name @ pi @ C @ E )
       => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Late__Semantics_OPar2B) ).

thf(761,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)],[148]) ).

thf(181,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/sandbox/benchmark/theBenchmark.p',fact_182_simps_I7_J) ).

thf(957,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)],[181]) ).

thf(143,axiom,
    ! [A: late_freeRes] :
      ( ! [B: name,C: name] :
          ( A
         != ( late_OutputR @ B @ C ) )
     => ( A = late_TauR ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_freeRes_Oexhaust) ).

thf(746,plain,
    ! [A: late_freeRes] :
      ( ! [B: name,C: name] :
          ( A
         != ( late_OutputR @ B @ C ) )
     => ( A = late_TauR ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(248,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/sandbox/benchmark/theBenchmark.p',fact_131_outputIneqTrans) ).

thf(1343,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)],[248]) ).

thf(251,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/sandbox/benchmark/theBenchmark.p',fact_135_simps_I4_J) ).

thf(1355,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)],[251]) ).

thf(11,axiom,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Late__Semantics1_Osubject_Odistinct_I1_J) ).

thf(297,plain,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(50,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( res @ A @ B )
     != ( bang @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_pi_Odistinct_I89_J) ).

thf(407,plain,
    ! [A: name,B: pi,C: pi] :
      ( ( res @ A @ B )
     != ( bang @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(256,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/sandbox/benchmark/theBenchmark.p',fact_108_outputCases) ).

thf(1370,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)],[256]) ).

thf(169,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: pi] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Par2F) ).

thf(862,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)],[169]) ).

thf(30,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( match @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_pi_Odistinct_I61_J) ).

thf(349,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)],[30]) ).

thf(33,axiom,
    ! [A: pi,B: pi,C: pi] :
      ( ( tau @ A )
     != ( sum @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_pi_Odistinct_I41_J) ).

thf(361,plain,
    ! [A: pi,B: pi,C: pi] :
      ( ( tau @ A )
     != ( sum @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(103,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( fresh @ TA @ TB )
      = ( ^ [A: TA,B: TB] :
            ~ ( member @ TA @ A @ ( supp @ TB @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_fresh__def) ).

thf(583,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( fresh @ TA @ TB )
      = ( ^ [A: TA,B: TB] :
            ~ ( member @ TA @ A @ ( supp @ TB @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(93,axiom,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Late__Semantics1_Osubject_Oinject_I2_J) ).

thf(551,plain,
    ! [A: name,B: name] :
      ( ( ( late_BoundOutputS @ A )
        = ( late_BoundOutputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(231,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/sandbox/benchmark/theBenchmark.p',fact_109_outputCases_H) ).

thf(1281,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)],[231]) ).

thf(163,axiom,
    ! [A: pi,B: pi,C: pi] :
      ( ( par @ A @ B )
     != ( bang @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_pi_Odistinct_I87_J) ).

thf(842,plain,
    ! [A: pi,B: pi,C: pi] :
      ( ( par @ A @ B )
     != ( bang @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(7,axiom,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).

thf(285,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(166,axiom,
    ! [A: pi,B: pi,C: pi > pi > $o] :
      ( ( late_bangPred @ A @ B )
     => ( ! [D: pi] : ( C @ D @ ( bang @ D ) )
       => ( ! [D: pi] : ( C @ D @ ( par @ D @ ( bang @ D ) ) )
         => ( C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_bangPred_Oinducts) ).

thf(852,plain,
    ! [A: pi,B: pi,C: pi > pi > $o] :
      ( ( late_bangPred @ A @ B )
     => ( ! [D: pi] : ( C @ D @ ( bang @ D ) )
       => ( ! [D: pi] : ( C @ D @ ( par @ D @ ( bang @ D ) ) )
         => ( C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(59,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/sandbox/benchmark/theBenchmark.p',fact_179_pi_Ofresh_I7_J) ).

thf(435,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)],[59]) ).

thf(22,axiom,
    ! [A: name,B: pi] :
      ( ( fresh @ name @ pi @ A @ ( tau @ B ) )
      = ( fresh @ name @ pi @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_pi_Ofresh_I3_J) ).

thf(329,plain,
    ! [A: name,B: pi] :
      ( ( fresh @ name @ pi @ A @ ( tau @ B ) )
      = ( fresh @ name @ pi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(218,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_resTrans_I1_J) ).

thf(1178,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)],[218]) ).

thf(133,axiom,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( ( fresh @ name @ pi @ C @ A )
       => ( fresh @ name @ late_residual @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_freshResidual) ).

thf(682,plain,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( ( fresh @ name @ pi @ C @ A )
       => ( fresh @ name @ late_residual @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(266,axiom,
    late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_cPar1_Ohyps) ).

thf(1407,plain,
    late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(180,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/sandbox/benchmark/theBenchmark.p',fact_149_matchCases) ).

thf(948,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)],[180]) ).

thf(42,axiom,
    ! [A: name,B: pi] : ( fresh @ name @ pi @ A @ ( res @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_freshRes) ).

thf(388,plain,
    ! [A: name,B: pi] : ( fresh @ name @ pi @ A @ ( res @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(112,axiom,
    ! [A: pi,B: name,C: pi] :
      ( ( tau @ A )
     != ( res @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_pi_Odistinct_I45_J) ).

thf(610,plain,
    ! [A: pi,B: name,C: pi] :
      ( ( tau @ A )
     != ( res @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(230,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: TB,D: TA > $o,E: late_freeRes,F: pi] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( finite_finite @ name @ ( supp @ TB @ name @ C ) )
             => ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
               => ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
                 => ( ! [G: late_subject,H: name,I: pi] :
                        ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ H @ A )
                       => ( ( fresh @ name @ late_subject @ H @ G )
                         => ( ( fresh @ name @ TB @ H @ C )
                           => ( ( D @ ( A @ G @ H @ I ) )
                             => ( fresh @ name @ TA @ H @ ( A @ G @ H @ I ) ) ) ) ) )
                   => ( ( late_residual_rec @ TA @ A @ B @ ( late_FreeR @ E @ F ) )
                      = ( B @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_residual_Orecs_I2_J) ).

thf(1270,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: TB,D: TA > $o,E: late_freeRes,F: pi] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( finite_finite @ name @ ( supp @ TB @ name @ C ) )
             => ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
               => ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
                 => ( ! [G: late_subject,H: name,I: pi] :
                        ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ H @ A )
                       => ( ( fresh @ name @ late_subject @ H @ G )
                         => ( ( fresh @ name @ TB @ H @ C )
                           => ( ( D @ ( A @ G @ H @ I ) )
                             => ( fresh @ name @ TA @ H @ ( A @ G @ H @ I ) ) ) ) ) )
                   => ( ( late_residual_rec @ TA @ A @ B @ ( late_FreeR @ E @ F ) )
                      = ( B @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(226,axiom,
    ! [A: pi,B: pi] :
      ( ( supp @ pi @ name @ ( par @ A @ B ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ A ) @ ( supp @ pi @ name @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_pi_Osupp_I8_J) ).

thf(1259,plain,
    ! [A: pi,B: pi] :
      ( ( supp @ pi @ name @ ( par @ A @ B ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ A ) @ ( supp @ pi @ name @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(70,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_pi_Odistinct_I75_J) ).

thf(471,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)],[70]) ).

thf(75,axiom,
    ! [A: pi,B: pi] :
      ( piNil
     != ( sum @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_pi_Odistinct_I11_J) ).

thf(488,plain,
    ! [A: pi,B: pi] :
      ( piNil
     != ( sum @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(25,axiom,
    pt_name @ late_freeRes,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes___Agent_Opt__name_8) ).

thf(339,plain,
    pt_name @ late_freeRes,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(88,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).

thf(537,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(212,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/sandbox/benchmark/theBenchmark.p',fact_136_inputCases_H) ).

thf(1155,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)],[212]) ).

thf(94,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
      ( ( ( abs_fun @ TB @ TA @ A @ B )
        = ( abs_fun @ TB @ TA @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_abs__fun__eq1) ).

thf(554,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
      ( ( ( abs_fun @ TB @ TA @ A @ B )
        = ( abs_fun @ TB @ TA @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(145,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/sandbox/benchmark/theBenchmark.p',fact_101_resTauOutputTrans) ).

thf(753,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)],[145]) ).

thf(115,axiom,
    ( subst_name
    = ( ^ [A: name,B: name,C: name] : ( if @ name @ ( A = B ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_subst__name__def) ).

thf(622,plain,
    ( subst_name
    = ( ^ [A: name,B: name,C: name] : ( if @ name @ ( A = B ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(228,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh @ name @ late_subject @ E @ B )
       => ( ( E != C )
         => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Late__Semantics_OResB) ).

thf(1263,plain,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh @ name @ late_subject @ E @ B )
       => ( ( E != C )
         => ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(189,axiom,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA > pi > $o,B: TA,C: pi] :
          ( ! [D: TA] : ( A @ D @ piNil )
         => ( ! [D: name,E: name,F: pi,G: TA] :
                ( ! [H: TA] : ( A @ H @ F )
               => ( A @ G @ ( output @ D @ E @ F ) ) )
           => ( ! [D: pi,E: TA] :
                  ( ! [F: TA] : ( A @ F @ D )
                 => ( A @ E @ ( tau @ D ) ) )
             => ( ! [D: name,E: name,F: pi,G: TA] :
                    ( ( fresh @ name @ TA @ E @ G )
                   => ( ( fresh @ name @ name @ E @ D )
                     => ( ! [H: TA] : ( A @ H @ F )
                       => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
               => ( ! [D: name,E: name,F: pi,G: TA] :
                      ( ! [H: TA] : ( A @ H @ F )
                     => ( A @ G @ ( match @ D @ E @ F ) ) )
                 => ( ! [D: name,E: name,F: pi,G: TA] :
                        ( ! [H: TA] : ( A @ H @ F )
                       => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
                   => ( ! [D: pi,E: pi,F: TA] :
                          ( ! [G: TA] : ( A @ G @ D )
                         => ( ! [G: TA] : ( A @ G @ E )
                           => ( A @ F @ ( sum @ D @ E ) ) ) )
                     => ( ! [D: pi,E: pi,F: TA] :
                            ( ! [G: TA] : ( A @ G @ D )
                           => ( ! [G: TA] : ( A @ G @ E )
                             => ( A @ F @ ( par @ D @ E ) ) ) )
                       => ( ! [D: name,E: pi,F: TA] :
                              ( ( fresh @ name @ TA @ D @ F )
                             => ( ! [G: TA] : ( A @ G @ E )
                               => ( A @ F @ ( res @ D @ E ) ) ) )
                         => ( ! [D: pi,E: TA] :
                                ( ! [F: TA] : ( A @ F @ D )
                               => ( A @ E @ ( bang @ D ) ) )
                           => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_pi_Ostrong__inducts) ).

thf(985,plain,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA > pi > $o,B: TA,C: pi] :
          ( ! [D: TA] : ( A @ D @ piNil )
         => ( ! [D: name,E: name,F: pi,G: TA] :
                ( ! [H: TA] : ( A @ H @ F )
               => ( A @ G @ ( output @ D @ E @ F ) ) )
           => ( ! [D: pi,E: TA] :
                  ( ! [F: TA] : ( A @ F @ D )
                 => ( A @ E @ ( tau @ D ) ) )
             => ( ! [D: name,E: name,F: pi,G: TA] :
                    ( ( fresh @ name @ TA @ E @ G )
                   => ( ( fresh @ name @ name @ E @ D )
                     => ( ! [H: TA] : ( A @ H @ F )
                       => ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
               => ( ! [D: name,E: name,F: pi,G: TA] :
                      ( ! [H: TA] : ( A @ H @ F )
                     => ( A @ G @ ( match @ D @ E @ F ) ) )
                 => ( ! [D: name,E: name,F: pi,G: TA] :
                        ( ! [H: TA] : ( A @ H @ F )
                       => ( A @ G @ ( mismatch @ D @ E @ F ) ) )
                   => ( ! [D: pi,E: pi,F: TA] :
                          ( ! [G: TA] : ( A @ G @ D )
                         => ( ! [G: TA] : ( A @ G @ E )
                           => ( A @ F @ ( sum @ D @ E ) ) ) )
                     => ( ! [D: pi,E: pi,F: TA] :
                            ( ! [G: TA] : ( A @ G @ D )
                           => ( ! [G: TA] : ( A @ G @ E )
                             => ( A @ F @ ( par @ D @ E ) ) ) )
                       => ( ! [D: name,E: pi,F: TA] :
                              ( ( fresh @ name @ TA @ D @ F )
                             => ( ! [G: TA] : ( A @ G @ E )
                               => ( A @ F @ ( res @ D @ E ) ) ) )
                         => ( ! [D: pi,E: TA] :
                                ( ! [F: TA] : ( A @ F @ D )
                               => ( A @ E @ ( bang @ D ) ) )
                           => ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(234,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh @ name @ pi @ F @ A )
         => ( ( fresh @ name @ pi @ F @ E )
           => ( ( fresh @ name @ pi @ C @ A )
             => ( ( fresh @ name @ pi @ C @ E )
               => ( ( F != B )
                 => ( ( fresh @ name @ pi @ F @ D )
                   => ( ( C != B )
                     => ( ( fresh @ name @ pi @ C @ G )
                       => ( ( F != C )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_transitions_OClose2) ).

thf(1297,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)],[234]) ).

thf(197,axiom,
    ! [A: name] : ( fresh @ name @ late_freeRes @ A @ late_TauR ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_freeRes_Ofresh_I2_J) ).

thf(1050,plain,
    ! [A: name] : ( fresh @ name @ late_freeRes @ A @ late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(36,axiom,
    pt_name @ late_subject,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject___Agent_Opt__name_10) ).

thf(371,plain,
    pt_name @ late_subject,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(242,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh @ name @ late_freeRes @ D @ B )
       => ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ResF) ).

thf(1324,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh @ name @ late_freeRes @ D @ B )
       => ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(44,axiom,
    ! [TA: $tType,A: TA] :
      ( ( finite_finite @ name @ ( supp @ TA @ name @ A ) )
     => ? [B: name] : ( fresh @ name @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_exists__fresh_H) ).

thf(393,plain,
    ! [TA: $tType,A: TA] :
      ( ( finite_finite @ name @ ( supp @ TA @ name @ A ) )
     => ? [B: name] : ( fresh @ name @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(177,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
       => ( ( fresh @ name @ pi @ C @ E )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Late__Semantics_OClose2) ).

thf(938,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)],[177]) ).

thf(82,axiom,
    fs_name @ name,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Oname___Agent_Ofs__name_6) ).

thf(508,plain,
    fs_name @ name,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(16,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( output @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_pi_Odistinct_I31_J) ).

thf(311,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)],[16]) ).

thf(150,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh @ name @ pi @ C @ A )
         => ( ( fresh @ name @ pi @ C @ E )
           => ( ( fresh @ name @ pi @ F @ A )
             => ( ( fresh @ name @ pi @ F @ E )
               => ( ( C != B )
                 => ( ( fresh @ name @ pi @ C @ G )
                   => ( ( F != B )
                     => ( ( fresh @ name @ pi @ F @ D )
                       => ( ( C != F )
                         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_transitions_OClose1) ).

thf(765,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)],[150]) ).

thf(46,axiom,
    pt_name @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Agent_Opt__name_3) ).

thf(398,plain,
    pt_name @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(191,axiom,
    ! [A: late_freeRes,B: pi] :
      ( ( supp @ late_residual @ name @ ( late_FreeR @ A @ B ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ late_freeRes @ name @ A ) @ ( supp @ pi @ name @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_residual_Osupp_I2_J) ).

thf(1026,plain,
    ! [A: late_freeRes,B: pi] :
      ( ( supp @ late_residual @ name @ ( late_FreeR @ A @ B ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ late_freeRes @ name @ A ) @ ( supp @ pi @ name @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(174,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ( ( late_transitions @ ( match @ A @ B @ C ) @ D )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_matchTrans) ).

thf(926,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)],[174]) ).

thf(27,axiom,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA] :
          ~ ! [B: name] :
              ~ ( fresh @ name @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_name__exists__fresh) ).

thf(343,plain,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA] :
          ~ ! [B: name] :
              ~ ( fresh @ name @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(240,axiom,
    ! [A: name,B: pi,C: pi] :
      ( ( fresh @ name @ pi @ A @ ( par @ B @ C ) )
      = ( ( fresh @ name @ pi @ A @ B )
        & ( fresh @ name @ pi @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_pi_Ofresh_I8_J) ).

thf(1318,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)],[240]) ).

thf(152,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh @ name @ pi @ A @ B )
     => ( ( subs @ B @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_forget) ).

thf(773,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)],[152]) ).

thf(104,axiom,
    fs_name @ late_subject,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject___Agent_Ofs__name_11) ).

thf(586,plain,
    fs_name @ late_subject,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(144,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_tauOutputTrans) ).

thf(750,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)],[144]) ).

thf(114,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( output @ A @ B @ C )
     != ( sum @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_pi_Odistinct_I27_J) ).

thf(618,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)],[114]) ).

thf(56,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/sandbox/benchmark/theBenchmark.p',fact_139_pi_Oinject_I8_J) ).

thf(425,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)],[56]) ).

thf(157,axiom,
    ! [A: name,B: pi,C: late_residual] :
      ~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_mismatchTrans) ).

thf(824,plain,
    ! [A: name,B: pi,C: late_residual] :
      ~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(235,axiom,
    ! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_resInputBoundOutputTrans) ).

thf(1301,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)],[235]) ).

thf(100,axiom,
    ! [A: pi,B: pi] :
      ( ( tau @ A )
     != ( bang @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_pi_Odistinct_I47_J) ).

thf(573,plain,
    ! [A: pi,B: pi] :
      ( ( tau @ A )
     != ( bang @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(135,axiom,
    ! [A: late_residual] :
      ~ ( late_transitions @ piNil @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_zeroTrans) ).

thf(689,plain,
    ! [A: late_residual] :
      ~ ( late_transitions @ piNil @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(62,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( output @ A @ B @ C )
     != ( input @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_pi_Odistinct_I21_J) ).

thf(444,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)],[62]) ).

thf(38,axiom,
    ! [A: name,B: name,C: name,D: name] :
      ( ( ( late_OutputR @ A @ B )
        = ( late_OutputR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Late__Semantics_OfreeRes_Oinject) ).

thf(375,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)],[38]) ).

thf(187,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 @ name @ late_freeRes @ H @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_resCasesF_H) ).

thf(975,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 @ name @ late_freeRes @ H @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(48,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( input @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_pi_Odistinct_I35_J) ).

thf(402,plain,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( input @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(142,axiom,
    ! [A: name,B: name,C: pi,D: late_residual] :
      ~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_resTrans_I2_J) ).

thf(743,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)],[142]) ).

thf(101,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( supp @ pi @ name @ ( mismatch @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ B ) @ ( supp @ pi @ name @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_pi_Osupp_I6_J) ).

thf(577,plain,
    ! [A: name,B: name,C: pi] :
      ( ( supp @ pi @ name @ ( mismatch @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ B ) @ ( supp @ pi @ name @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(225,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/sandbox/benchmark/theBenchmark.p',fact_103_resOutputTauTrans) ).

thf(1256,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)],[225]) ).

thf(238,axiom,
    ! [TA: $tType,A: TA > late_freeRes > $o,B: TA,C: late_freeRes] :
      ( ! [D: name,E: name,F: TA] : ( A @ F @ ( late_OutputR @ D @ E ) )
     => ( ! [D: TA] : ( A @ D @ late_TauR )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_freeRes_Ostrong__inducts) ).

thf(1312,plain,
    ! [TA: $tType,A: TA > late_freeRes > $o,B: TA,C: late_freeRes] :
      ( ! [D: name,E: name,F: TA] : ( A @ F @ ( late_OutputR @ D @ E ) )
     => ( ! [D: TA] : ( A @ D @ late_TauR )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(200,axiom,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_pi_Odistinct_I85_J) ).

thf(1058,plain,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( par @ A @ B )
     != ( res @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(245,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_outputTauTrans) ).

thf(1332,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)],[245]) ).

thf(68,axiom,
    ! [TA: $tType,A: name > name > TA,B: TA,C: name,D: name] :
      ( ( late_case_freeRes @ TA @ A @ B @ ( late_OutputR @ C @ D ) )
      = ( A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_freeRes_Ocase_I1_J) ).

thf(466,plain,
    ! [TA: $tType,A: name > name > TA,B: TA,C: name,D: name] :
      ( ( late_case_freeRes @ TA @ A @ B @ ( late_OutputR @ C @ D ) )
      = ( A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(24,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( match @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_pi_Odistinct_I37_J) ).

thf(335,plain,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( match @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(89,axiom,
    ! [A: name,B: name] :
      ( ( supp @ late_freeRes @ name @ ( late_OutputR @ A @ B ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( supp @ name @ name @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_freeRes_Osupp_I1_J) ).

thf(540,plain,
    ! [A: name,B: name] :
      ( ( supp @ late_freeRes @ name @ ( late_OutputR @ A @ B ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( supp @ name @ name @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(222,axiom,
    ! [A: pi,B: name,C: name] :
      ( ( subs @ ( bang @ A ) @ B @ C )
      = ( bang @ ( subs @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_simps_I10_J) ).

thf(1194,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)],[222]) ).

thf(49,axiom,
    pt_name @ name,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Oname___Agent_Opt__name_5) ).

thf(406,plain,
    pt_name @ name,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(160,axiom,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Late__Semantics_OfreeRes_Odistinct_I1_J) ).

thf(831,plain,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(267,axiom,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( A != B )
     => ( ( A != C )
       => ( ( subs @ ( res @ A @ D ) @ B @ C )
          = ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_simps_I9_J) ).

thf(1408,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)],[267]) ).

thf(3,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).

thf(274,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(155,axiom,
    ! [TA: $tType,A: TA > ( set @ name ),B: TA > pi > $o,C: TA,D: pi] :
      ( ! [E: TA] : ( finite_finite @ name @ ( A @ E ) )
     => ( ! [E: TA] : ( B @ E @ piNil )
       => ( ! [E: name,F: name,G: pi,H: TA] :
              ( ! [I: TA] : ( B @ I @ G )
             => ( B @ H @ ( output @ E @ F @ G ) ) )
         => ( ! [E: pi,F: TA] :
                ( ! [G: TA] : ( B @ G @ E )
               => ( B @ F @ ( tau @ E ) ) )
           => ( ! [E: name,F: name,G: pi,H: TA] :
                  ( ~ ( member @ name @ F @ ( A @ H ) )
                 => ( ( fresh @ name @ name @ F @ E )
                   => ( ! [I: TA] : ( B @ I @ G )
                     => ( B @ H @ ( input @ E @ F @ G ) ) ) ) )
             => ( ! [E: name,F: name,G: pi,H: TA] :
                    ( ! [I: TA] : ( B @ I @ G )
                   => ( B @ H @ ( match @ E @ F @ G ) ) )
               => ( ! [E: name,F: name,G: pi,H: TA] :
                      ( ! [I: TA] : ( B @ I @ G )
                     => ( B @ H @ ( mismatch @ E @ F @ G ) ) )
                 => ( ! [E: pi,F: pi,G: TA] :
                        ( ! [H: TA] : ( B @ H @ E )
                       => ( ! [H: TA] : ( B @ H @ F )
                         => ( B @ G @ ( sum @ E @ F ) ) ) )
                   => ( ! [E: pi,F: pi,G: TA] :
                          ( ! [H: TA] : ( B @ H @ E )
                         => ( ! [H: TA] : ( B @ H @ F )
                           => ( B @ G @ ( par @ E @ F ) ) ) )
                     => ( ! [E: name,F: pi,G: TA] :
                            ( ~ ( member @ name @ E @ ( A @ G ) )
                           => ( ! [H: TA] : ( B @ H @ F )
                             => ( B @ G @ ( res @ E @ F ) ) ) )
                       => ( ! [E: pi,F: TA] :
                              ( ! [G: TA] : ( B @ G @ E )
                             => ( B @ F @ ( bang @ E ) ) )
                         => ( B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_pi_Ostrong__induct_H) ).

thf(784,plain,
    ! [TA: $tType,A: TA > ( set @ name ),B: TA > pi > $o,C: TA,D: pi] :
      ( ! [E: TA] : ( finite_finite @ name @ ( A @ E ) )
     => ( ! [E: TA] : ( B @ E @ piNil )
       => ( ! [E: name,F: name,G: pi,H: TA] :
              ( ! [I: TA] : ( B @ I @ G )
             => ( B @ H @ ( output @ E @ F @ G ) ) )
         => ( ! [E: pi,F: TA] :
                ( ! [G: TA] : ( B @ G @ E )
               => ( B @ F @ ( tau @ E ) ) )
           => ( ! [E: name,F: name,G: pi,H: TA] :
                  ( ~ ( member @ name @ F @ ( A @ H ) )
                 => ( ( fresh @ name @ name @ F @ E )
                   => ( ! [I: TA] : ( B @ I @ G )
                     => ( B @ H @ ( input @ E @ F @ G ) ) ) ) )
             => ( ! [E: name,F: name,G: pi,H: TA] :
                    ( ! [I: TA] : ( B @ I @ G )
                   => ( B @ H @ ( match @ E @ F @ G ) ) )
               => ( ! [E: name,F: name,G: pi,H: TA] :
                      ( ! [I: TA] : ( B @ I @ G )
                     => ( B @ H @ ( mismatch @ E @ F @ G ) ) )
                 => ( ! [E: pi,F: pi,G: TA] :
                        ( ! [H: TA] : ( B @ H @ E )
                       => ( ! [H: TA] : ( B @ H @ F )
                         => ( B @ G @ ( sum @ E @ F ) ) ) )
                   => ( ! [E: pi,F: pi,G: TA] :
                          ( ! [H: TA] : ( B @ H @ E )
                         => ( ! [H: TA] : ( B @ H @ F )
                           => ( B @ G @ ( par @ E @ F ) ) ) )
                     => ( ! [E: name,F: pi,G: TA] :
                            ( ~ ( member @ name @ E @ ( A @ G ) )
                           => ( ! [H: TA] : ( B @ H @ F )
                             => ( B @ G @ ( res @ E @ F ) ) ) )
                       => ( ! [E: pi,F: TA] :
                              ( ! [G: TA] : ( B @ G @ E )
                             => ( B @ F @ ( bang @ E ) ) )
                         => ( B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(54,axiom,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ! [A: TA,B: name,C: name] :
          ( ( finite_finite @ name @ ( supp @ TA @ name @ A ) )
         => ( ( fresh @ name @ ( name > ( noption @ TA ) ) @ B @ ( abs_fun @ name @ TA @ C @ A ) )
            = ( ( B = C )
              | ( fresh @ name @ TA @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_abs__fresh_I2_J) ).

thf(419,plain,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ! [A: TA,B: name,C: name] :
          ( ( finite_finite @ name @ ( supp @ TA @ name @ A ) )
         => ( ( fresh @ name @ ( name > ( noption @ TA ) ) @ B @ ( abs_fun @ name @ TA @ C @ A ) )
            = ( ( B = C )
              | ( fresh @ name @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(249,axiom,
    ! [TA: $tType,A: TA > $o,B: name > name > TA,C: TA] :
      ( ! [D: name,E: name] : ( A @ ( B @ D @ E ) )
     => ( ( A @ C )
       => ( ( late_freeRes_rec @ TA @ B @ C @ late_TauR )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_freeRes_Orecs_I2_J) ).

thf(1349,plain,
    ! [TA: $tType,A: TA > $o,B: name > name > TA,C: TA] :
      ( ! [D: name,E: name] : ( A @ ( B @ D @ E ) )
     => ( ( A @ C )
       => ( ( late_freeRes_rec @ TA @ B @ C @ late_TauR )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(98,axiom,
    ! [A: name] :
      ( ( supp @ late_subject @ name @ ( late_BoundOutputS @ A ) )
      = ( supp @ name @ name @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_subject_Osupp_I2_J) ).

thf(567,plain,
    ! [A: name] :
      ( ( supp @ late_subject @ name @ ( late_BoundOutputS @ A ) )
      = ( supp @ name @ name @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(108,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( match @ A @ B @ C )
     != ( sum @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_pi_Odistinct_I63_J) ).

thf(599,plain,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( match @ A @ B @ C )
     != ( sum @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(216,axiom,
    alpha = late_TauR,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_cComm2_Ohyps_I9_J) ).

thf(1175,plain,
    alpha = late_TauR,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(149,axiom,
    late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_H_091x_058_058_061b_093_092_060close_062) ).

thf(764,plain,
    late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(110,axiom,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: name,B: name,C: TA] :
          ( ( fresh @ name @ ( name > ( noption @ TA ) ) @ A @ ( abs_fun @ name @ TA @ B @ C ) )
          = ( ( A = B )
            | ( fresh @ name @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_name__fresh__abs) ).

thf(604,plain,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: name,B: name,C: TA] :
          ( ( fresh @ name @ ( name > ( noption @ TA ) ) @ A @ ( abs_fun @ name @ TA @ B @ C ) )
          = ( ( A = B )
            | ( fresh @ name @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(83,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/sandbox/benchmark/theBenchmark.p',fact_144_pi_Oinject_I3_J) ).

thf(509,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)],[83]) ).

thf(125,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( input @ A @ B @ C )
     != ( sum @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_pi_Odistinct_I53_J) ).

thf(649,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)],[125]) ).

thf(195,axiom,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh @ name @ pi @ A @ B )
     => ( ( A != C )
       => ( fresh @ name @ pi @ A @ ( subs @ B @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_fresh__fact1) ).

thf(1043,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)],[195]) ).

thf(77,axiom,
    ! [A: name,B: pi] :
      ( ( fresh @ name @ pi @ A @ ( bang @ B ) )
      = ( fresh @ name @ pi @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_pi_Ofresh_I10_J) ).

thf(494,plain,
    ! [A: name,B: pi] :
      ( ( fresh @ name @ pi @ A @ ( bang @ B ) )
      = ( fresh @ name @ pi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(118,axiom,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh @ name @ pi @ A @ ( input @ B @ C @ D ) )
      = ( ( fresh @ name @ name @ A @ B )
        & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_pi_Ofresh_I4_J) ).

thf(631,plain,
    ! [A: name,B: name,C: name,D: pi] :
      ( ( fresh @ name @ pi @ A @ ( input @ B @ C @ D ) )
      = ( ( fresh @ name @ name @ A @ B )
        & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(87,axiom,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA] : ( finite_finite @ name @ ( supp @ TA @ name @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_fs__name1) ).

thf(535,plain,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA] : ( finite_finite @ name @ ( supp @ TA @ name @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(192,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/sandbox/benchmark/theBenchmark.p',fact_152_mismatchCases) ).

thf(1029,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)],[192]) ).

thf(210,axiom,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA > late_residual > $o,B: TA,C: late_residual] :
          ( ! [D: late_subject,E: name,F: pi,G: TA] :
              ( ( fresh @ name @ TA @ E @ G )
             => ( ( fresh @ name @ late_subject @ E @ D )
               => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
         => ( ! [D: late_freeRes,E: pi,F: TA] : ( A @ F @ ( late_FreeR @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_residual_Ostrong__induct) ).

thf(1149,plain,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA > late_residual > $o,B: TA,C: late_residual] :
          ( ! [D: late_subject,E: name,F: pi,G: TA] :
              ( ( fresh @ name @ TA @ E @ G )
             => ( ( fresh @ name @ late_subject @ E @ D )
               => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
         => ( ! [D: late_freeRes,E: pi,F: TA] : ( A @ F @ ( late_FreeR @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(151,axiom,
    ! [A: pi,B: pi,C: pi] :
      ( ( tau @ A )
     != ( par @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_pi_Odistinct_I43_J) ).

thf(769,plain,
    ! [A: pi,B: pi,C: pi] :
      ( ( tau @ A )
     != ( par @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(190,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
       => ( ( fresh @ name @ pi @ C @ A )
         => ( ( fresh @ name @ pi @ C @ E )
           => ( ( C != B )
             => ( ( C != F )
               => ( ( fresh @ name @ pi @ C @ G )
                 => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_transitions_OComm1) ).

thf(1022,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)],[190]) ).

thf(233,axiom,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA > late_residual > $o,B: TA,C: late_residual] :
          ( ! [D: late_subject,E: name,F: pi,G: TA] :
              ( ( fresh @ name @ TA @ E @ G )
             => ( ( fresh @ name @ late_subject @ E @ D )
               => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
         => ( ! [D: late_freeRes,E: pi,F: TA] : ( A @ F @ ( late_FreeR @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_residual_Ostrong__inducts) ).

thf(1293,plain,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: TA > late_residual > $o,B: TA,C: late_residual] :
          ( ! [D: late_subject,E: name,F: pi,G: TA] :
              ( ( fresh @ name @ TA @ E @ G )
             => ( ( fresh @ name @ late_subject @ E @ D )
               => ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
         => ( ! [D: late_freeRes,E: pi,F: TA] : ( A @ F @ ( late_FreeR @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(217,axiom,
    fresh @ name @ pi @ x @ r,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062x_A_092_060sharp_062_AR_092_060close_062) ).

thf(1177,plain,
    fresh @ name @ pi @ x @ r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(67,axiom,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( sum @ A @ B )
     != ( res @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_pi_Odistinct_I81_J) ).

thf(462,plain,
    ! [A: pi,B: pi,C: name,D: pi] :
      ( ( sum @ A @ B )
     != ( res @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(28,axiom,
    ! [A: name] :
      ( ( supp @ late_subject @ name @ ( late_InputS @ A ) )
      = ( supp @ name @ name @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_subject_Osupp_I1_J) ).

thf(345,plain,
    ! [A: name] :
      ( ( supp @ late_subject @ name @ ( late_InputS @ A ) )
      = ( supp @ name @ name @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(168,axiom,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
     => ~ ( ( fresh @ name @ late_freeRes @ A @ D )
          | ( fresh @ name @ late_freeRes @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_outputFreshTrans) ).

thf(858,plain,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
      ( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
     => ~ ( ( fresh @ name @ late_freeRes @ A @ D )
          | ( fresh @ name @ late_freeRes @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(47,axiom,
    ! [A: name,B: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Late__Semantics1_Osubject_Oinject_I1_J) ).

thf(399,plain,
    ! [A: name,B: name] :
      ( ( ( late_InputS @ A )
        = ( late_InputS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(158,axiom,
    ( subs
    = ( ^ [A: pi,B: name,C: name] :
          ( pi_rec @ pi @ piNil
          @ ^ [D: name,E: name,F: pi] : ( output @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
          @ ^ [D: pi] : tau
          @ ^ [D: name,E: name,F: pi] : ( input @ ( subst_name @ D @ B @ C ) @ E )
          @ ^ [D: name,E: name,F: pi] : ( match @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
          @ ^ [D: name,E: name,F: pi] : ( mismatch @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
          @ ^ [D: pi,E: pi] : sum
          @ ^ [D: pi,E: pi] : par
          @ ^ [D: name,E: pi] : ( res @ D )
          @ ^ [D: pi] : bang
          @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_subs__def) ).

thf(827,plain,
    ( subs
    = ( ^ [A: pi,B: name,C: name] :
          ( pi_rec @ pi @ piNil
          @ ^ [D: name,E: name,F: pi] : ( output @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
          @ ^ [D: pi] : tau
          @ ^ [D: name,E: name,F: pi] : ( input @ ( subst_name @ D @ B @ C ) @ E )
          @ ^ [D: name,E: name,F: pi] : ( match @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
          @ ^ [D: name,E: name,F: pi] : ( mismatch @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
          @ ^ [D: pi,E: pi] : sum
          @ ^ [D: pi,E: pi] : par
          @ ^ [D: name,E: pi] : ( res @ D )
          @ ^ [D: pi] : bang
          @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(171,axiom,
    ! [A: pi,B: name,C: name] :
      ( ( subs @ ( tau @ A ) @ B @ C )
      = ( tau @ ( subs @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_simps_I2_J) ).

thf(868,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)],[171]) ).

thf(154,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( match @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_pi_Odistinct_I65_J) ).

thf(780,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)],[154]) ).

thf(65,axiom,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Late__Semantics_Osubject_Odistinct_I1_J) ).

thf(455,plain,
    ! [A: name,B: name] :
      ( ( late_InputS @ A )
     != ( late_BoundOutputS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(60,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: name > name > TB,C: TB,D: late_freeRes] :
      ( ( A @ ( late_case_freeRes @ TB @ B @ C @ D ) )
      = ( late_case_freeRes @ TA
        @ ^ [E: name,F: name] : ( A @ ( B @ E @ F ) )
        @ ( A @ C )
        @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_freeRes_Ocase__distrib) ).

thf(438,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: name > name > TB,C: TB,D: late_freeRes] :
      ( ( A @ ( late_case_freeRes @ TB @ B @ C @ D ) )
      = ( late_case_freeRes @ TA
        @ ^ [E: name,F: name] : ( A @ ( B @ E @ F ) )
        @ ( A @ C )
        @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(58,axiom,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( mismatch @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_pi_Odistinct_I39_J) ).

thf(431,plain,
    ! [A: pi,B: name,C: name,D: pi] :
      ( ( tau @ A )
     != ( mismatch @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(126,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/sandbox/benchmark/theBenchmark.p',fact_162_pi_Oinject_I4_J) ).

thf(653,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)],[126]) ).

thf(134,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( sum @ A @ B )
     != ( par @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_pi_Odistinct_I79_J) ).

thf(685,plain,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( sum @ A @ B )
     != ( par @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(215,axiom,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).

thf(1171,plain,
    ! [A: name,B: name] :
      ( ( late_OutputR @ A @ B )
     != late_TauR ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(120,axiom,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: name,B: name,C: TA] :
          ( ( fresh @ name @ ( name > ( noption @ TA ) ) @ A @ ( abs_fun @ name @ TA @ B @ C ) )
          = ( ( A = B )
            | ( fresh @ name @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_abs__fresh_I1_J) ).

thf(636,plain,
    ! [TA: $tType] :
      ( ( fs_name @ TA )
     => ! [A: name,B: name,C: TA] :
          ( ( fresh @ name @ ( name > ( noption @ TA ) ) @ A @ ( abs_fun @ name @ TA @ B @ C ) )
          = ( ( A = B )
            | ( fresh @ name @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(137,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/sandbox/benchmark/theBenchmark.p',fact_156_Mismatch) ).

thf(695,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)],[137]) ).

thf(130,axiom,
    late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_cComm2_Ohyps_I2_J) ).

thf(675,plain,
    late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(236,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/sandbox/benchmark/theBenchmark.p',fact_186_sumCases) ).

thf(1304,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)],[236]) ).

thf(179,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( output @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_pi_Odistinct_I29_J) ).

thf(944,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)],[179]) ).

thf(132,axiom,
    ! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Late__Semantics_OInput) ).

thf(680,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)],[132]) ).

thf(124,axiom,
    fs_name @ pi,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Opi___Agent_Ofs__name) ).

thf(648,plain,
    fs_name @ pi,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(85,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: TB,D: TA > $o,E: late_residual] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( finite_finite @ name @ ( supp @ TB @ name @ C ) )
             => ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
               => ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
                 => ( ! [F: late_subject,G: name] :
                        ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ G @ A )
                       => ( ( fresh @ name @ late_subject @ G @ F )
                         => ( ( fresh @ name @ TB @ G @ C )
                           => ! [H: pi] :
                                ( ( D @ ( A @ F @ G @ H ) )
                               => ( fresh @ name @ TA @ G @ ( A @ F @ G @ H ) ) ) ) ) )
                   => ? [F: TA] :
                        ( ( late_r582136743ec_set @ TA @ A @ B @ E @ F )
                        & ! [G: TA] :
                            ( ( late_r582136743ec_set @ TA @ A @ B @ E @ G )
                           => ( G = F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_residual_Orec__unique) ).

thf(516,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: TB,D: TA > $o,E: late_residual] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( finite_finite @ name @ ( supp @ TB @ name @ C ) )
             => ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
               => ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
                 => ( ! [F: late_subject,G: name] :
                        ( ( fresh @ name @ ( late_subject > name > pi > TA ) @ G @ A )
                       => ( ( fresh @ name @ late_subject @ G @ F )
                         => ( ( fresh @ name @ TB @ G @ C )
                           => ! [H: pi] :
                                ( ( D @ ( A @ F @ G @ H ) )
                               => ( fresh @ name @ TA @ G @ ( A @ F @ G @ H ) ) ) ) ) )
                   => ? [F: TA] :
                        ( ( late_r582136743ec_set @ TA @ A @ B @ E @ F )
                        & ! [G: TA] :
                            ( ( late_r582136743ec_set @ TA @ A @ B @ E @ G )
                           => ( G = F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(208,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/sandbox/benchmark/theBenchmark.p',fact_105_resOutputOutputTrans) ).

thf(1145,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)],[208]) ).

thf(185,axiom,
    ! [A: pi,B: late_residual] :
      ( ( late_transitions @ ( bang @ A ) @ B )
     => ~ ! [C: pi] :
            ( ( ( bang @ A )
              = ( bang @ C ) )
           => ~ ( late_transitions @ ( par @ C @ ( bang @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_bangCases) ).

thf(968,plain,
    ! [A: pi,B: late_residual] :
      ( ( late_transitions @ ( bang @ A ) @ B )
     => ~ ! [C: pi] :
            ( ( ( bang @ A )
              = ( bang @ C ) )
           => ~ ( late_transitions @ ( par @ C @ ( bang @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(219,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/sandbox/benchmark/theBenchmark.p',fact_133_simps_I3_J) ).

thf(1181,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)],[219]) ).

thf(95,axiom,
    ! [TA: $tType,A: TA > $o,B: name > name > TA,C: TA,D: name,E: name] :
      ( ! [F: name,G: name] : ( A @ ( B @ F @ G ) )
     => ( ( A @ C )
       => ( ( late_freeRes_rec @ TA @ B @ C @ ( late_OutputR @ D @ E ) )
          = ( B @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_freeRes_Orecs_I1_J) ).

thf(557,plain,
    ! [TA: $tType,A: TA > $o,B: name > name > TA,C: TA,D: name,E: name] :
      ( ! [F: name,G: name] : ( A @ ( B @ F @ G ) )
     => ( ( A @ C )
       => ( ( late_freeRes_rec @ TA @ B @ C @ ( late_OutputR @ D @ E ) )
          = ( B @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(6,axiom,
    ! [A: pi] :
      ( ( supp @ pi @ name @ ( tau @ A ) )
      = ( supp @ pi @ name @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_pi_Osupp_I3_J) ).

thf(282,plain,
    ! [A: pi] :
      ( ( supp @ pi @ name @ ( tau @ A ) )
      = ( supp @ pi @ name @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(140,axiom,
    ! [A: name,B: name,C: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Output) ).

thf(707,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)],[140]) ).

thf(229,axiom,
    x != a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_cComm2_Ohyps_I5_J) ).

thf(1267,plain,
    x != a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(102,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( supp @ TA @ TB )
      = ( ^ [A: TA] :
            ( collect @ TB
            @ ^ [B: TB] :
                ~ ( fresh @ TB @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_supp__fresh__iff) ).

thf(580,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( supp @ TA @ TB )
      = ( ^ [A: TA] :
            ( collect @ TB
            @ ^ [B: TB] :
                ~ ( fresh @ TB @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(167,axiom,
    ! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
      ~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_resInputFreeTrans) ).

thf(855,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)],[167]) ).

thf(61,axiom,
    ! [TA: $tType,A: name > TA,B: name > TA,C: name] :
      ( ( late_case_subject @ TA @ A @ B @ ( late_BoundOutputS @ C ) )
      = ( B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_subject_Ocase_I2_J) ).

thf(441,plain,
    ! [TA: $tType,A: name > TA,B: name > TA,C: name] :
      ( ( late_case_subject @ TA @ A @ B @ ( late_BoundOutputS @ C ) )
      = ( B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(227,axiom,
    late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ a @ b ) @ p2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_cComm2_Ohyps_I1_J) ).

thf(1262,plain,
    late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ a @ b ) @ p2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(122,axiom,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: late_residual,D: TA] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( late_r582136743ec_set @ TA @ A @ B @ C @ D )
             => ( finite_finite @ name @ ( supp @ TA @ name @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_residual_Orec__fin__supp) ).

thf(643,plain,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ! [A: late_subject > name > pi > TA,B: late_freeRes > pi > TA,C: late_residual,D: TA] :
          ( ( finite_finite @ name @ ( supp @ ( late_subject > name > pi > TA ) @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( late_freeRes > pi > TA ) @ name @ B ) )
           => ( ( late_r582136743ec_set @ TA @ A @ B @ C @ D )
             => ( finite_finite @ name @ ( supp @ TA @ name @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(265,axiom,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh @ name @ late_residual @ A @ ( late_FreeR @ B @ C ) )
      = ( ( fresh @ name @ late_freeRes @ A @ B )
        & ( fresh @ name @ pi @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_residual_Ofresh_I2_J) ).

thf(1404,plain,
    ! [A: name,B: late_freeRes,C: pi] :
      ( ( fresh @ name @ late_residual @ A @ ( late_FreeR @ B @ C ) )
      = ( ( fresh @ name @ late_freeRes @ A @ B )
        & ( fresh @ name @ pi @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(127,axiom,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( output @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_pi_Odistinct_I1_J) ).

thf(656,plain,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( output @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(198,axiom,
    ! [A: pi,B: pi,C: name,D: name] :
      ( ( subs @ ( par @ A @ B ) @ C @ D )
      = ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_simps_I8_J) ).

thf(1052,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)],[198]) ).

thf(107,axiom,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( input @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_pi_Odistinct_I5_J) ).

thf(595,plain,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( input @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(78,axiom,
    ! [A: name,B: name,C: name] :
      ( ( fresh @ name @ late_freeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( ( fresh @ name @ name @ A @ B )
        & ( fresh @ name @ name @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_freeRes_Ofresh_I1_J) ).

thf(497,plain,
    ! [A: name,B: name,C: name] :
      ( ( fresh @ name @ late_freeRes @ A @ ( late_OutputR @ B @ C ) )
      = ( ( fresh @ name @ name @ A @ B )
        & ( fresh @ name @ name @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(271,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/sandbox/benchmark/theBenchmark.p',fact_20_tauCases_H) ).

thf(1421,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)],[271]) ).

thf(206,axiom,
    ! [A: pi,B: late_subject,C: name,D: pi,E: name] :
      ( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
     => ( ( fresh @ name @ pi @ E @ A )
       => ( ( E != C )
         => ( fresh @ name @ pi @ E @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_freshBoundDerivative_I2_J) ).

thf(1084,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)],[206]) ).

thf(73,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( output @ A @ B @ C )
     != ( tau @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_pi_Odistinct_I19_J) ).

thf(482,plain,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( output @ A @ B @ C )
     != ( tau @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(129,axiom,
    ! [A: pi] :
      ( piNil
     != ( bang @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_pi_Odistinct_I17_J) ).

thf(671,plain,
    ! [A: pi] :
      ( piNil
     != ( bang @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(241,axiom,
    ! [A: name,B: name] :
      ( ( subs @ piNil @ A @ B )
      = piNil ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_simps_I1_J) ).

thf(1321,plain,
    ! [A: name,B: name] :
      ( ( subs @ piNil @ A @ B )
      = piNil ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(268,axiom,
    x != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cComm2_Ohyps_I6_J) ).

thf(1412,plain,
    x != b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(147,axiom,
    ! [TA: $tType,A: TA > late_freeRes > $o,B: TA,C: late_freeRes] :
      ( ! [D: name,E: name,F: TA] : ( A @ F @ ( late_OutputR @ D @ E ) )
     => ( ! [D: TA] : ( A @ D @ late_TauR )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_freeRes_Ostrong__induct_H) ).

thf(759,plain,
    ! [TA: $tType,A: TA > late_freeRes > $o,B: TA,C: late_freeRes] :
      ( ! [D: name,E: name,F: TA] : ( A @ F @ ( late_OutputR @ D @ E ) )
     => ( ! [D: TA] : ( A @ D @ late_TauR )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(261,axiom,
    ! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
      ( ( late_BoundR @ A @ B @ C )
     != ( late_FreeR @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_residual_Odistinct_I1_J) ).

thf(1390,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)],[261]) ).

thf(35,axiom,
    ! [A: pi] :
      ( ( supp @ pi @ name @ ( bang @ A ) )
      = ( supp @ pi @ name @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_pi_Osupp_I10_J) ).

thf(368,plain,
    ! [A: pi] :
      ( ( supp @ pi @ name @ ( bang @ A ) )
      = ( supp @ pi @ name @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(138,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 @ name @ late_subject @ C @ B )
           => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_transitions_OPar2B) ).

thf(699,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 @ name @ late_subject @ C @ B )
           => ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(183,axiom,
    ! [A: pi,B: pi] :
      ( piNil
     != ( par @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_pi_Odistinct_I13_J) ).

thf(963,plain,
    ! [A: pi,B: pi] :
      ( piNil
     != ( par @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(18,axiom,
    pt_name @ pi,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Opi___Agent_Opt__name_2) ).

thf(319,plain,
    pt_name @ pi,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(201,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/sandbox/benchmark/theBenchmark.p',fact_145_simps_I5_J) ).

thf(1062,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)],[201]) ).

thf(43,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( sum @ A @ B )
        = ( sum @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_pi_Oinject_I6_J) ).

thf(390,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)],[43]) ).

thf(72,axiom,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( match @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_pi_Odistinct_I7_J) ).

thf(478,plain,
    ! [A: name,B: name,C: pi] :
      ( piNil
     != ( match @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(92,axiom,
    ! [TA: $tType,A: TA > late_subject > $o,B: TA,C: late_subject] :
      ( ! [D: name,E: TA] : ( A @ E @ ( late_InputS @ D ) )
     => ( ! [D: name,E: TA] : ( A @ E @ ( late_BoundOutputS @ D ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_subject_Ostrong__inducts) ).

thf(549,plain,
    ! [TA: $tType,A: TA > late_subject > $o,B: TA,C: late_subject] :
      ( ! [D: name,E: TA] : ( A @ E @ ( late_InputS @ D ) )
     => ( ! [D: name,E: TA] : ( A @ E @ ( late_BoundOutputS @ D ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(9,axiom,
    ! [A: pi,B: pi] :
      ( ( supp @ pi @ name @ ( sum @ A @ B ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ A ) @ ( supp @ pi @ name @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_pi_Osupp_I7_J) ).

thf(290,plain,
    ! [A: pi,B: pi] :
      ( ( supp @ pi @ name @ ( sum @ A @ B ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ pi @ name @ A ) @ ( supp @ pi @ name @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(39,axiom,
    ! [A: name,B: name] :
      ( ( fresh @ name @ late_subject @ A @ ( late_BoundOutputS @ B ) )
      = ( fresh @ name @ name @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_subject_Ofresh_I2_J) ).

thf(378,plain,
    ! [A: name,B: name] :
      ( ( fresh @ name @ late_subject @ A @ ( late_BoundOutputS @ B ) )
      = ( fresh @ name @ name @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(17,axiom,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( input @ A @ B @ C )
     != ( bang @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_pi_Odistinct_I59_J) ).

thf(315,plain,
    ! [A: name,B: name,C: pi,D: pi] :
      ( ( input @ A @ B @ C )
     != ( bang @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(184,axiom,
    fresh @ name @ pi @ x @ p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_cComm2_Ohyps_I3_J) ).

thf(967,plain,
    fresh @ name @ pi @ x @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(161,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( input @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_pi_Odistinct_I55_J) ).

thf(835,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)],[161]) ).

thf(258,axiom,
    ! [A: late_residual] :
      ~ ( late_transitions @ piNil @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_nilCases_H) ).

thf(1380,plain,
    ! [A: late_residual] :
      ~ ( late_transitions @ piNil @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(209,axiom,
    fresh @ name @ pi @ x @ ( par @ q @ r ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_cComm2_Ohyps_I4_J) ).

thf(1148,plain,
    fresh @ name @ pi @ x @ ( par @ q @ r ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(55,axiom,
    ! [TA: $tType,A: name > TA,B: name > TA,C: name] :
      ( ( late_case_subject @ TA @ A @ B @ ( late_InputS @ C ) )
      = ( A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_subject_Ocase_I1_J) ).

thf(422,plain,
    ! [TA: $tType,A: name > TA,B: name > TA,C: name] :
      ( ( late_case_subject @ TA @ A @ B @ ( late_InputS @ C ) )
      = ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(1,conjecture,
    late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) @ r ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) @ r ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(273,plain,
    ~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) @ r ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(170,axiom,
    ! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
      ~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_inputFreeTrans) ).

thf(865,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)],[170]) ).

thf(109,axiom,
    fs_name @ late_residual,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual___Agent_Ofs__name_13) ).

thf(603,plain,
    fs_name @ late_residual,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(97,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/sandbox/benchmark/theBenchmark.p',fact_163_pi_Oinject_I5_J) ).

thf(564,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)],[97]) ).

thf(13,axiom,
    ! [TA: $tType,A: TA] :
      ( ( finite_finite @ name @ ( supp @ TA @ name @ A ) )
     => ~ ! [B: name] :
            ~ ( fresh @ name @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_exists__fresh) ).

thf(305,plain,
    ! [TA: $tType,A: TA] :
      ( ( finite_finite @ name @ ( supp @ TA @ name @ A ) )
     => ~ ! [B: name] :
            ~ ( fresh @ name @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(246,axiom,
    ! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Tau) ).

thf(1335,plain,
    ! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(223,axiom,
    ! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
      ( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
     => ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
       => ( ( fresh @ name @ pi @ F @ A )
         => ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Late__Semantics_OClose1) ).

thf(1197,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)],[223]) ).

thf(182,axiom,
    ! [A: pi,B: late_residual,C: name] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( match @ C @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Match) ).

thf(960,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)],[182]) ).

thf(52,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( pt_name @ TB )
        & ( pt_name @ TA ) )
     => ( pt_name @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Agent_Opt__name) ).

thf(415,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( pt_name @ TB )
        & ( pt_name @ TA ) )
     => ( pt_name @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(253,axiom,
    ! [A: pi,B: pi,C: pi,D: pi] :
      ( ( ( par @ A @ B )
        = ( par @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_pi_Oinject_I7_J) ).

thf(1363,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)],[253]) ).

thf(239,axiom,
    ! [A: name,B: name,C: pi,D: pi,E: pi] :
      ( ( mismatch @ A @ B @ C )
     != ( par @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_pi_Odistinct_I73_J) ).

thf(1314,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)],[239]) ).

thf(86,axiom,
    ! [A: name,B: pi] :
      ( ( supp @ pi @ name @ ( res @ A @ B ) )
      = ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_pi_Osupp_I9_J) ).

thf(532,plain,
    ! [A: name,B: pi] :
      ( ( supp @ pi @ name @ ( res @ A @ B ) )
      = ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(202,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh @ name @ pi @ A @ B )
     => ( ( res @ C @ B )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_substRes2) ).

thf(1065,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)],[202]) ).

thf(250,axiom,
    ! [A: pi,B: name] :
      ( ( subs @ A @ B @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__identity) ).

thf(1352,plain,
    ! [A: pi,B: name] :
      ( ( subs @ A @ B @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(23,axiom,
    ! [A: late_subject > $o,B: late_subject] :
      ( ! [C: name] : ( A @ ( late_InputS @ C ) )
     => ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_subject_Oinducts) ).

thf(332,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)],[23]) ).

thf(66,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( supp @ pi @ name @ ( output @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ B ) @ ( supp @ pi @ name @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_pi_Osupp_I2_J) ).

thf(459,plain,
    ! [A: name,B: name,C: pi] :
      ( ( supp @ pi @ name @ ( output @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ B ) @ ( supp @ pi @ name @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(188,axiom,
    ! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
      ( ( ( late_FreeR @ A @ B )
        = ( late_FreeR @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_residual_Oinject_I2_J) ).

thf(982,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)],[188]) ).

thf(4,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: name > TA,C: name > TA,D: late_subject] :
      ( ( A @ ( late_case_subject @ TA @ B @ C @ D ) )
      = ( late_case_subject @ TB
        @ ^ [E: name] : ( A @ ( B @ E ) )
        @ ^ [E: name] : ( A @ ( C @ E ) )
        @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_subject_Ocase__distrib) ).

thf(277,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: name > TA,C: name > TA,D: late_subject] :
      ( ( A @ ( late_case_subject @ TA @ B @ C @ D ) )
      = ( late_case_subject @ TB
        @ ^ [E: name] : ( A @ ( B @ E ) )
        @ ^ [E: name] : ( A @ ( C @ E ) )
        @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(172,axiom,
    ( late_bangPred
    = ( ^ [A: pi,B: pi] :
          ( ? [C: pi] :
              ( ( A = C )
              & ( B
                = ( bang @ C ) ) )
          | ? [C: pi] :
              ( ( A = C )
              & ( B
                = ( par @ C @ ( bang @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_bangPred_Osimps) ).

thf(871,plain,
    ( late_bangPred
    = ( ^ [A: pi,B: pi] :
          ( ? [C: pi] :
              ( ( A = C )
              & ( B
                = ( bang @ C ) ) )
          | ? [C: pi] :
              ( ( A = C )
              & ( B
                = ( par @ C @ ( bang @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(111,axiom,
    ! [A: late_subject,B: name,C: pi] :
      ( ( supp @ late_residual @ name @ ( late_BoundR @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ late_subject @ name @ A ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_residual_Osupp_I1_J) ).

thf(607,plain,
    ! [A: late_subject,B: name,C: pi] :
      ( ( supp @ late_residual @ name @ ( late_BoundR @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ late_subject @ name @ A ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(45,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( supp @ pi @ name @ ( match @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ B ) @ ( supp @ pi @ name @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_pi_Osupp_I5_J) ).

thf(395,plain,
    ! [A: name,B: name,C: pi] :
      ( ( supp @ pi @ name @ ( match @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ B ) @ ( supp @ pi @ name @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(116,axiom,
    ! [A: name,B: name,C: pi,D: name,E: pi] :
      ( ( match @ A @ B @ C )
     != ( res @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_pi_Odistinct_I67_J) ).

thf(624,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)],[116]) ).

thf(162,axiom,
    ! [A: pi,B: late_residual,C: pi] :
      ( ( late_transitions @ A @ B )
     => ( late_transitions @ ( sum @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_Sum1) ).

thf(839,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)],[162]) ).

thf(20,axiom,
    ! [A: name,B: name,C: pi] :
      ( ( supp @ pi @ name @ ( input @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_pi_Osupp_I4_J) ).

thf(322,plain,
    ! [A: name,B: name,C: pi] :
      ( ( supp @ pi @ name @ ( input @ A @ B @ C ) )
      = ( sup_sup @ ( set @ name ) @ ( supp @ name @ name @ A ) @ ( supp @ ( name > ( noption @ pi ) ) @ name @ ( abs_fun @ name @ pi @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(74,axiom,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ! [A: TA,B: name > name > pi > TA > TA,C: pi > TA > TA,D: name > name > pi > TA > TA,E: name > name > pi > TA > TA,F: name > name > pi > TA > TA,G: pi > pi > TA > TA > TA,H: pi > pi > TA > TA > TA,I: name > pi > TA > TA,J: pi > TA > TA,K: pi,L: TA] :
          ( ( finite_finite @ name @ ( supp @ TA @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > TA > TA ) @ name @ B ) )
           => ( ( finite_finite @ name @ ( supp @ ( pi > TA > TA ) @ name @ C ) )
             => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > TA > TA ) @ name @ D ) )
               => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > TA > TA ) @ name @ E ) )
                 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > TA > TA ) @ name @ F ) )
                   => ( ( finite_finite @ name @ ( supp @ ( pi > pi > TA > TA > TA ) @ name @ G ) )
                     => ( ( finite_finite @ name @ ( supp @ ( pi > pi > TA > TA > TA ) @ name @ H ) )
                       => ( ( finite_finite @ name @ ( supp @ ( name > pi > TA > TA ) @ name @ I ) )
                         => ( ( finite_finite @ name @ ( supp @ ( pi > TA > TA ) @ name @ J ) )
                           => ( ( pi_rec_set @ TA @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
                             => ( finite_finite @ name @ ( supp @ TA @ name @ L ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_pi_Orec__fin__supp) ).

thf(486,plain,
    ! [TA: $tType] :
      ( ( pt_name @ TA )
     => ! [A: TA,B: name > name > pi > TA > TA,C: pi > TA > TA,D: name > name > pi > TA > TA,E: name > name > pi > TA > TA,F: name > name > pi > TA > TA,G: pi > pi > TA > TA > TA,H: pi > pi > TA > TA > TA,I: name > pi > TA > TA,J: pi > TA > TA,K: pi,L: TA] :
          ( ( finite_finite @ name @ ( supp @ TA @ name @ A ) )
         => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > TA > TA ) @ name @ B ) )
           => ( ( finite_finite @ name @ ( supp @ ( pi > TA > TA ) @ name @ C ) )
             => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > TA > TA ) @ name @ D ) )
               => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > TA > TA ) @ name @ E ) )
                 => ( ( finite_finite @ name @ ( supp @ ( name > name > pi > TA > TA ) @ name @ F ) )
                   => ( ( finite_finite @ name @ ( supp @ ( pi > pi > TA > TA > TA ) @ name @ G ) )
                     => ( ( finite_finite @ name @ ( supp @ ( pi > pi > TA > TA > TA ) @ name @ H ) )
                       => ( ( finite_finite @ name @ ( supp @ ( name > pi > TA > TA ) @ name @ I ) )
                         => ( ( finite_finite @ name @ ( supp @ ( pi > TA > TA ) @ name @ J ) )
                           => ( ( pi_rec_set @ TA @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
                             => ( finite_finite @ name @ ( supp @ TA @ name @ L ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(69,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TB,B: TA,C: TB] :
      ( ( supports @ TB @ TA @ A @ B )
     => ( ( finite_finite @ TB @ A )
       => ( ~ ( member @ TB @ C @ A )
         => ( fresh @ TB @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_supports__fresh) ).

thf(469,plain,
    ! [TA: $tType,TB: $tType,A: set @ TB,B: TA,C: TB] :
      ( ( supports @ TB @ TA @ A @ B )
     => ( ( finite_finite @ TB @ A )
       => ( ~ ( member @ TB @ C @ A )
         => ( fresh @ TB @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(220,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/sandbox/benchmark/theBenchmark.p',fact_19_tauCases) ).

thf(1184,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)],[220]) ).

thf(90,axiom,
    ! [A: pi,B: pi] :
      ( ( ( bang @ A )
        = ( bang @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_pi_Oinject_I9_J) ).

thf(543,plain,
    ! [A: pi,B: pi] :
      ( ( ( bang @ A )
        = ( bang @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(121,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( output @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_pi_Odistinct_I25_J) ).

thf(639,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)],[121]) ).

thf(131,axiom,
    ! [A: name,B: pi,C: name] :
      ( ( fresh @ name @ pi @ A @ B )
     => ( ( subs @ ( res @ C @ B ) @ C @ A )
        = ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_substRes3) ).

thf(676,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)],[131]) ).

thf(207,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 @ name @ late_subject @ 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 @ name @ late_subject @ H @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_parCasesB_H) ).

thf(1088,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 @ name @ late_subject @ 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 @ name @ late_subject @ H @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(203,axiom,
    ! [A: name,B: pi,C: name,D: name] :
      ( ( fresh @ name @ pi @ A @ B )
     => ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
        = ( subs @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_substTrans) ).

thf(1069,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)],[203]) ).

thf(186,axiom,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh @ name @ pi @ D @ A )
       => ( fresh @ name @ late_freeRes @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_freshFreeDerivative_I1_J) ).

thf(972,plain,
    ! [A: pi,B: late_freeRes,C: pi,D: name] :
      ( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
     => ( ( fresh @ name @ pi @ D @ A )
       => ( fresh @ name @ late_freeRes @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(194,axiom,
    ! [A: late_freeRes > $o,B: late_freeRes] :
      ( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
     => ( ( A @ late_TauR )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_freeRes_Oinducts) ).

thf(1037,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)],[194]) ).

thf(96,axiom,
    ! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
      ( ( input @ A @ B @ C )
     != ( mismatch @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_pi_Odistinct_I51_J) ).

thf(560,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)],[96]) ).

thf(1429,plain,
    $false,
    inference(cvc4,[status(thm)],[645,1036,1337,1168,846,628,1083,941,777,365,1369,1200,1290,1401,308,1073,873,614,1426,384,500,1164,1327,340,930,829,709,417,288,1359,1386,301,320,1366,1055,570,372,504,1330,587,702,934,357,1191,1398,325,448,1415,475,492,756,591,1418,353,821,1383,348,634,692,293,1394,660,411,428,849,507,1377,280,307,452,512,546,1306,381,1047,1153,761,957,746,1343,1355,297,407,1370,862,349,361,583,551,1281,842,285,852,435,329,1178,682,1407,948,388,610,1270,1259,471,488,339,537,1155,554,753,622,1263,985,1297,1050,371,1324,393,938,508,311,765,398,1026,926,343,1318,773,586,750,618,425,824,1301,573,689,444,375,975,402,743,577,1256,1312,1058,1332,466,335,540,1194,406,831,1408,274,784,419,1349,567,599,1175,764,604,509,649,1043,494,631,535,1029,1149,769,1022,1293,1177,462,345,858,399,827,868,780,455,438,431,653,685,1171,636,695,675,1304,944,680,648,516,1145,968,1181,557,282,707,1267,580,855,441,1262,643,1404,656,1052,595,497,1421,1084,482,671,1321,1412,759,1390,368,699,963,319,1062,390,478,549,290,378,315,967,835,1380,1148,422,273,865,603,564,305,1335,1197,960,415,1363,1314,532,1065,1352,332,459,982,277,871,607,395,624,839,322,486,469,1184,543,639,676,1088,1069,972,1037,560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ITP186^2 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n015.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat May 18 15:36:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.04/1.13  % [INFO] 	 Parsing done (264ms). 
% 2.04/1.14  % [INFO] 	 Running in sequential loop mode. 
% 2.87/1.45  % [INFO] 	 eprover registered as external prover. 
% 2.87/1.45  % [INFO] 	 cvc4 registered as external prover. 
% 2.87/1.45  % [INFO] 	 Scanning for conjecture ... 
% 3.19/1.59  % [INFO] 	 Found a conjecture (or negated_conjecture) and 274 axioms. Running axiom selection ... 
% 3.52/1.71  % [INFO] 	 Axiom selection finished. Selected 270 axioms (removed 4 axioms). 
% 4.54/2.03  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.84/2.06  % [INFO] 	 Type checking passed. 
% 4.84/2.06  % [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 ... 
% 232.46/171.37  % External prover 'cvc4' found a proof!
% 232.46/171.37  % [INFO] 	 Killing All external provers ... 
% 232.46/171.37  % Time passed: 170845ms (effective reasoning time: 170226ms)
% 232.46/171.38  % 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)>
% 232.46/171.38  % Axioms used in derivation (270): fact_237_subject_Osupp_I1_J, fact_235_pi_Osupp_I3_J, fact_87_subject_Ostrong__induct_H, fact_177_residual_Ostrong__induct_H, fact_249_freeRes_Osupp_I1_J, fact_166_pi_Odistinct_I23_J, fact_54_Late__Semantics_OComm1, fact_126_Late__Semantics_OInput, fact_202_pi_Odistinct_I83_J, fact_5_cComm2_Ohyps_I8_J, tcon_Late__Semantics_OfreeRes___Agent_Opt__name_8, fact_142_name__fresh__abs, fact_216_Bang, fact_81_pi_Odistinct_I85_J, fact_174_subject_Ocase_I1_J, fact_229_exists__fresh, fact_234_subject_Ocase__distrib, fact_201_pi_Odistinct_I17_J, fact_158_pi_Odistinct_I65_J, fact_60_freeRes_Orecs_I2_J, fact_225_bangPred_Oinducts, fact_1_cComm2_Ohyps_I5_J, fact_58_freeRes_Oexhaust, fact_16_cComm2_Ohyps_I2_J, fact_212_pi_Odistinct_I69_J, fact_9_cComm2_Ohyps_I1_J, fact_185_pi_Odistinct_I33_J, fact_140_residual_Oinject_I1_J, tcon_Agent_Opi___Agent_Ofs__name, fact_17_residual_Oinject_I2_J, fact_33_residual_Odistinct_I1_J, fact_245_pi_Osupp_I4_J, fact_179_pi_Ofresh_I7_J, fact_232_pi_Osupp_I9_J, fact_84_resCases_H, fact_24_pi_Ofresh_I3_J, tcon_Late__Semantics_Osubject___Agent_Ofs__name_11, fact_243_residual_Orec__unique, fact_105_resOutputOutputTrans, fact_252_pi_Osupp_I6_J, fact_71_simps_I9_J, fact_192_pi_Odistinct_I81_J, fact_14_subst__identity, tcon_Late__Semantics_Oresidual___Agent_Opt__name_12, fact_37_parCasesB, fact_241_residual_Orecs_I1_J, fact_208_pi_Odistinct_I1_J, fact_10_simps_I8_J, fact_193_pi_Odistinct_I53_J, fact_68_Late__Semantics1_Osubject_Oinject_I2_J, fact_124_outputFreshTrans, fact_97_resTauBoundTrans, fact_153_mismatchTrans, fact_233_freeRes_Ocase__distrib, fact_159_pi_Odistinct_I75_J, fact_89_Late__Semantics_Osubject_Odistinct_I1_J, fact_127_transitions_OInput, fact_65_Late__Semantics_OClose2, fact_122_resTrans_I1_J, fact_90_resCasesB_H, fact_175_pi_Ostrong__inducts, fact_151_matchCases_H, fact_51_transitions_OComm1, fact_220_pi_Oinducts, fact_32_residual_Oinducts, fact_38_Late__Semantics_OPar2B, fact_27_freshBoundDerivative_I2_J, fact_106_resInputBoundOutputTrans, fact_167_pi_Odistinct_I25_J, fact_70_residual_Ofresh_I2_J, fact_20_tauCases_H, fact_19_tauCases, fact_157_pi_Odistinct_I73_J, fact_134_substInput, fact_52_freshFreeDerivative_I2_J, fact_101_resTauOutputTrans, fact_176_pi_Ostrong__induct, fact_94_Open, fact_111_pi_Ofresh_I2_J, fact_150_matchTrans, tcon_Set_Oset___Agent_Opt__name_1, fact_100_transitions_OPar2B, fact_46_Collect__mem__eq, fact_130_Output, fact_199_pi_Odistinct_I15_J, fact_56_Late__Semantics1_Osubject_Oinject_I1_J, fact_146_simps_I6_J, fact_137_pi_Ofresh_I9_J, fact_213_pi_Odistinct_I63_J, fact_210_pi_Odistinct_I77_J, fact_165_pi_Odistinct_I51_J, tcon_Late__Semantics_Osubject___Agent_Opt__name_10, fact_39_Late__Semantics_OPar1B, fact_57_Late__Semantics1_OfreeRes_Oinject, fact_178_pi_Ofresh_I10_J, fact_61_subject_Orecs_I1_J, tcon_Agent_Oname___Agent_Opt__name_5, fact_242_residual_Orec__fresh, fact_118_pi_Odistinct_I35_J, fact_102_Late__Semantics_OClose1, fact_55_Tau, fact_194_pi_Odistinct_I27_J, fact_236_subject_Osupp_I2_J, fact_239_fs__name1, fact_41_freeRes_Ostrong__inducts, fact_254_pi_Orec__fin__supp, fact_244_residual_Orec__fin__supp, fact_162_pi_Oinject_I4_J, fact_31_residual_Ostrong__inducts, fact_22_pi_Ofresh_I8_J, fact_171_freeRes_Ocase_I2_J, fact_211_pi_Odistinct_I71_J, fact_30_residual_Ostrong__induct, fact_144_pi_Oinject_I3_J, fact_62_freeRes_Orecs_I1_J, fact_143_abs__fresh_I1_J, fact_0_cComm2_Ohyps_I9_J, fact_128_inputBoundOutputTrans, fact_78_resCasesF, fact_205_pi_Odistinct_I89_J, fact_83_pi_Odistinct_I45_J, tcon_Late__Semantics_Oresidual___Agent_Ofs__name_13, fact_155_Match, fact_75_subject_Oexhaust, fact_119_pi_Odistinct_I19_J, fact_112_pi_Odistinct_I21_J, fact_28_name__exists__fresh, fact_169_pi_Odistinct_I37_J, fact_133_simps_I3_J, fact_110_name__fresh, fact_67_Late__Semantics_Osubject_Oinject_I2_J, fact_93_substRes2, fact_195_pi_Odistinct_I41_J, fact_69_freeRes_Ofresh_I2_J, tcon_fun___Agent_Opt__name, fact_113_pi_Oinject_I1_J, fact_182_simps_I7_J, fact_35_fresh__fact1, fact_116_pi_Odistinct_I29_J, fact_86_subject_Ostrong__inducts, fact_45_mem__Collect__eq, fact_204_pi_Oinject_I9_J, fact_198_pi_Odistinct_I13_J, fact_43_freeRes_Oinducts, fact_8_cComm2_Ohyps_I4_J, fact_154_mismatchCases_H, fact_168_pi_Odistinct_I39_J, fact_180_simps_I10_J, fact_226_subs__def, fact_115_pi_Odistinct_I57_J, fact_63_transitions_OClose2, fact_218_pi_Ostrong__induct_H, tcon_Nominal_Onoption___Agent_Opt__name_7, fact_76_Late__Semantics1_Osubject_Odistinct_I1_J, fact_107_outputTauTrans, fact_131_outputIneqTrans, fact_11_Par1F, fact_42_freeRes_Ostrong__induct_H, tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_9, fact_29_tauBoundTrans, fact_34_fresh__fact2, fact_207_pi_Odistinct_I3_J, fact_129_inputIneqTrans, fact_251_pi_Osupp_I2_J, fact_64_transitions_OClose1, fact_47_Collect__cong, fact_74_subject_Orecs_I2_J, fact_188_Sum1, fact_163_pi_Oinject_I5_J, fact_147_pi_Ofresh_I5_J, fact_148_pi_Ofresh_I6_J, fact_170_abs__fun__eq1, fact_247_pi_Osupp_I7_J, fact_96_freshBoundDerivative_I1_J, fact_141_subst__name__def, fact_3__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_H_091x_058_058_061b_093_092_060close_062, fact_160_pi_Odistinct_I67_J, fact_196_nilCases_H, fact_59_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_223_bangPred_Osimps, fact_95_freshFreeDerivative_I1_J, fact_4_Free_Ohyps, fact_215_pi_Odistinct_I7_J, fact_13__092_060open_062x_A_092_060sharp_062_AR_092_060close_062, fact_161_pi_Odistinct_I61_J, fact_98_parCasesB_H, fact_173_freeRes_Ocase_I1_J, fact_139_pi_Oinject_I8_J, fact_7_cComm2_Ohyps_I7_J, fact_117_pi_Odistinct_I31_J, fact_230_supp__fresh__iff, fact_15_cPar1_Ohyps, fact_85_transitions_OResB, fact_231_fresh__def, fact_82_freshRes, fact_91_freshResidual, fact_99_transitions_OPar1B, fact_191_pi_Odistinct_I79_J, fact_103_resOutputTauTrans, fact_246_residual_Osupp_I1_J, fact_209_pi_Odistinct_I5_J, tcon_HOL_Obool___Agent_Ofs__name_4, fact_200_pi_Odistinct_I11_J, fact_184_pi_Odistinct_I59_J, fact_79_resCasesF_H, fact_108_outputCases, fact_240_residual_Orecs_I2_J, fact_149_matchCases, fact_214_pi_Odistinct_I9_J, fact_77_Late__Semantics_OResB, fact_172_subject_Ocase_I2_J, fact_228_exists__fresh_H, fact_72_subject_Ofresh_I1_J, fact_40_pi_Odistinct_I43_J, fact_104_resOutputInputTrans, fact_109_outputCases_H, fact_248_pi_Osupp_I8_J, fact_21_Late__Semantics_OfreeRes_Oinject, fact_53_Late__Semantics_OComm2, fact_227_abs__fresh_I2_J, fact_156_Mismatch, fact_186_sumCases, fact_25_simps_I2_J, fact_250_residual_Osupp_I2_J, fact_255_supports__fresh, fact_114_pi_Odistinct_I55_J, fact_181_pi_Ofresh_I1_J, fact_18_pi_Oinject_I7_J, fact_66_freeRes_Ofresh_I1_J, fact_132_residual_Ofresh_I1_J, fact_36_forget, fact_145_simps_I5_J, tcon_Agent_Opi___Agent_Opt__name_2, fact_206_pi_Odistinct_I87_J, fact_120_resTrans_I2_J, fact_203_pi_Oinject_I6_J, fact_221_aux2, fact_238_pi_Osupp_I10_J, fact_136_inputCases_H, tcon_Agent_Oname___Agent_Ofs__name_6, fact_190_pi_Odistinct_I47_J, fact_197_zeroTrans, fact_2_cComm2_Ohyps_I6_J, fact_26_pi_Oinject_I2_J, fact_135_simps_I4_J, fact_88_subject_Oinducts, fact_73_subject_Ofresh_I2_J, fact_152_mismatchCases, fact_217_bangCases, fact_189_Sum2, fact_219_resZeroTrans, fact_12_Par2F, fact_92_substRes3, fact_183_simps_I1_J, fact_224_aux1, fact_138_pi_Ofresh_I4_J, fact_23_substTrans, fact_50_transitions_OComm2, fact_44_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_49_tauOutputTrans, tcon_HOL_Obool___Agent_Opt__name_3, fact_222_bangPred_Ocases, fact_187_sumCases_H, fact_125_resInputFreeTrans, fact_253_pi_Osupp_I5_J, fact_123_outputBoundTrans, fact_6_cComm2_Ohyps_I3_J, fact_121_inputFreeTrans, fact_164_pi_Odistinct_I49_J, fact_80_ResF
% 232.46/171.38  % No. of inferences in proof: 544
% 232.46/171.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 170845 ms resp. 170226 ms w/o parsing
% 233.27/171.63  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 233.27/171.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------