TSTP Solution File: ITP148^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP148^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:23:23 EDT 2024

% Result   : Theorem 69.24s 27.02s
% Output   : Refutation 70.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  460
% Syntax   : Number of formulae    :  814 ( 222 unt; 108 typ;   0 def)
%            Number of atoms       : 1718 ( 899 equ;   4 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 5310 (  42   ~;   4   |;  32   &;4484   @)
%                                         (   0 <=>; 748  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :   12 (  11 usr)
%            Number of type conns  : 1867 (1867   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  103 (  99 usr;  15 con; 0-3 aty)
%            Number of variables   : 2158 ( 138   ^1998   !;  22   ?;2158   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_real_real_type,type,
    set_real_real: $tType ).

thf(set_a_complex_type,type,
    set_a_complex: $tType ).

thf(set_complex_a_type,type,
    set_complex_a: $tType ).

thf(set_real_a_type,type,
    set_real_a: $tType ).

thf(set_complex_type,type,
    set_complex: $tType ).

thf(set_a_a_type,type,
    set_a_a: $tType ).

thf(set_real_type,type,
    set_real: $tType ).

thf(set_a_type,type,
    set_a: $tType ).

thf(complex_type,type,
    complex: $tType ).

thf(real_type,type,
    real: $tType ).

thf(a_type,type,
    a: $tType ).

thf(bij_be209634132omplex_type,type,
    bij_be209634132omplex: ( complex > complex ) > set_complex > set_complex > $o ).

thf(bij_betw_complex_a_type,type,
    bij_betw_complex_a: ( complex > a ) > set_complex > set_a > $o ).

thf(bij_be122140626omplex_type,type,
    bij_be122140626omplex: ( real > complex ) > set_real > set_complex > $o ).

thf(bij_betw_real_real_type,type,
    bij_betw_real_real: ( real > real ) > set_real > set_real > $o ).

thf(bij_betw_real_a_type,type,
    bij_betw_real_a: ( real > a ) > set_real > set_a > $o ).

thf(bij_betw_a_complex_type,type,
    bij_betw_a_complex: ( a > complex ) > set_a > set_complex > $o ).

thf(bij_betw_a_a_type,type,
    bij_betw_a_a: ( a > a ) > set_a > set_a > $o ).

thf(comp_c130555887omplex_type,type,
    comp_c130555887omplex: ( complex > complex ) > ( complex > complex ) > complex > complex ).

thf(comp_c595887981x_real_type,type,
    comp_c595887981x_real: ( complex > complex ) > ( real > complex ) > real > complex ).

thf(comp_c124850173plex_a_type,type,
    comp_c124850173plex_a: ( complex > complex ) > ( a > complex ) > a > complex ).

thf(comp_c819638635l_real_type,type,
    comp_c819638635l_real: ( complex > real ) > ( real > complex ) > real > real ).

thf(comp_complex_real_a_type,type,
    comp_complex_real_a: ( complex > real ) > ( a > complex ) > a > real ).

thf(comp_c274302683omplex_type,type,
    comp_c274302683omplex: ( complex > a ) > ( complex > complex ) > complex > a ).

thf(comp_complex_a_real_type,type,
    comp_complex_a_real: ( complex > a ) > ( real > complex ) > real > a ).

thf(comp_complex_a_a_type,type,
    comp_complex_a_a: ( complex > a ) > ( a > complex ) > a > a ).

thf(comp_r667767405omplex_type,type,
    comp_r667767405omplex: ( real > complex ) > ( complex > real ) > complex > complex ).

thf(comp_r701421291x_real_type,type,
    comp_r701421291x_real: ( real > complex ) > ( real > real ) > real > complex ).

thf(comp_real_complex_a_type,type,
    comp_real_complex_a: ( real > complex ) > ( a > real ) > a > complex ).

thf(comp_r422820971omplex_type,type,
    comp_r422820971omplex: ( real > real ) > ( complex > real ) > complex > real ).

thf(comp_real_real_real_type,type,
    comp_real_real_real: ( real > real ) > ( real > real ) > real > real ).

thf(comp_real_real_a_type,type,
    comp_real_real_a: ( real > real ) > ( a > real ) > a > real ).

thf(comp_real_a_complex_type,type,
    comp_real_a_complex: ( real > a ) > ( complex > real ) > complex > a ).

thf(comp_real_a_real_type,type,
    comp_real_a_real: ( real > a ) > ( real > real ) > real > a ).

thf(comp_real_a_a_type,type,
    comp_real_a_a: ( real > a ) > ( a > real ) > a > a ).

thf(comp_a1063143865omplex_type,type,
    comp_a1063143865omplex: ( a > complex ) > ( complex > a ) > complex > complex ).

thf(comp_a_complex_real_type,type,
    comp_a_complex_real: ( a > complex ) > ( real > a ) > real > complex ).

thf(comp_a_complex_a_type,type,
    comp_a_complex_a: ( a > complex ) > ( a > a ) > a > complex ).

thf(comp_a_real_complex_type,type,
    comp_a_real_complex: ( a > real ) > ( complex > a ) > complex > real ).

thf(comp_a_real_real_type,type,
    comp_a_real_real: ( a > real ) > ( real > a ) > real > real ).

thf(comp_a_real_a_type,type,
    comp_a_real_a: ( a > real ) > ( a > a ) > a > real ).

thf(comp_a_a_complex_type,type,
    comp_a_a_complex: ( a > a ) > ( complex > a ) > complex > a ).

thf(comp_a_a_real_type,type,
    comp_a_a_real: ( a > a ) > ( real > a ) > real > a ).

thf(comp_a_a_a_type,type,
    comp_a_a_a: ( a > a ) > ( a > a ) > a > a ).

thf(id_complex_a_type,type,
    id_complex_a: ( complex > a ) > complex > a ).

thf(id_real_a_type,type,
    id_real_a: ( real > a ) > real > a ).

thf(id_a_a_type,type,
    id_a_a: ( a > a ) > a > a ).

thf(id_complex_type,type,
    id_complex: complex > complex ).

thf(id_real_type,type,
    id_real: real > real ).

thf(id_a_type,type,
    id_a: a > a ).

thf(inj_on893405649omplex_type,type,
    inj_on893405649omplex: ( ( complex > a ) > complex > complex ) > set_complex_a > $o ).

thf(inj_on1576005937plex_a_type,type,
    inj_on1576005937plex_a: ( ( complex > a ) > complex > a ) > set_complex_a > $o ).

thf(inj_on958237983real_a_type,type,
    inj_on958237983real_a: ( ( real > real ) > real > a ) > set_real_real > $o ).

thf(inj_on319905617omplex_type,type,
    inj_on319905617omplex: ( ( real > a ) > real > complex ) > set_real_a > $o ).

thf(inj_on_real_a_real_a_type,type,
    inj_on_real_a_real_a: ( ( real > a ) > real > a ) > set_real_a > $o ).

thf(inj_on_a_complex_a_a_type,type,
    inj_on_a_complex_a_a: ( ( a > complex ) > a > a ) > set_a_complex > $o ).

thf(inj_on_a_a_a_complex_type,type,
    inj_on_a_a_a_complex: ( ( a > a ) > a > complex ) > set_a_a > $o ).

thf(inj_on_a_a_a_a_type,type,
    inj_on_a_a_a_a: ( ( a > a ) > a > a ) > set_a_a > $o ).

thf(inj_on94911183omplex_type,type,
    inj_on94911183omplex: ( complex > complex ) > set_complex > $o ).

thf(inj_on_complex_a_type,type,
    inj_on_complex_a: ( complex > a ) > set_complex > $o ).

thf(inj_on_real_complex_type,type,
    inj_on_real_complex: ( real > complex ) > set_real > $o ).

thf(inj_on_real_real_type,type,
    inj_on_real_real: ( real > real ) > set_real > $o ).

thf(inj_on_real_a_type,type,
    inj_on_real_a: ( real > a ) > set_real > $o ).

thf(inj_on_a_complex_type,type,
    inj_on_a_complex: ( a > complex ) > set_a > $o ).

thf(inj_on_a_a_type,type,
    inj_on_a_a: ( a > a ) > set_a > $o ).

thf(zero_zero_complex_type,type,
    zero_zero_complex: complex ).

thf(zero_zero_a_type,type,
    zero_zero_a: a ).

thf(top_top_complex_o_type,type,
    top_top_complex_o: complex > $o ).

thf(top_top_a_o_type,type,
    top_top_a_o: a > $o ).

thf(top_to525076535plex_a_type,type,
    top_to525076535plex_a: set_complex_a ).

thf(top_to1446257885l_real_type,type,
    top_to1446257885l_real: set_real_real ).

thf(top_top_set_real_a_type,type,
    top_top_set_real_a: set_real_a ).

thf(top_to2109114701omplex_type,type,
    top_to2109114701omplex: set_a_complex ).

thf(top_top_set_a_a_type,type,
    top_top_set_a_a: set_a_a ).

thf(top_top_set_complex_type,type,
    top_top_set_complex: set_complex ).

thf(top_top_set_real_type,type,
    top_top_set_real: set_real ).

thf(top_top_set_a_type,type,
    top_top_set_a: set_a ).

thf(path_arc_complex_type,type,
    path_arc_complex: ( real > complex ) > $o ).

thf(path_arc_real_type,type,
    path_arc_real: ( real > real ) > $o ).

thf(path_arc_a_type,type,
    path_arc_a: ( real > a ) > $o ).

thf(path_path_complex_type,type,
    path_path_complex: ( real > complex ) > $o ).

thf(path_path_real_type,type,
    path_path_real: ( real > real ) > $o ).

thf(path_path_a_type,type,
    path_path_a: ( real > a ) > $o ).

thf(path_p769714271omplex_type,type,
    path_p769714271omplex: ( real > complex ) > complex ).

thf(path_pathfinish_a_type,type,
    path_pathfinish_a: ( real > a ) > a ).

thf(path_p797330068omplex_type,type,
    path_p797330068omplex: ( real > complex ) > complex ).

thf(path_pathstart_a_type,type,
    path_pathstart_a: ( real > a ) > a ).

thf(path_rectpath_type,type,
    path_rectpath: complex > complex > real > complex ).

thf(path_s36253918omplex_type,type,
    path_s36253918omplex: ( real > complex ) > $o ).

thf(path_s1005760220h_real_type,type,
    path_s1005760220h_real: ( real > real ) > $o ).

thf(path_simple_path_a_type,type,
    path_simple_path_a: ( real > a ) > $o ).

thf(poinca1910941596x_of_a_type,type,
    poinca1910941596x_of_a: a > complex ).

thf(poinca837721858l_of_a_type,type,
    poinca837721858l_of_a: complex > a ).

thf(real_V762982918plex_a_type,type,
    real_V762982918plex_a: ( complex > a ) > $o ).

thf(real_V912435428omplex_type,type,
    real_V912435428omplex: ( a > complex ) > $o ).

thf(real_V451440129omplex_type,type,
    real_V451440129omplex: ( a > complex ) > $o ).

thf(real_V670066493omplex_type,type,
    real_V670066493omplex: ( complex > complex ) > $o ).

thf(real_V1327653935plex_a_type,type,
    real_V1327653935plex_a: ( complex > a ) > $o ).

thf(real_V1948715323omplex_type,type,
    real_V1948715323omplex: ( real > complex ) > $o ).

thf(real_V1354572473l_real_type,type,
    real_V1354572473l_real: ( real > real ) > $o ).

thf(real_V779700657real_a_type,type,
    real_V779700657real_a: ( real > a ) > $o ).

thf(real_V1477106445omplex_type,type,
    real_V1477106445omplex: ( a > complex ) > $o ).

thf(real_V202220639ar_a_a_type,type,
    real_V202220639ar_a_a: ( a > a ) > $o ).

thf(collect_complex_type,type,
    collect_complex: ( complex > $o ) > set_complex ).

thf(collect_a_type,type,
    collect_a: ( a > $o ) > set_a ).

thf(member_complex_type,type,
    member_complex: complex > set_complex > $o ).

thf(member_a_type,type,
    member_a: a > set_a > $o ).

thf(c_type,type,
    c: real > a ).

thf(208,axiom,
    ! [A: complex > complex,B: real > complex] :
      ( ( real_V670066493omplex @ A )
     => ( ( inj_on94911183omplex @ A @ top_top_set_complex )
       => ( ( path_s36253918omplex @ ( comp_c595887981x_real @ A @ B ) )
          = ( path_s36253918omplex @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_simple__path__linear__image__eq) ).

thf(1036,plain,
    ! [A: complex > complex,B: real > complex] :
      ( ( real_V670066493omplex @ A )
     => ( ( inj_on94911183omplex @ A @ top_top_set_complex )
       => ( ( path_s36253918omplex @ ( comp_c595887981x_real @ A @ B ) )
          = ( path_s36253918omplex @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(300,axiom,
    ! [A: complex,B: complex] :
      ( ( path_p769714271omplex @ ( path_rectpath @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_pathfinish__rectpath) ).

thf(1337,plain,
    ! [A: complex,B: complex] :
      ( ( path_p769714271omplex @ ( path_rectpath @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(253,axiom,
    ! [A: real > real,B: a > real,C: a,D: complex > real,E: a > complex,F: real > a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_real_a_a @ ( comp_real_a_real @ F @ A ) @ B @ C )
        = ( comp_complex_a_a @ ( comp_real_a_complex @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_type__copy__map__cong0) ).

thf(1190,plain,
    ! [A: real > real,B: a > real,C: a,D: complex > real,E: a > complex,F: real > a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_real_a_a @ ( comp_real_a_real @ F @ A ) @ B @ C )
        = ( comp_complex_a_a @ ( comp_real_a_complex @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(151,axiom,
    ( top_top_set_complex
    = ( collect_complex @ top_top_complex_o ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_top__set__def) ).

thf(846,plain,
    ( top_top_set_complex
    = ( collect_complex @ top_top_complex_o ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(84,axiom,
    ! [A: complex > a,B: set_complex,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
        = ( bij_be209634132omplex @ ( comp_a1063143865omplex @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_bij__betw__comp__iff) ).

thf(628,plain,
    ! [A: complex > a,B: set_complex,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
        = ( bij_be209634132omplex @ ( comp_a1063143865omplex @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(231,axiom,
    ( comp_a_complex_a
    = ( ^ [A: a > complex,B: a > a,C: a] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_comp__def) ).

thf(1110,plain,
    ( comp_a_complex_a
    = ( ^ [A: a > complex,B: a > a,C: a] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(40,axiom,
    ! [A: a > complex,B: complex > a,C: complex > complex] :
      ( ( comp_a1063143865omplex @ A @ ( comp_c274302683omplex @ B @ C ) )
      = ( comp_c130555887omplex @ ( comp_a1063143865omplex @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_fun_Omap__comp) ).

thf(481,plain,
    ! [A: a > complex,B: complex > a,C: complex > complex] :
      ( ( comp_a1063143865omplex @ A @ ( comp_c274302683omplex @ B @ C ) )
      = ( comp_c130555887omplex @ ( comp_a1063143865omplex @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(100,axiom,
    ! [A: a > a,B: set_a,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_a_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
        = ( bij_betw_a_a @ ( comp_a_a_a @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_bij__betw__comp__iff) ).

thf(683,plain,
    ! [A: a > a,B: set_a,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_a_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
        = ( bij_betw_a_a @ ( comp_a_a_a @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(218,axiom,
    ! [A: a > complex,B: complex > a,C: a > complex] :
      ( ( comp_c124850173plex_a @ ( comp_a1063143865omplex @ A @ B ) @ C )
      = ( comp_a_complex_a @ A @ ( comp_complex_a_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_comp__assoc) ).

thf(1068,plain,
    ! [A: a > complex,B: complex > a,C: a > complex] :
      ( ( comp_c124850173plex_a @ ( comp_a1063143865omplex @ A @ B ) @ C )
      = ( comp_a_complex_a @ A @ ( comp_complex_a_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(330,axiom,
    ! [A: complex > complex,B: real > complex] :
      ( ( path_p769714271omplex @ ( comp_c595887981x_real @ A @ B ) )
      = ( A @ ( path_p769714271omplex @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_pathfinish__compose) ).

thf(1443,plain,
    ! [A: complex > complex,B: real > complex] :
      ( ( path_p769714271omplex @ ( comp_c595887981x_real @ A @ B ) )
      = ( A @ ( path_p769714271omplex @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(196,axiom,
    ! [A: a > complex,B: a > a,C: a > complex,D: a > a] :
      ( ( ( comp_a_complex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ! [E: a] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_comp__eq__elim) ).

thf(994,plain,
    ! [A: a > complex,B: a > a,C: a > complex,D: a > a] :
      ( ( ( comp_a_complex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ! [E: a] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(323,axiom,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
       => ( ( path_arc_complex @ ( comp_a_complex_real @ A @ B ) )
          = ( path_arc_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_arc__linear__image__eq) ).

thf(1422,plain,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
       => ( ( path_arc_complex @ ( comp_a_complex_real @ A @ B ) )
          = ( path_arc_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(11,axiom,
    ( comp_a_a_a
    = ( ^ [A: a > a,B: a > a,C: a] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comp__def) ).

thf(379,plain,
    ( comp_a_a_a
    = ( ^ [A: a > a,B: a > a,C: a] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(80,axiom,
    ! [A: a > a,B: complex > a,C: complex > a,D: complex] :
      ( ( ( comp_a_a_complex @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comp__eq__dest__lhs) ).

thf(614,plain,
    ! [A: a > a,B: complex > a,C: complex > a,D: complex] :
      ( ( ( comp_a_a_complex @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(249,axiom,
    ! [A: real > a,B: real > real,C: a > a,D: real > a,E: real] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comp__eq__dest) ).

thf(1173,plain,
    ! [A: real > a,B: real > real,C: a > a,D: real > a,E: real] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(54,axiom,
    ! [A: a > a,B: complex > a,C: a > a,D: complex > a,E: complex] :
      ( ( ( comp_a_a_complex @ A @ B )
        = ( comp_a_a_complex @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_comp__eq__dest) ).

thf(523,plain,
    ! [A: a > a,B: complex > a,C: a > a,D: complex > a,E: complex] :
      ( ( ( comp_a_a_complex @ A @ B )
        = ( comp_a_a_complex @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(244,axiom,
    ! [A: complex > a] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( inj_on_a_complex_a_a @ ( comp_complex_a_a @ A ) @ top_to2109114701omplex ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_fun_Oinj__map) ).

thf(1158,plain,
    ! [A: complex > a] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( inj_on_a_complex_a_a @ ( comp_complex_a_a @ A ) @ top_to2109114701omplex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(70,axiom,
    ! [A: a > a,B: complex > a,C: complex > a,D: complex] :
      ( ( ( comp_a_a_complex @ A @ B )
        = ( comp_a_a_complex @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_comp__eq__id__dest) ).

thf(582,plain,
    ! [A: a > a,B: complex > a,C: complex > a,D: complex] :
      ( ( ( comp_a_a_complex @ A @ B )
        = ( comp_a_a_complex @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(160,axiom,
    ! [A: a > complex,B: set_a,C: set_complex,D: complex > complex,E: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( bij_be209634132omplex @ D @ C @ E )
        = ( bij_betw_a_complex @ ( comp_c124850173plex_a @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_bij__betw__comp__iff) ).

thf(873,plain,
    ! [A: a > complex,B: set_a,C: set_complex,D: complex > complex,E: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( bij_be209634132omplex @ D @ C @ E )
        = ( bij_betw_a_complex @ ( comp_c124850173plex_a @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(259,axiom,
    ! [A: a > complex,B: complex > complex] :
      ( ( real_V1477106445omplex @ A )
     => ( ( real_V670066493omplex @ B )
       => ( real_V1477106445omplex @ ( comp_c124850173plex_a @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_linear__compose) ).

thf(1205,plain,
    ! [A: a > complex,B: complex > complex] :
      ( ( real_V1477106445omplex @ A )
     => ( ( real_V670066493omplex @ B )
       => ( real_V1477106445omplex @ ( comp_c124850173plex_a @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(324,axiom,
    ! [A: a > complex,B: real > a] :
      ( ( path_p797330068omplex @ ( comp_a_complex_real @ A @ B ) )
      = ( A @ ( path_pathstart_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_pathstart__compose) ).

thf(1426,plain,
    ! [A: a > complex,B: real > a] :
      ( ( path_p797330068omplex @ ( comp_a_complex_real @ A @ B ) )
      = ( A @ ( path_pathstart_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(14,axiom,
    ! [A: a > a,B: a > a,C: a > a,D: a] :
      ( ( ( comp_a_a_a @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comp__eq__dest__lhs) ).

thf(385,plain,
    ! [A: a > a,B: a > a,C: a > a,D: a] :
      ( ( ( comp_a_a_a @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(239,axiom,
    ! [A: real > a,B: real > real,C: real > a,D: real > real,E: real] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comp__eq__dest) ).

thf(1137,plain,
    ! [A: real > a,B: real > real,C: real > a,D: real > real,E: real] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(136,axiom,
    real_V1327653935plex_a @ poinca837721858l_of_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_real__of__linear) ).

thf(797,plain,
    real_V1327653935plex_a @ poinca837721858l_of_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(173,axiom,
    ! [A: real > real,B: complex > real,C: a > real,D: complex > a,E: real > a,F: a > a] :
      ( ( ( comp_r422820971omplex @ A @ B )
        = ( comp_a_real_complex @ C @ D ) )
     => ( ( ( comp_real_a_a @ E @ C )
          = F )
       => ( ( comp_real_a_complex @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_a_a_complex @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_rewriteR__comp__comp2) ).

thf(913,plain,
    ! [A: real > real,B: complex > real,C: a > real,D: complex > a,E: real > a,F: a > a] :
      ( ( ( comp_r422820971omplex @ A @ B )
        = ( comp_a_real_complex @ C @ D ) )
     => ( ( ( comp_real_a_a @ E @ C )
          = F )
       => ( ( comp_real_a_complex @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_a_a_complex @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(57,axiom,
    ! [A: complex > complex,B: complex] :
      ( ( bij_be209634132omplex @ A @ top_top_set_complex @ top_top_set_complex )
     => ~ ! [C: complex] :
            ( ( B
              = ( A @ C ) )
           => ~ ! [D: complex] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_bij__pointE) ).

thf(538,plain,
    ! [A: complex > complex,B: complex] :
      ( ( bij_be209634132omplex @ A @ top_top_set_complex @ top_top_set_complex )
     => ~ ! [C: complex] :
            ( ( B
              = ( A @ C ) )
           => ~ ! [D: complex] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(335,axiom,
    ! [A: a > complex,B: complex > a,C: complex,D: a > complex,E: real > a,F: real] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a1063143865omplex @ A @ B @ C )
        = ( comp_a_complex_real @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_comp__cong) ).

thf(1458,plain,
    ! [A: a > complex,B: complex > a,C: complex,D: a > complex,E: real > a,F: real] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a1063143865omplex @ A @ B @ C )
        = ( comp_a_complex_real @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(96,axiom,
    ! [A: complex > a,B: complex > complex,C: a > a,D: complex > a,E: a > complex,F: a > a] :
      ( ( ( comp_c274302683omplex @ A @ B )
        = ( comp_a_a_complex @ C @ D ) )
     => ( ( ( comp_complex_a_a @ D @ E )
          = F )
       => ( ( comp_complex_a_a @ A @ ( comp_c124850173plex_a @ B @ E ) )
          = ( comp_a_a_a @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_rewriteL__comp__comp2) ).

thf(670,plain,
    ! [A: complex > a,B: complex > complex,C: a > a,D: complex > a,E: a > complex,F: a > a] :
      ( ( ( comp_c274302683omplex @ A @ B )
        = ( comp_a_a_complex @ C @ D ) )
     => ( ( ( comp_complex_a_a @ D @ E )
          = F )
       => ( ( comp_complex_a_a @ A @ ( comp_c124850173plex_a @ B @ E ) )
          = ( comp_a_a_a @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(264,axiom,
    ! [A: real > real,B: real > a] :
      ( ( real_V1354572473l_real @ A )
     => ( ( real_V779700657real_a @ B )
       => ( real_V779700657real_a @ ( comp_real_a_real @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_linear__compose) ).

thf(1222,plain,
    ! [A: real > real,B: real > a] :
      ( ( real_V1354572473l_real @ A )
     => ( ( real_V779700657real_a @ B )
       => ( real_V779700657real_a @ ( comp_real_a_real @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(176,axiom,
    ! [A: real > a] :
      ( ( path_simple_path_a @ A )
     => ( ( ( path_pathfinish_a @ A )
         != ( path_pathstart_a @ A ) )
       => ( path_arc_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_simple__path__imp__arc) ).

thf(930,plain,
    ! [A: real > a] :
      ( ( path_simple_path_a @ A )
     => ( ( ( path_pathfinish_a @ A )
         != ( path_pathstart_a @ A ) )
       => ( path_arc_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(225,axiom,
    ! [A: a > real,B: complex > a,C: real > real,D: complex > real,E: real > a,F: real > a] :
      ( ( ( comp_a_real_complex @ A @ B )
        = ( comp_r422820971omplex @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_a_a_complex @ ( comp_real_a_a @ E @ A ) @ B )
          = ( comp_real_a_complex @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_rewriteR__comp__comp2) ).

thf(1095,plain,
    ! [A: a > real,B: complex > a,C: real > real,D: complex > real,E: real > a,F: real > a] :
      ( ( ( comp_a_real_complex @ A @ B )
        = ( comp_r422820971omplex @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_a_a_complex @ ( comp_real_a_a @ E @ A ) @ B )
          = ( comp_real_a_complex @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(255,axiom,
    ! [A: a > complex,B: set_a,C: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( inj_on_a_complex @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_bij__betw__imp__inj__on) ).

thf(1196,plain,
    ! [A: a > complex,B: set_a,C: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( inj_on_a_complex @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(168,axiom,
    ! [A: complex > complex,B: a > complex,C: a > a] :
      ( ( comp_c124850173plex_a @ A @ ( comp_a_complex_a @ B @ C ) )
      = ( comp_a_complex_a @ ( comp_c124850173plex_a @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_fun_Omap__comp) ).

thf(898,plain,
    ! [A: complex > complex,B: a > complex,C: a > a] :
      ( ( comp_c124850173plex_a @ A @ ( comp_a_complex_a @ B @ C ) )
      = ( comp_a_complex_a @ ( comp_c124850173plex_a @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(150,axiom,
    ! [A: a > real,B: real > a,C: real > real,D: real > real,E: real > a,F: real > a] :
      ( ( ( comp_a_real_real @ A @ B )
        = ( comp_real_real_real @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_a_a_real @ ( comp_real_a_a @ E @ A ) @ B )
          = ( comp_real_a_real @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_rewriteR__comp__comp2) ).

thf(841,plain,
    ! [A: a > real,B: real > a,C: real > real,D: real > real,E: real > a,F: real > a] :
      ( ( ( comp_a_real_real @ A @ B )
        = ( comp_real_real_real @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_a_a_real @ ( comp_real_a_a @ E @ A ) @ B )
          = ( comp_real_a_real @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(340,axiom,
    ! [A: real > complex] :
      ( ( ( path_p769714271omplex @ A )
       != ( path_p797330068omplex @ A ) )
     => ( ( path_s36253918omplex @ A )
        = ( path_arc_complex @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_simple__path__eq__arc) ).

thf(1475,plain,
    ! [A: real > complex] :
      ( ( ( path_p769714271omplex @ A )
       != ( path_p797330068omplex @ A ) )
     => ( ( path_s36253918omplex @ A )
        = ( path_arc_complex @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(28,axiom,
    ! [A: set_complex,B: set_complex] :
      ( ( bij_be209634132omplex @ id_complex @ A @ B )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_bij__betw__id__iff) ).

thf(436,plain,
    ! [A: set_complex,B: set_complex] :
      ( ( bij_be209634132omplex @ id_complex @ A @ B )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(274,axiom,
    ! [A: real > a] :
      ( ( comp_real_a_real @ A @ id_real )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_comp__id) ).

thf(1254,plain,
    ! [A: real > a] :
      ( ( comp_real_a_real @ A @ id_real )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(112,axiom,
    ! [A: a > complex,B: a > a,C: a > complex,D: a] :
      ( ( ( comp_a_complex_a @ A @ B )
        = ( comp_c124850173plex_a @ id_complex @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_comp__eq__id__dest) ).

thf(719,plain,
    ! [A: a > complex,B: a > a,C: a > complex,D: a] :
      ( ( ( comp_a_complex_a @ A @ B )
        = ( comp_c124850173plex_a @ id_complex @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(132,axiom,
    ! [A: a > complex] :
      ( ( real_V912435428omplex @ A )
     => ( real_V1477106445omplex @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_bounded__linear_Olinear) ).

thf(785,plain,
    ! [A: a > complex] :
      ( ( real_V912435428omplex @ A )
     => ( real_V1477106445omplex @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(9,axiom,
    ! [A: a > a,B: a > a,C: set_a] :
      ( ( inj_on_a_a @ ( comp_a_a_a @ A @ B ) @ C )
     => ( inj_on_a_a @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_inj__on__imageI2) ).

thf(372,plain,
    ! [A: a > a,B: a > a,C: set_a] :
      ( ( inj_on_a_a @ ( comp_a_a_a @ A @ B ) @ C )
     => ( inj_on_a_a @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(48,axiom,
    ! [A: a > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( inj_on_a_a @ A @ top_top_set_a )
       => ? [B: a > a] :
            ( ( real_V202220639ar_a_a @ B )
            & ( ( comp_a_a_a @ B @ A )
              = id_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_linear__injective__left__inverse) ).

thf(504,plain,
    ! [A: a > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( inj_on_a_a @ A @ top_top_set_a )
       => ? [B: a > a] :
            ( ( real_V202220639ar_a_a @ B )
            & ( ( comp_a_a_a @ B @ A )
              = id_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(277,axiom,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( inj_on_a_a @ A @ top_top_set_a )
       => ( ( path_path_a @ ( comp_a_a_real @ A @ B ) )
          = ( path_path_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_path__linear__image__eq) ).

thf(1264,plain,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( inj_on_a_a @ A @ top_top_set_a )
       => ( ( path_path_a @ ( comp_a_a_real @ A @ B ) )
          = ( path_path_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(334,axiom,
    ! [A: a > complex,B: real > a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( inj_on_real_a @ B @ top_top_set_real )
       => ( inj_on_real_complex @ ( comp_a_complex_real @ A @ B ) @ top_top_set_real ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_inj__compose) ).

thf(1455,plain,
    ! [A: a > complex,B: real > a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( inj_on_real_a @ B @ top_top_set_real )
       => ( inj_on_real_complex @ ( comp_a_complex_real @ A @ B ) @ top_top_set_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(296,axiom,
    ! [A: complex > complex,B: a > complex,C: real > a] :
      ( ( comp_c595887981x_real @ A @ ( comp_a_complex_real @ B @ C ) )
      = ( comp_a_complex_real @ ( comp_c124850173plex_a @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_fun_Omap__comp) ).

thf(1323,plain,
    ! [A: complex > complex,B: a > complex,C: real > a] :
      ( ( comp_c595887981x_real @ A @ ( comp_a_complex_real @ B @ C ) )
      = ( comp_a_complex_real @ ( comp_c124850173plex_a @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(81,axiom,
    ! [A: set_a] :
      ( ! [B: a] : ( member_a @ B @ A )
     => ( top_top_set_a = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_UNIV__eq__I) ).

thf(619,plain,
    ! [A: set_a] :
      ( ! [B: a] : ( member_a @ B @ A )
     => ( top_top_set_a = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(223,axiom,
    ! [A: a > complex] :
      ( ( comp_a_complex_a @ A @ id_a )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_comp__id) ).

thf(1087,plain,
    ! [A: a > complex] :
      ( ( comp_a_complex_a @ A @ id_a )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(342,axiom,
    ! [A: real > a,B: a > real,C: complex > a,D: a > complex,E: real > a,F: real > complex] :
      ( ( ( comp_real_a_a @ A @ B )
        = ( comp_complex_a_a @ C @ D ) )
     => ( ( ( comp_a_complex_real @ D @ E )
          = F )
       => ( ( comp_real_a_real @ A @ ( comp_a_real_real @ B @ E ) )
          = ( comp_complex_a_real @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_rewriteL__comp__comp2) ).

thf(1479,plain,
    ! [A: real > a,B: a > real,C: complex > a,D: a > complex,E: real > a,F: real > complex] :
      ( ( ( comp_real_a_a @ A @ B )
        = ( comp_complex_a_a @ C @ D ) )
     => ( ( ( comp_a_complex_real @ D @ E )
          = F )
       => ( ( comp_real_a_real @ A @ ( comp_a_real_real @ B @ E ) )
          = ( comp_complex_a_real @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(303,axiom,
    ! [A: a > complex,B: real > a,C: real > complex,D: a > real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = C )
     => ( ( comp_a_complex_a @ A @ ( comp_real_a_a @ B @ D ) )
        = ( comp_real_complex_a @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_rewriteL__comp__comp) ).

thf(1347,plain,
    ! [A: a > complex,B: real > a,C: real > complex,D: a > real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = C )
     => ( ( comp_a_complex_a @ A @ ( comp_real_a_a @ B @ D ) )
        = ( comp_real_complex_a @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(202,axiom,
    ! [A: complex > a,B: real > complex,C: a > a,D: real > a,E: a > real,F: a > a] :
      ( ( ( comp_complex_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ( ( ( comp_real_a_a @ D @ E )
          = F )
       => ( ( comp_complex_a_a @ A @ ( comp_real_complex_a @ B @ E ) )
          = ( comp_a_a_a @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_rewriteL__comp__comp2) ).

thf(1013,plain,
    ! [A: complex > a,B: real > complex,C: a > a,D: real > a,E: a > real,F: a > a] :
      ( ( ( comp_complex_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ( ( ( comp_real_a_a @ D @ E )
          = F )
       => ( ( comp_complex_a_a @ A @ ( comp_real_complex_a @ B @ E ) )
          = ( comp_a_a_a @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(163,axiom,
    inj_on_complex_a @ poinca837721858l_of_a @ top_top_set_complex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_real__of__inj) ).

thf(881,plain,
    inj_on_complex_a @ poinca837721858l_of_a @ top_top_set_complex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(226,axiom,
    bij_betw_complex_a @ poinca837721858l_of_a @ top_top_set_complex @ top_top_set_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_real__of__bij) ).

thf(1100,plain,
    bij_betw_complex_a @ poinca837721858l_of_a @ top_top_set_complex @ top_top_set_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(289,axiom,
    ! [A: a > complex,B: real > a,C: real > complex,D: real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_comp__eq__dest__lhs) ).

thf(1302,plain,
    ! [A: a > complex,B: real > a,C: real > complex,D: real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(134,axiom,
    ! [A: real > a] :
      ( ( ( path_pathfinish_a @ A )
       != ( path_pathstart_a @ A ) )
     => ( ( path_simple_path_a @ A )
        = ( path_arc_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_simple__path__eq__arc) ).

thf(789,plain,
    ! [A: real > a] :
      ( ( ( path_pathfinish_a @ A )
       != ( path_pathstart_a @ A ) )
     => ( ( path_simple_path_a @ A )
        = ( path_arc_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(332,axiom,
    ( comp_a_complex_real
    = ( ^ [A: a > complex,B: real > a,C: real] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_comp__def) ).

thf(1450,plain,
    ( comp_a_complex_real
    = ( ^ [A: a > complex,B: real > a,C: real] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(73,axiom,
    ! [A: set_complex,B: a > complex,C: complex > a] :
      ( ! [D: complex] :
          ( ( member_complex @ D @ A )
         => ( ( B @ ( C @ D ) )
            = D ) )
     => ( inj_on_complex_a @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_inj__on__inverseI) ).

thf(591,plain,
    ! [A: set_complex,B: a > complex,C: complex > a] :
      ( ! [D: complex] :
          ( ( member_complex @ D @ A )
         => ( ( B @ ( C @ D ) )
            = D ) )
     => ( inj_on_complex_a @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(209,axiom,
    ! [A: set_complex] : ( inj_on94911183omplex @ id_complex @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_inj__on__id) ).

thf(1040,plain,
    ! [A: set_complex] : ( inj_on94911183omplex @ id_complex @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(90,axiom,
    ! [A: set_a,B: a > complex] :
      ( ! [C: a,D: a] :
          ( ( member_a @ C @ A )
         => ( ( member_a @ D @ A )
           => ( ( ( B @ C )
                = ( B @ D ) )
             => ( C = D ) ) ) )
     => ( inj_on_a_complex @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_inj__onI) ).

thf(646,plain,
    ! [A: set_a,B: a > complex] :
      ( ! [C: a,D: a] :
          ( ( member_a @ C @ A )
         => ( ( member_a @ D @ A )
           => ( ( ( B @ C )
                = ( B @ D ) )
             => ( C = D ) ) ) )
     => ( inj_on_a_complex @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(188,axiom,
    ! [A: real > real,B: a > real,C: a,D: a > real,E: a > a,F: real > a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_real_a_a @ ( comp_real_a_real @ F @ A ) @ B @ C )
        = ( comp_a_a_a @ ( comp_real_a_a @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_type__copy__map__cong0) ).

thf(966,plain,
    ! [A: real > real,B: a > real,C: a,D: a > real,E: a > a,F: real > a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_real_a_a @ ( comp_real_a_real @ F @ A ) @ B @ C )
        = ( comp_a_a_a @ ( comp_real_a_a @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(309,axiom,
    ! [A: a > complex,B: real > a,C: real > complex,D: real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = ( comp_c595887981x_real @ id_complex @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_comp__eq__id__dest) ).

thf(1373,plain,
    ! [A: a > complex,B: real > a,C: real > complex,D: real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = ( comp_c595887981x_real @ id_complex @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(30,axiom,
    ! [A: complex > complex,B: complex > complex] :
      ( ( ( comp_c130555887omplex @ A @ B )
        = id_complex )
     => ( ( ( comp_c130555887omplex @ B @ A )
          = id_complex )
       => ( bij_be209634132omplex @ B @ top_top_set_complex @ top_top_set_complex ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_o__bij) ).

thf(443,plain,
    ! [A: complex > complex,B: complex > complex] :
      ( ( ( comp_c130555887omplex @ A @ B )
        = id_complex )
     => ( ( ( comp_c130555887omplex @ B @ A )
          = id_complex )
       => ( bij_be209634132omplex @ B @ top_top_set_complex @ top_top_set_complex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(204,axiom,
    ! [A: real > a,B: a > real,C: a > a,D: a > a,E: real > a,F: real > a] :
      ( ( ( comp_real_a_a @ A @ B )
        = ( comp_a_a_a @ C @ D ) )
     => ( ( ( comp_a_a_real @ D @ E )
          = F )
       => ( ( comp_real_a_real @ A @ ( comp_a_real_real @ B @ E ) )
          = ( comp_a_a_real @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_rewriteL__comp__comp2) ).

thf(1020,plain,
    ! [A: real > a,B: a > real,C: a > a,D: a > a,E: real > a,F: real > a] :
      ( ( ( comp_real_a_a @ A @ B )
        = ( comp_a_a_a @ C @ D ) )
     => ( ( ( comp_a_a_real @ D @ E )
          = F )
       => ( ( comp_real_a_real @ A @ ( comp_a_real_real @ B @ E ) )
          = ( comp_a_a_real @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(67,axiom,
    ! [A: set_a] : ( inj_on_a_a @ id_a @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_inj__on__id) ).

thf(574,plain,
    ! [A: set_a] : ( inj_on_a_a @ id_a @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(310,axiom,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( path_p797330068omplex @ ( comp_a_complex_real @ A @ B ) )
        = ( A @ ( path_pathstart_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_pathstart__linear__image__eq) ).

thf(1377,plain,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( path_p797330068omplex @ ( comp_a_complex_real @ A @ B ) )
        = ( A @ ( path_pathstart_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(161,axiom,
    ! [A: real > complex] :
      ( ( path_s36253918omplex @ A )
     => ( path_path_complex @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_simple__path__imp__path) ).

thf(877,plain,
    ! [A: real > complex] :
      ( ( path_s36253918omplex @ A )
     => ( path_path_complex @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(185,axiom,
    ! [A: complex > a,B: real > complex,C: real > a,D: a > a] :
      ( ( ( comp_complex_a_real @ A @ B )
        = C )
     => ( ( comp_complex_a_real @ ( comp_a_a_complex @ D @ A ) @ B )
        = ( comp_a_a_real @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_rewriteR__comp__comp) ).

thf(956,plain,
    ! [A: complex > a,B: real > complex,C: real > a,D: a > a] :
      ( ( ( comp_complex_a_real @ A @ B )
        = C )
     => ( ( comp_complex_a_real @ ( comp_a_a_complex @ D @ A ) @ B )
        = ( comp_a_a_real @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(220,axiom,
    ! [A: complex > real,B: a > complex,C: real > real,D: a > real,E: real > a,F: real > a] :
      ( ( ( comp_complex_real_a @ A @ B )
        = ( comp_real_real_a @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_complex_a_a @ ( comp_real_a_complex @ E @ A ) @ B )
          = ( comp_real_a_a @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_rewriteR__comp__comp2) ).

thf(1072,plain,
    ! [A: complex > real,B: a > complex,C: real > real,D: a > real,E: real > a,F: real > a] :
      ( ( ( comp_complex_real_a @ A @ B )
        = ( comp_real_real_a @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_complex_a_a @ ( comp_real_a_complex @ E @ A ) @ B )
          = ( comp_real_a_a @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(234,axiom,
    ! [A: real > a,B: real > real] :
      ( ( inj_on_real_a @ A @ top_top_set_real )
     => ( ( inj_on_real_real @ B @ top_top_set_real )
       => ( inj_on_real_a @ ( comp_real_a_real @ A @ B ) @ top_top_set_real ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_inj__compose) ).

thf(1119,plain,
    ! [A: real > a,B: real > real] :
      ( ( inj_on_real_a @ A @ top_top_set_real )
     => ( ( inj_on_real_real @ B @ top_top_set_real )
       => ( inj_on_real_a @ ( comp_real_a_real @ A @ B ) @ top_top_set_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(93,axiom,
    ! [A: complex > a,B: a > a] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( real_V202220639ar_a_a @ B )
       => ( real_V1327653935plex_a @ ( comp_a_a_complex @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_linear__compose) ).

thf(660,plain,
    ! [A: complex > a,B: a > a] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( real_V202220639ar_a_a @ B )
       => ( real_V1327653935plex_a @ ( comp_a_a_complex @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(194,axiom,
    ! [A: complex > a] :
      ( ( real_V762982918plex_a @ A )
     => ( real_V1327653935plex_a @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_bounded__linear_Olinear) ).

thf(988,plain,
    ! [A: complex > a] :
      ( ( real_V762982918plex_a @ A )
     => ( real_V1327653935plex_a @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(318,axiom,
    ! [A: complex,B: complex] :
      ( ( path_p797330068omplex @ ( path_rectpath @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_pathstart__rectpath) ).

thf(1405,plain,
    ! [A: complex,B: complex] :
      ( ( path_p797330068omplex @ ( path_rectpath @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(257,axiom,
    ( comp_a_a_real
    = ( ^ [A: a > a,B: real > a,C: real] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comp__def) ).

thf(1201,plain,
    ( comp_a_a_real
    = ( ^ [A: a > a,B: real > a,C: real] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(228,axiom,
    ( comp_a_a_real
    = ( ^ [A: a > a,B: real > a,C: real] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_comp__apply) ).

thf(1104,plain,
    ( comp_a_a_real
    = ( ^ [A: a > a,B: real > a,C: real] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(55,axiom,
    ! [A: set_complex,B: complex > a] :
      ( ! [C: complex,D: complex] :
          ( ( member_complex @ C @ A )
         => ( ( member_complex @ D @ A )
           => ( ( ( B @ C )
                = ( B @ D ) )
             => ( C = D ) ) ) )
     => ( inj_on_complex_a @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_inj__onI) ).

thf(527,plain,
    ! [A: set_complex,B: complex > a] :
      ( ! [C: complex,D: complex] :
          ( ( member_complex @ C @ A )
         => ( ( member_complex @ D @ A )
           => ( ( ( B @ C )
                = ( B @ D ) )
             => ( C = D ) ) ) )
     => ( inj_on_complex_a @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(248,axiom,
    ! [A: complex > a,B: complex > complex,C: complex,D: a > a,E: complex > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ F @ A ) @ B @ C )
        = ( comp_a1063143865omplex @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_type__copy__map__cong0) ).

thf(1169,plain,
    ! [A: complex > a,B: complex > complex,C: complex,D: a > a,E: complex > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ F @ A ) @ B @ C )
        = ( comp_a1063143865omplex @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(101,axiom,
    ! [A: a > a,B: a > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( ( inj_on_a_a @ B @ top_top_set_a )
       => ( inj_on_a_a @ ( comp_a_a_a @ A @ B ) @ top_top_set_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_inj__compose) ).

thf(687,plain,
    ! [A: a > a,B: a > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( ( inj_on_a_a @ B @ top_top_set_a )
       => ( inj_on_a_a @ ( comp_a_a_a @ A @ B ) @ top_top_set_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(98,axiom,
    ! [A: complex > complex,B: set_complex,C: set_complex,D: complex > a,E: set_a] :
      ( ( bij_be209634132omplex @ A @ B @ C )
     => ( ( bij_betw_complex_a @ D @ C @ E )
       => ( bij_betw_complex_a @ ( comp_c274302683omplex @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_bij__betw__trans) ).

thf(678,plain,
    ! [A: complex > complex,B: set_complex,C: set_complex,D: complex > a,E: set_a] :
      ( ( bij_be209634132omplex @ A @ B @ C )
     => ( ( bij_betw_complex_a @ D @ C @ E )
       => ( bij_betw_complex_a @ ( comp_c274302683omplex @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(328,axiom,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( path_pathfinish_a @ ( comp_complex_a_real @ A @ B ) )
        = ( A @ ( path_p769714271omplex @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_pathfinish__linear__image) ).

thf(1438,plain,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( path_pathfinish_a @ ( comp_complex_a_real @ A @ B ) )
        = ( A @ ( path_p769714271omplex @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(256,axiom,
    ( path_arc_a
    = ( ^ [A: real > a] :
          ( ( path_simple_path_a @ A )
          & ( ( path_pathfinish_a @ A )
           != ( path_pathstart_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_arc__simple__path) ).

thf(1199,plain,
    ( path_arc_a
    = ( ^ [A: real > a] :
          ( ( path_simple_path_a @ A )
          & ( ( path_pathfinish_a @ A )
           != ( path_pathstart_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(124,axiom,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
       => ( ( path_simple_path_a @ ( comp_complex_a_real @ A @ B ) )
          = ( path_s36253918omplex @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_simple__path__linear__image__eq) ).

thf(761,plain,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
       => ( ( path_simple_path_a @ ( comp_complex_a_real @ A @ B ) )
          = ( path_s36253918omplex @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(12,axiom,
    ! [A: a] : ( member_a @ A @ top_top_set_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_iso__tuple__UNIV__I) ).

thf(381,plain,
    ! [A: a] : ( member_a @ A @ top_top_set_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(7,axiom,
    ! [A: complex > a,B: a > complex,C: complex > a] :
      ( ( comp_a_a_complex @ ( comp_complex_a_a @ A @ B ) @ C )
      = ( comp_c274302683omplex @ A @ ( comp_a1063143865omplex @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_comp__assoc) ).

thf(366,plain,
    ! [A: complex > a,B: a > complex,C: complex > a] :
      ( ( comp_a_a_complex @ ( comp_complex_a_a @ A @ B ) @ C )
      = ( comp_c274302683omplex @ A @ ( comp_a1063143865omplex @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(292,axiom,
    ! [A: a > complex,B: real > a,C: real > real] :
      ( ( comp_a_complex_real @ A @ ( comp_real_a_real @ B @ C ) )
      = ( comp_r701421291x_real @ ( comp_a_complex_real @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_fun_Omap__comp) ).

thf(1311,plain,
    ! [A: a > complex,B: real > a,C: real > real] :
      ( ( comp_a_complex_real @ A @ ( comp_real_a_real @ B @ C ) )
      = ( comp_r701421291x_real @ ( comp_a_complex_real @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(111,axiom,
    ! [A: real > a,B: complex > real,C: complex > a,D: a > a] :
      ( ( ( comp_real_a_complex @ A @ B )
        = C )
     => ( ( comp_real_a_complex @ ( comp_a_a_real @ D @ A ) @ B )
        = ( comp_a_a_complex @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_rewriteR__comp__comp) ).

thf(714,plain,
    ! [A: real > a,B: complex > real,C: complex > a,D: a > a] :
      ( ( ( comp_real_a_complex @ A @ B )
        = C )
     => ( ( comp_real_a_complex @ ( comp_a_a_real @ D @ A ) @ B )
        = ( comp_a_a_complex @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(180,axiom,
    ! [A: a > complex,B: a > a,C: set_a] :
      ( ( inj_on_a_complex @ ( comp_a_complex_a @ A @ B ) @ C )
     => ( inj_on_a_a @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_inj__on__imageI2) ).

thf(942,plain,
    ! [A: a > complex,B: a > a,C: set_a] :
      ( ( inj_on_a_complex @ ( comp_a_complex_a @ A @ B ) @ C )
     => ( inj_on_a_a @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(29,axiom,
    ! [A: complex > a,B: set_complex,C: complex,D: complex] :
      ( ( inj_on_complex_a @ A @ B )
     => ( ( ( A @ C )
          = ( A @ D ) )
       => ( ( member_complex @ C @ B )
         => ( ( member_complex @ D @ B )
           => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_inj__onD) ).

thf(439,plain,
    ! [A: complex > a,B: set_complex,C: complex,D: complex] :
      ( ( inj_on_complex_a @ A @ B )
     => ( ( ( A @ C )
          = ( A @ D ) )
       => ( ( member_complex @ C @ B )
         => ( ( member_complex @ D @ B )
           => ( C = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(212,axiom,
    ! [A: complex > complex,B: a > complex,C: set_a] :
      ( ( inj_on_a_complex @ ( comp_c124850173plex_a @ A @ B ) @ C )
     => ( inj_on_a_complex @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_inj__on__imageI2) ).

thf(1047,plain,
    ! [A: complex > complex,B: a > complex,C: set_a] :
      ( ( inj_on_a_complex @ ( comp_c124850173plex_a @ A @ B ) @ C )
     => ( inj_on_a_complex @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(137,axiom,
    ! [A: real > a,B: real > real,C: a > a,D: real > a] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_comp__eq__elim) ).

thf(798,plain,
    ! [A: real > a,B: real > real,C: a > a,D: real > a] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(130,axiom,
    ! [A: real > real,B: set_real,C: set_real,D: real > a,E: set_a] :
      ( ( bij_betw_real_real @ A @ B @ C )
     => ( ( bij_betw_real_a @ D @ C @ E )
       => ( bij_betw_real_a @ ( comp_real_a_real @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_bij__betw__trans) ).

thf(778,plain,
    ! [A: real > real,B: set_real,C: set_real,D: real > a,E: set_a] :
      ( ( bij_betw_real_real @ A @ B @ C )
     => ( ( bij_betw_real_a @ D @ C @ E )
       => ( bij_betw_real_a @ ( comp_real_a_real @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(210,axiom,
    ! [A: complex > complex,B: a > complex] :
      ( ( inj_on94911183omplex @ A @ top_top_set_complex )
     => ( ( inj_on_a_complex @ B @ top_top_set_a )
       => ( inj_on_a_complex @ ( comp_c124850173plex_a @ A @ B ) @ top_top_set_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_inj__compose) ).

thf(1042,plain,
    ! [A: complex > complex,B: a > complex] :
      ( ( inj_on94911183omplex @ A @ top_top_set_complex )
     => ( ( inj_on_a_complex @ B @ top_top_set_a )
       => ( inj_on_a_complex @ ( comp_c124850173plex_a @ A @ B ) @ top_top_set_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(305,axiom,
    ! [A: a > complex,B: real > a,C: real > complex,D: real > real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = C )
     => ( ( comp_a_complex_real @ A @ ( comp_real_a_real @ B @ D ) )
        = ( comp_r701421291x_real @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_rewriteL__comp__comp) ).

thf(1355,plain,
    ! [A: a > complex,B: real > a,C: real > complex,D: real > real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = C )
     => ( ( comp_a_complex_real @ A @ ( comp_real_a_real @ B @ D ) )
        = ( comp_r701421291x_real @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(157,axiom,
    ! [A: a > a,B: real > a] :
      ( ( path_pathfinish_a @ ( comp_a_a_real @ A @ B ) )
      = ( A @ ( path_pathfinish_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_pathfinish__compose) ).

thf(862,plain,
    ! [A: a > a,B: real > a] :
      ( ( path_pathfinish_a @ ( comp_a_a_real @ A @ B ) )
      = ( A @ ( path_pathfinish_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(75,axiom,
    ! [A: complex > a,B: set_complex,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
       => ( bij_betw_complex_a @ ( comp_a_a_complex @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_bij__betw__trans) ).

thf(598,plain,
    ! [A: complex > a,B: set_complex,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
       => ( bij_betw_complex_a @ ( comp_a_a_complex @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(349,axiom,
    ! [A: complex > complex,B: a > complex,C: real > a] :
      ( ( comp_a_complex_real @ ( comp_c124850173plex_a @ A @ B ) @ C )
      = ( comp_c595887981x_real @ A @ ( comp_a_complex_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_comp__assoc) ).

thf(1502,plain,
    ! [A: complex > complex,B: a > complex,C: real > a] :
      ( ( comp_a_complex_real @ ( comp_c124850173plex_a @ A @ B ) @ C )
      = ( comp_c595887981x_real @ A @ ( comp_a_complex_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(64,axiom,
    ! [A: set_complex,B: complex > a,C: complex > a,D: set_a] :
      ( ! [E: complex] :
          ( ( member_complex @ E @ A )
         => ( ( B @ E )
            = ( C @ E ) ) )
     => ( ( bij_betw_complex_a @ B @ A @ D )
        = ( bij_betw_complex_a @ C @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_bij__betw__cong) ).

thf(561,plain,
    ! [A: set_complex,B: complex > a,C: complex > a,D: set_a] :
      ( ! [E: complex] :
          ( ( member_complex @ E @ A )
         => ( ( B @ E )
            = ( C @ E ) ) )
     => ( ( bij_betw_complex_a @ B @ A @ D )
        = ( bij_betw_complex_a @ C @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(103,axiom,
    ! [A: a > complex,B: complex > a,C: complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = id_complex )
     => ( ( A @ ( B @ C ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_pointfree__idE) ).

thf(693,plain,
    ! [A: a > complex,B: complex > a,C: complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = id_complex )
     => ( ( A @ ( B @ C ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(41,axiom,
    ! [A: complex > a,B: complex > complex,C: complex > a,D: a > a] :
      ( ( ( comp_c274302683omplex @ A @ B )
        = C )
     => ( ( comp_c274302683omplex @ ( comp_a_a_complex @ D @ A ) @ B )
        = ( comp_a_a_complex @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_rewriteR__comp__comp) ).

thf(484,plain,
    ! [A: complex > a,B: complex > complex,C: complex > a,D: a > a] :
      ( ( ( comp_c274302683omplex @ A @ B )
        = C )
     => ( ( comp_c274302683omplex @ ( comp_a_a_complex @ D @ A ) @ B )
        = ( comp_a_a_complex @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(5,axiom,
    ! [A: set_complex] : ( bij_be209634132omplex @ id_complex @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_bij__betw__id) ).

thf(361,plain,
    ! [A: set_complex] : ( bij_be209634132omplex @ id_complex @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(162,axiom,
    ( real_V912435428omplex
    = ( ^ [A: a > complex] :
          ( ( real_V1477106445omplex @ A )
          & ( real_V451440129omplex @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_bounded__linear__def) ).

thf(879,plain,
    ( real_V912435428omplex
    = ( ^ [A: a > complex] :
          ( ( real_V1477106445omplex @ A )
          & ( real_V451440129omplex @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(146,axiom,
    ! [A: a > a,B: a > complex] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( real_V1477106445omplex @ B )
       => ( real_V1477106445omplex @ ( comp_a_complex_a @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_linear__compose) ).

thf(830,plain,
    ! [A: a > a,B: a > complex] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( real_V1477106445omplex @ B )
       => ( real_V1477106445omplex @ ( comp_a_complex_a @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(109,axiom,
    real_V1327653935plex_a = real_V762982918plex_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_linear__conv__bounded__linear) ).

thf(710,plain,
    real_V1327653935plex_a = real_V762982918plex_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(229,axiom,
    ( id_complex
    = ( ^ [A: complex] : A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_id__apply) ).

thf(1106,plain,
    ( id_complex
    = ( ^ [A: complex] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(60,axiom,
    ! [A: complex] : ( member_complex @ A @ top_top_set_complex ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_UNIV__I) ).

thf(551,plain,
    ! [A: complex] : ( member_complex @ A @ top_top_set_complex ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(237,axiom,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: complex > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = C )
     => ( ( comp_c130555887omplex @ A @ ( comp_a1063143865omplex @ B @ D ) )
        = ( comp_a1063143865omplex @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_rewriteL__comp__comp) ).

thf(1128,plain,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: complex > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = C )
     => ( ( comp_c130555887omplex @ A @ ( comp_a1063143865omplex @ B @ D ) )
        = ( comp_a1063143865omplex @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(317,axiom,
    ! [A: real > a,B: a > complex] :
      ( ( real_V779700657real_a @ A )
     => ( ( real_V1477106445omplex @ B )
       => ( real_V1948715323omplex @ ( comp_a_complex_real @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_linear__compose) ).

thf(1402,plain,
    ! [A: real > a,B: a > complex] :
      ( ( real_V779700657real_a @ A )
     => ( ( real_V1477106445omplex @ B )
       => ( real_V1948715323omplex @ ( comp_a_complex_real @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(306,axiom,
    ! [A: a > complex,B: a > a,C: real > a] :
      ( ( comp_a_complex_real @ ( comp_a_complex_a @ A @ B ) @ C )
      = ( comp_a_complex_real @ A @ ( comp_a_a_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_comp__assoc) ).

thf(1360,plain,
    ! [A: a > complex,B: a > a,C: real > a] :
      ( ( comp_a_complex_real @ ( comp_a_complex_a @ A @ B ) @ C )
      = ( comp_a_complex_real @ A @ ( comp_a_a_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(279,axiom,
    ! [A: real > complex] :
      ( ( path_s36253918omplex @ A )
     => ( ( path_arc_complex @ A )
        | ( ( path_p769714271omplex @ A )
          = ( path_p797330068omplex @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_simple__path__cases) ).

thf(1270,plain,
    ! [A: real > complex] :
      ( ( path_s36253918omplex @ A )
     => ( ( path_arc_complex @ A )
        | ( ( path_p769714271omplex @ A )
          = ( path_p797330068omplex @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(217,axiom,
    ! [A: a > a,B: real > a,C: real > a,D: real > real,E: real] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_comp__eq__dest) ).

thf(1064,plain,
    ! [A: a > a,B: real > a,C: real > a,D: real > real,E: real] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(266,axiom,
    ! [A: a > complex,B: set_a,C: set_complex,D: complex > complex,E: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( bij_be209634132omplex @ D @ C @ E )
       => ( bij_betw_a_complex @ ( comp_c124850173plex_a @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_bij__betw__trans) ).

thf(1227,plain,
    ! [A: a > complex,B: set_a,C: set_complex,D: complex > complex,E: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( bij_be209634132omplex @ D @ C @ E )
       => ( bij_betw_a_complex @ ( comp_c124850173plex_a @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(114,axiom,
    ! [A: a > complex] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( inj_on893405649omplex @ ( comp_a1063143865omplex @ A ) @ top_to525076535plex_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_fun_Oinj__map) ).

thf(725,plain,
    ! [A: a > complex] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( inj_on893405649omplex @ ( comp_a1063143865omplex @ A ) @ top_to525076535plex_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(200,axiom,
    ! [A: a > complex,B: a > a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( inj_on_a_a @ B @ top_top_set_a )
       => ( inj_on_a_complex @ ( comp_a_complex_a @ A @ B ) @ top_top_set_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_inj__compose) ).

thf(1006,plain,
    ! [A: a > complex,B: a > a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( inj_on_a_a @ B @ top_top_set_a )
       => ( inj_on_a_complex @ ( comp_a_complex_a @ A @ B ) @ top_top_set_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(3,axiom,
    ! [A: complex > a,B: set_complex,C: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( inj_on_complex_a @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_bij__betw__imp__inj__on) ).

thf(356,plain,
    ! [A: complex > a,B: set_complex,C: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( inj_on_complex_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(159,axiom,
    ! [A: real > a,B: real > real,C: real > a,D: real] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_a_a_real @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_comp__eq__id__dest) ).

thf(869,plain,
    ! [A: real > a,B: real > real,C: real > a,D: real] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_a_a_real @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(46,axiom,
    ! [A: set_complex] :
      ( ! [B: complex] : ( member_complex @ B @ A )
     => ( top_top_set_complex = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_UNIV__eq__I) ).

thf(499,plain,
    ! [A: set_complex] :
      ( ! [B: complex] : ( member_complex @ B @ A )
     => ( top_top_set_complex = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(316,axiom,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: a > a,E: real > a,F: real > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ( ( ( comp_a_a_real @ D @ E )
          = F )
       => ( ( comp_c595887981x_real @ A @ ( comp_a_complex_real @ B @ E ) )
          = ( comp_a_complex_real @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_rewriteL__comp__comp2) ).

thf(1397,plain,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: a > a,E: real > a,F: real > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ( ( ( comp_a_a_real @ D @ E )
          = F )
       => ( ( comp_c595887981x_real @ A @ ( comp_a_complex_real @ B @ E ) )
          = ( comp_a_complex_real @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(52,axiom,
    ( inj_on_complex_a
    = ( ^ [A: complex > a,B: set_complex] :
        ! [C: complex] :
          ( ( member_complex @ C @ B )
         => ! [D: complex] :
              ( ( member_complex @ D @ B )
             => ( ( ( A @ C )
                  = ( A @ D ) )
               => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_inj__on__def) ).

thf(519,plain,
    ( inj_on_complex_a
    = ( ^ [A: complex > a,B: set_complex] :
        ! [C: complex] :
          ( ( member_complex @ C @ B )
         => ! [D: complex] :
              ( ( member_complex @ D @ B )
             => ( ( ( A @ C )
                  = ( A @ D ) )
               => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(119,axiom,
    ! [A: a > complex,B: complex > a] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = id_complex )
     => ( ( ( comp_complex_a_a @ B @ A )
          = id_a )
       => ( bij_betw_complex_a @ B @ top_top_set_complex @ top_top_set_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_o__bij) ).

thf(742,plain,
    ! [A: a > complex,B: complex > a] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = id_complex )
     => ( ( ( comp_complex_a_a @ B @ A )
          = id_a )
       => ( bij_betw_complex_a @ B @ top_top_set_complex @ top_top_set_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(69,axiom,
    ! [A: complex > a,B: set_complex,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
        = ( bij_betw_complex_a @ ( comp_a_a_complex @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_bij__betw__comp__iff) ).

thf(578,plain,
    ! [A: complex > a,B: set_complex,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
        = ( bij_betw_complex_a @ ( comp_a_a_complex @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(104,axiom,
    ( comp_complex_a_a
    = ( ^ [A: complex > a,B: a > complex,C: a] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_comp__def) ).

thf(697,plain,
    ( comp_complex_a_a
    = ( ^ [A: complex > a,B: a > complex,C: a] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(268,axiom,
    real_V1477106445omplex = real_V912435428omplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_linear__conv__bounded__linear) ).

thf(1234,plain,
    real_V1477106445omplex = real_V912435428omplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(298,axiom,
    ! [A: real > complex] :
      ( ( path_s36253918omplex @ A )
     => ( ( ( path_p769714271omplex @ A )
         != ( path_p797330068omplex @ A ) )
       => ( path_arc_complex @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_simple__path__imp__arc) ).

thf(1329,plain,
    ! [A: real > complex] :
      ( ( path_s36253918omplex @ A )
     => ( ( ( path_p769714271omplex @ A )
         != ( path_p797330068omplex @ A ) )
       => ( path_arc_complex @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(245,axiom,
    ! [A: real > a] :
      ( ( path_simple_path_a @ A )
     => ( path_path_a @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_simple__path__imp__path) ).

thf(1160,plain,
    ! [A: real > a] :
      ( ( path_simple_path_a @ A )
     => ( path_path_a @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(251,axiom,
    ! [A: complex > a,B: a > complex,C: complex > a,D: a > complex] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_complex_a_a @ C @ D ) )
     => ! [E: a] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_comp__eq__elim) ).

thf(1182,plain,
    ! [A: complex > a,B: a > complex,C: complex > a,D: a > complex] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_complex_a_a @ C @ D ) )
     => ! [E: a] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(336,axiom,
    ! [A: a > complex,B: complex > a,C: real > complex] :
      ( ( comp_a_complex_real @ A @ ( comp_complex_a_real @ B @ C ) )
      = ( comp_c595887981x_real @ ( comp_a1063143865omplex @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_fun_Omap__comp) ).

thf(1461,plain,
    ! [A: a > complex,B: complex > a,C: real > complex] :
      ( ( comp_a_complex_real @ A @ ( comp_complex_a_real @ B @ C ) )
      = ( comp_c595887981x_real @ ( comp_a1063143865omplex @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(169,axiom,
    ! [A: complex > complex,B: complex > a] :
      ( ( real_V670066493omplex @ A )
     => ( ( real_V1327653935plex_a @ B )
       => ( real_V1327653935plex_a @ ( comp_c274302683omplex @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_linear__compose) ).

thf(901,plain,
    ! [A: complex > complex,B: complex > a] :
      ( ( real_V670066493omplex @ A )
     => ( ( real_V1327653935plex_a @ B )
       => ( real_V1327653935plex_a @ ( comp_c274302683omplex @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(88,axiom,
    ! [A: complex] : ( member_complex @ A @ top_top_set_complex ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_iso__tuple__UNIV__I) ).

thf(642,plain,
    ! [A: complex] : ( member_complex @ A @ top_top_set_complex ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(86,axiom,
    ! [A: a > a] :
      ( ( comp_a_a_a @ id_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_id__comp) ).

thf(637,plain,
    ! [A: a > a] :
      ( ( comp_a_a_a @ id_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(42,axiom,
    ! [A: complex > a] :
      ( ( real_V762982918plex_a @ A )
     => ( real_V762982918plex_a @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_bounded__linear_Obounded__linear) ).

thf(489,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(331,axiom,
    ! [A: complex > complex,B: real > complex] :
      ( ( real_V670066493omplex @ A )
     => ( ( path_p797330068omplex @ ( comp_c595887981x_real @ A @ B ) )
        = ( A @ ( path_p797330068omplex @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_pathstart__linear__image__eq) ).

thf(1446,plain,
    ! [A: complex > complex,B: real > complex] :
      ( ( real_V670066493omplex @ A )
     => ( ( path_p797330068omplex @ ( comp_c595887981x_real @ A @ B ) )
        = ( A @ ( path_p797330068omplex @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(189,axiom,
    ( id_complex
    = ( ^ [A: complex] : A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_id__def) ).

thf(970,plain,
    ( id_complex
    = ( ^ [A: complex] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(286,axiom,
    ( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a )
    = id_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_real__of__complex__of) ).

thf(1292,plain,
    ( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a )
    = id_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(177,axiom,
    ! [A: a > complex] :
      ( ( real_V1477106445omplex @ A )
     => ( ( real_V451440129omplex @ A )
       => ( real_V912435428omplex @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_bounded__linear_Ointro) ).

thf(933,plain,
    ! [A: a > complex] :
      ( ( real_V1477106445omplex @ A )
     => ( ( real_V451440129omplex @ A )
       => ( real_V912435428omplex @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(82,axiom,
    ! [A: complex > a,B: set_complex,C: complex,D: complex] :
      ( ( inj_on_complex_a @ A @ B )
     => ( ( C != D )
       => ( ( member_complex @ C @ B )
         => ( ( member_complex @ D @ B )
           => ( ( A @ C )
             != ( A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_inj__on__contraD) ).

thf(622,plain,
    ! [A: complex > a,B: set_complex,C: complex,D: complex] :
      ( ( inj_on_complex_a @ A @ B )
     => ( ( C != D )
       => ( ( member_complex @ C @ B )
         => ( ( member_complex @ D @ B )
           => ( ( A @ C )
             != ( A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(16,axiom,
    ! [A: a > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( inj_on_a_a_a_a @ ( comp_a_a_a @ A ) @ top_top_set_a_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_fun_Oinj__map) ).

thf(393,plain,
    ! [A: a > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( inj_on_a_a_a_a @ ( comp_a_a_a @ A ) @ top_top_set_a_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(197,axiom,
    ! [A: a > complex,B: complex > a,C: complex,D: a > complex,E: complex > a,F: complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a1063143865omplex @ A @ B @ C )
        = ( comp_a1063143865omplex @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_comp__cong) ).

thf(997,plain,
    ! [A: a > complex,B: complex > a,C: complex,D: a > complex,E: complex > a,F: complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a1063143865omplex @ A @ B @ C )
        = ( comp_a1063143865omplex @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(106,axiom,
    ! [A: real > a,B: set_real,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_real_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
       => ( bij_betw_real_a @ ( comp_a_a_real @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_bij__betw__trans) ).

thf(701,plain,
    ! [A: real > a,B: set_real,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_real_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
       => ( bij_betw_real_a @ ( comp_a_a_real @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(91,axiom,
    ( comp_a_a_complex
    = ( ^ [A: a > a,B: complex > a,C: complex] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comp__def) ).

thf(654,plain,
    ( comp_a_a_complex
    = ( ^ [A: a > a,B: complex > a,C: complex] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(242,axiom,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
       => ( ( path_arc_a @ ( comp_complex_a_real @ A @ B ) )
          = ( path_arc_complex @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_arc__linear__image__eq) ).

thf(1150,plain,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
       => ( ( path_arc_a @ ( comp_complex_a_real @ A @ B ) )
          = ( path_arc_complex @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(341,axiom,
    path_simple_path_a @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).

thf(1478,plain,
    path_simple_path_a @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(66,axiom,
    ! [A: complex > a] :
      ( ! [B: complex,C: complex] :
          ( ( ( A @ B )
            = ( A @ C ) )
         => ( B = C ) )
     => ( inj_on_complex_a @ A @ top_top_set_complex ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_injI) ).

thf(569,plain,
    ! [A: complex > a] :
      ( ! [B: complex,C: complex] :
          ( ( ( A @ B )
            = ( A @ C ) )
         => ( B = C ) )
     => ( inj_on_complex_a @ A @ top_top_set_complex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(325,axiom,
    ! [A: a > complex,B: real > a,C: real,D: a > complex,E: complex > a,F: complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a_complex_real @ A @ B @ C )
        = ( comp_a1063143865omplex @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_comp__cong) ).

thf(1429,plain,
    ! [A: a > complex,B: real > a,C: real,D: a > complex,E: complex > a,F: complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a_complex_real @ A @ B @ C )
        = ( comp_a1063143865omplex @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(135,axiom,
    ! [A: real > a,B: a > real,C: a > a,D: a > a] :
      ( ( ( comp_real_a_a @ A @ B )
        = C )
     => ( ( comp_real_a_a @ ( comp_a_a_real @ D @ A ) @ B )
        = ( comp_a_a_a @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_rewriteR__comp__comp) ).

thf(792,plain,
    ! [A: real > a,B: a > real,C: a > a,D: a > a] :
      ( ( ( comp_real_a_a @ A @ B )
        = C )
     => ( ( comp_real_a_a @ ( comp_a_a_real @ D @ A ) @ B )
        = ( comp_a_a_a @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(49,axiom,
    ( bij_betw_complex_a
    = ( ^ [A: complex > a,B: set_complex,C: set_a] :
        ? [D: a > complex] :
          ( ! [E: complex] :
              ( ( member_complex @ E @ B )
             => ( ( member_a @ ( A @ E ) @ C )
                & ( ( D @ ( A @ E ) )
                  = E ) ) )
          & ! [E: a] :
              ( ( member_a @ E @ C )
             => ( ( member_complex @ ( D @ E ) @ B )
                & ( ( A @ ( D @ E ) )
                  = E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_bij__betw__iff__bijections) ).

thf(508,plain,
    ( bij_betw_complex_a
    = ( ^ [A: complex > a,B: set_complex,C: set_a] :
        ? [D: a > complex] :
          ( ! [E: complex] :
              ( ( member_complex @ E @ B )
             => ( ( member_a @ ( A @ E ) @ C )
                & ( ( D @ ( A @ E ) )
                  = E ) ) )
          & ! [E: a] :
              ( ( member_a @ E @ C )
             => ( ( member_complex @ ( D @ E ) @ B )
                & ( ( A @ ( D @ E ) )
                  = E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(71,axiom,
    ! [A: a > complex,B: set_a,C: set_complex,D: a] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( member_a @ D @ B )
       => ( member_complex @ ( A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_bij__betw__apply) ).

thf(586,plain,
    ! [A: a > complex,B: set_a,C: set_complex,D: a] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( member_a @ D @ B )
       => ( member_complex @ ( A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(125,axiom,
    ! [A: real > complex] :
      ( ( path_arc_complex @ A )
     => ( path_path_complex @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_arc__imp__path) ).

thf(765,plain,
    ! [A: real > complex] :
      ( ( path_arc_complex @ A )
     => ( path_path_complex @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(214,axiom,
    ! [A: complex > a,B: a > complex,C: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = id_a )
     => ( ( A @ ( B @ C ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_pointfree__idE) ).

thf(1054,plain,
    ! [A: complex > a,B: a > complex,C: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = id_a )
     => ( ( A @ ( B @ C ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(63,axiom,
    ! [A: a > complex,B: complex > a,C: complex > complex] :
      ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ A @ B ) @ C )
      = ( comp_a1063143865omplex @ A @ ( comp_c274302683omplex @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_comp__assoc) ).

thf(558,plain,
    ! [A: a > complex,B: complex > a,C: complex > complex] :
      ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ A @ B ) @ C )
      = ( comp_a1063143865omplex @ A @ ( comp_c274302683omplex @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(219,axiom,
    ! [A: a > complex] :
      ( ( real_V912435428omplex @ A )
     => ( real_V912435428omplex @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_bounded__linear_Obounded__linear) ).

thf(1071,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(184,axiom,
    ! [A: real > a] :
      ( ( path_arc_a @ A )
     => ( ( path_pathfinish_a @ A )
       != ( path_pathstart_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_arc__distinct__ends) ).

thf(953,plain,
    ! [A: real > a] :
      ( ( path_arc_a @ A )
     => ( ( path_pathfinish_a @ A )
       != ( path_pathstart_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(252,axiom,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: a > a,E: a > a,F: a > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ( ( ( comp_a_a_a @ D @ E )
          = F )
       => ( ( comp_c124850173plex_a @ A @ ( comp_a_complex_a @ B @ E ) )
          = ( comp_a_complex_a @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_rewriteL__comp__comp2) ).

thf(1185,plain,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: a > a,E: a > a,F: a > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ( ( ( comp_a_a_a @ D @ E )
          = F )
       => ( ( comp_c124850173plex_a @ A @ ( comp_a_complex_a @ B @ E ) )
          = ( comp_a_complex_a @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(21,axiom,
    ( comp_a_a_complex
    = ( ^ [A: a > a,B: complex > a,C: complex] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_comp__apply) ).

thf(412,plain,
    ( comp_a_a_complex
    = ( ^ [A: a > a,B: complex > a,C: complex] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(273,axiom,
    ! [A: real > a] :
      ( ( comp_a_a_real @ id_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_id__comp) ).

thf(1251,plain,
    ! [A: real > a] :
      ( ( comp_a_a_real @ id_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(263,axiom,
    ! [A: complex > a,B: a > complex] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( ( inj_on_a_complex @ B @ top_top_set_a )
       => ( inj_on_a_a @ ( comp_complex_a_a @ A @ B ) @ top_top_set_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_inj__compose) ).

thf(1219,plain,
    ! [A: complex > a,B: a > complex] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( ( inj_on_a_complex @ B @ top_top_set_a )
       => ( inj_on_a_a @ ( comp_complex_a_a @ A @ B ) @ top_top_set_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(280,axiom,
    ! [A: complex > a,B: a > complex,C: real > a] :
      ( ( comp_complex_a_real @ A @ ( comp_a_complex_real @ B @ C ) )
      = ( comp_a_a_real @ ( comp_complex_a_a @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_fun_Omap__comp) ).

thf(1273,plain,
    ! [A: complex > a,B: a > complex,C: real > a] :
      ( ( comp_complex_a_real @ A @ ( comp_a_complex_real @ B @ C ) )
      = ( comp_a_a_real @ ( comp_complex_a_a @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(155,axiom,
    ! [A: a > complex] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
       => ? [B: complex > a] :
            ( ( real_V1327653935plex_a @ B )
            & ( ( comp_complex_a_a @ B @ A )
              = id_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_linear__injective__left__inverse) ).

thf(856,plain,
    ! [A: a > complex] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
       => ? [B: complex > a] :
            ( ( real_V1327653935plex_a @ B )
            & ( ( comp_complex_a_a @ B @ A )
              = id_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(120,axiom,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: a > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = C )
     => ( ( comp_c124850173plex_a @ A @ ( comp_a_complex_a @ B @ D ) )
        = ( comp_a_complex_a @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_rewriteL__comp__comp) ).

thf(745,plain,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: a > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = C )
     => ( ( comp_c124850173plex_a @ A @ ( comp_a_complex_a @ B @ D ) )
        = ( comp_a_complex_a @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(76,axiom,
    ! [A: complex > a,B: a > complex,C: a,D: a > a,E: complex > a,F: complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_complex_a_a @ A @ B @ C )
        = ( comp_a_a_complex @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_comp__cong) ).

thf(601,plain,
    ! [A: complex > a,B: a > complex,C: a,D: a > a,E: complex > a,F: complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_complex_a_a @ A @ B @ C )
        = ( comp_a_a_complex @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(121,axiom,
    ! [A: a > complex,B: complex > a,C: complex > complex,D: complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_comp__eq__dest__lhs) ).

thf(750,plain,
    ! [A: a > complex,B: complex > a,C: complex > complex,D: complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(351,axiom,
    ! [A: complex > a,B: a > complex,C: real > a] :
      ( ( comp_a_a_real @ ( comp_complex_a_a @ A @ B ) @ C )
      = ( comp_complex_a_real @ A @ ( comp_a_complex_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_comp__assoc) ).

thf(1510,plain,
    ! [A: complex > a,B: a > complex,C: real > a] :
      ( ( comp_a_a_real @ ( comp_complex_a_a @ A @ B ) @ C )
      = ( comp_complex_a_real @ A @ ( comp_a_complex_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(241,axiom,
    ! [A: complex > a,B: a > complex,C: a > a,D: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_a_a_a @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_comp__eq__id__dest) ).

thf(1146,plain,
    ! [A: complex > a,B: a > complex,C: a > a,D: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_a_a_a @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(26,axiom,
    ! [A: complex > a,B: a > complex,C: complex > a] :
      ( ( comp_c274302683omplex @ A @ ( comp_a1063143865omplex @ B @ C ) )
      = ( comp_a_a_complex @ ( comp_complex_a_a @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_fun_Omap__comp) ).

thf(430,plain,
    ! [A: complex > a,B: a > complex,C: complex > a] :
      ( ( comp_c274302683omplex @ A @ ( comp_a1063143865omplex @ B @ C ) )
      = ( comp_a_a_complex @ ( comp_complex_a_a @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(243,axiom,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( path_pathstart_a @ ( comp_a_a_real @ A @ B ) )
        = ( A @ ( path_pathstart_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_pathstart__linear__image__eq) ).

thf(1154,plain,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( path_pathstart_a @ ( comp_a_a_real @ A @ B ) )
        = ( A @ ( path_pathstart_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(24,axiom,
    ! [A: a > complex,B: set_a,C: a,D: a] :
      ( ( inj_on_a_complex @ A @ B )
     => ( ( ( A @ C )
          = ( A @ D ) )
       => ( ( member_a @ C @ B )
         => ( ( member_a @ D @ B )
           => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_inj__onD) ).

thf(423,plain,
    ! [A: a > complex,B: set_a,C: a,D: a] :
      ( ( inj_on_a_complex @ A @ B )
     => ( ( ( A @ C )
          = ( A @ D ) )
       => ( ( member_a @ C @ B )
         => ( ( member_a @ D @ B )
           => ( C = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(313,axiom,
    real_V912435428omplex @ poinca1910941596x_of_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_complex__of__bounded__linear) ).

thf(1389,plain,
    real_V912435428omplex @ poinca1910941596x_of_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(128,axiom,
    ! [A: complex > a,B: a > complex,C: a,D: a > a,E: a > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_c124850173plex_a @ ( comp_a1063143865omplex @ F @ A ) @ B @ C )
        = ( comp_a_complex_a @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_type__copy__map__cong0) ).

thf(772,plain,
    ! [A: complex > a,B: a > complex,C: a,D: a > a,E: a > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_c124850173plex_a @ ( comp_a1063143865omplex @ F @ A ) @ B @ C )
        = ( comp_a_complex_a @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(170,axiom,
    ! [A: real > a,B: real > real] :
      ( ( path_pathfinish_a @ ( comp_real_a_real @ A @ B ) )
      = ( A @ ( path_pathfinish_real @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_pathfinish__compose) ).

thf(904,plain,
    ! [A: real > a,B: real > real] :
      ( ( path_pathfinish_a @ ( comp_real_a_real @ A @ B ) )
      = ( A @ ( path_pathfinish_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(191,axiom,
    ! [A: real > a,B: real > real,C: real > a,D: real > real] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_comp__eq__elim) ).

thf(975,plain,
    ! [A: real > a,B: real > real,C: real > a,D: real > real] :
      ( ( ( comp_real_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(58,axiom,
    ! [A: a > complex,B: set_a,C: set_complex,D: complex > a,E: set_a] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( bij_betw_complex_a @ D @ C @ E )
       => ( bij_betw_a_a @ ( comp_complex_a_a @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_bij__betw__trans) ).

thf(545,plain,
    ! [A: a > complex,B: set_a,C: set_complex,D: complex > a,E: set_a] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( bij_betw_complex_a @ D @ C @ E )
       => ( bij_betw_a_a @ ( comp_complex_a_a @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(344,axiom,
    ( path_arc_complex
    = ( ^ [A: real > complex] :
          ( ( path_s36253918omplex @ A )
          & ( ( path_p769714271omplex @ A )
           != ( path_p797330068omplex @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_arc__simple__path) ).

thf(1488,plain,
    ( path_arc_complex
    = ( ^ [A: real > complex] :
          ( ( path_s36253918omplex @ A )
          & ( ( path_p769714271omplex @ A )
           != ( path_p797330068omplex @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(133,axiom,
    ! [A: real > a,B: real > real,C: set_real] :
      ( ( inj_on_real_a @ ( comp_real_a_real @ A @ B ) @ C )
     => ( inj_on_real_real @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_inj__on__imageI2) ).

thf(787,plain,
    ! [A: real > a,B: real > real,C: set_real] :
      ( ( inj_on_real_a @ ( comp_real_a_real @ A @ B ) @ C )
     => ( inj_on_real_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(215,axiom,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( inj_on_real_a @ A @ top_top_set_real )
       => ( ( path_simple_path_a @ ( comp_real_a_real @ A @ B ) )
          = ( path_s1005760220h_real @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_simple__path__linear__image__eq) ).

thf(1058,plain,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( inj_on_real_a @ A @ top_top_set_real )
       => ( ( path_simple_path_a @ ( comp_real_a_real @ A @ B ) )
          = ( path_s1005760220h_real @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(299,axiom,
    ! [A: real > a,B: a > real,C: a > a,D: a > complex] :
      ( ( ( comp_real_a_a @ A @ B )
        = C )
     => ( ( comp_real_complex_a @ ( comp_a_complex_real @ D @ A ) @ B )
        = ( comp_a_complex_a @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_rewriteR__comp__comp) ).

thf(1332,plain,
    ! [A: real > a,B: a > real,C: a > a,D: a > complex] :
      ( ( ( comp_real_a_a @ A @ B )
        = C )
     => ( ( comp_real_complex_a @ ( comp_a_complex_real @ D @ A ) @ B )
        = ( comp_a_complex_a @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(224,axiom,
    ! [A: complex > a,B: real > complex,C: real > a,D: real > real,E: a > real,F: a > real] :
      ( ( ( comp_complex_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ( ( ( comp_real_real_a @ D @ E )
          = F )
       => ( ( comp_complex_a_a @ A @ ( comp_real_complex_a @ B @ E ) )
          = ( comp_real_a_a @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_rewriteL__comp__comp2) ).

thf(1090,plain,
    ! [A: complex > a,B: real > complex,C: real > a,D: real > real,E: a > real,F: a > real] :
      ( ( ( comp_complex_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ( ( ( comp_real_real_a @ D @ E )
          = F )
       => ( ( comp_complex_a_a @ A @ ( comp_real_complex_a @ B @ E ) )
          = ( comp_real_a_a @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(139,axiom,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( inj_on_a_a @ A @ top_top_set_a )
       => ( ( path_arc_a @ ( comp_a_a_real @ A @ B ) )
          = ( path_arc_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_arc__linear__image__eq) ).

thf(804,plain,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( inj_on_a_a @ A @ top_top_set_a )
       => ( ( path_arc_a @ ( comp_a_a_real @ A @ B ) )
          = ( path_arc_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(107,axiom,
    ! [A: a > a,B: real > a,C: real > a,D: real > real] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_comp__eq__elim) ).

thf(704,plain,
    ! [A: a > a,B: real > a,C: real > a,D: real > real] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_real_a_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(337,axiom,
    ! [A: a > complex,B: real > a,C: a > complex,D: real > a,E: real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = ( comp_a_complex_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comp__eq__dest) ).

thf(1464,plain,
    ! [A: a > complex,B: real > a,C: a > complex,D: real > a,E: real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = ( comp_a_complex_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(77,axiom,
    ! [A: a > a,B: complex > a,C: a > a,D: complex > a] :
      ( ( ( comp_a_a_complex @ A @ B )
        = ( comp_a_a_complex @ C @ D ) )
     => ! [E: complex] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_comp__eq__elim) ).

thf(604,plain,
    ! [A: a > a,B: complex > a,C: a > a,D: complex > a] :
      ( ( ( comp_a_a_complex @ A @ B )
        = ( comp_a_a_complex @ C @ D ) )
     => ! [E: complex] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(254,axiom,
    ( id_a
    = ( ^ [A: a] : A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_id__apply) ).

thf(1194,plain,
    ( id_a
    = ( ^ [A: a] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(19,axiom,
    ! [A: a > a] :
      ( ( comp_a_a_a @ id_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_fun_Omap__id) ).

thf(406,plain,
    ! [A: a > a] :
      ( ( comp_a_a_a @ id_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(233,axiom,
    ( top_top_set_a
    = ( collect_a @ top_top_a_o ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_top__set__def) ).

thf(1117,plain,
    ( top_top_set_a
    = ( collect_a @ top_top_a_o ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(117,axiom,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( path_pathfinish_a @ ( comp_a_a_real @ A @ B ) )
        = ( A @ ( path_pathfinish_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_pathfinish__linear__image) ).

thf(736,plain,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( path_pathfinish_a @ ( comp_a_a_real @ A @ B ) )
        = ( A @ ( path_pathfinish_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(195,axiom,
    ! [A: a > complex,B: complex > a,C: complex > complex,D: complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = ( comp_c130555887omplex @ id_complex @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_comp__eq__id__dest) ).

thf(990,plain,
    ! [A: a > complex,B: complex > a,C: complex > complex,D: complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = ( comp_c130555887omplex @ id_complex @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(65,axiom,
    ? [A: a] : ( member_a @ A @ top_top_set_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_UNIV__witness) ).

thf(567,plain,
    ? [A: a] : ( member_a @ A @ top_top_set_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(235,axiom,
    ! [A: real > a,B: set_real,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_real_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
        = ( bij_betw_real_a @ ( comp_a_a_real @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_bij__betw__comp__iff) ).

thf(1122,plain,
    ! [A: real > a,B: set_real,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_real_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
        = ( bij_betw_real_a @ ( comp_a_a_real @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(290,axiom,
    ! [A: a > complex,B: real > a,C: set_real] :
      ( ( inj_on_real_complex @ ( comp_a_complex_real @ A @ B ) @ C )
     => ( inj_on_real_a @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_inj__on__imageI2) ).

thf(1307,plain,
    ! [A: a > complex,B: real > a,C: set_real] :
      ( ( inj_on_real_complex @ ( comp_a_complex_real @ A @ B ) @ C )
     => ( inj_on_real_a @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(99,axiom,
    ! [A: a > complex,B: set_a,C: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ? [D: complex > a] : ( bij_betw_complex_a @ D @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_bij__betw__inv) ).

thf(681,plain,
    ! [A: a > complex,B: set_a,C: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ? [D: complex > a] : ( bij_betw_complex_a @ D @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(319,axiom,
    ! [A: complex > complex,B: real > complex] :
      ( ( real_V670066493omplex @ A )
     => ( ( path_p769714271omplex @ ( comp_c595887981x_real @ A @ B ) )
        = ( A @ ( path_p769714271omplex @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_pathfinish__linear__image) ).

thf(1408,plain,
    ! [A: complex > complex,B: real > complex] :
      ( ( real_V670066493omplex @ A )
     => ( ( path_p769714271omplex @ ( comp_c595887981x_real @ A @ B ) )
        = ( A @ ( path_p769714271omplex @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(39,axiom,
    ! [A: complex > complex,B: set_complex,C: set_complex,D: complex > a,E: set_a] :
      ( ( bij_be209634132omplex @ A @ B @ C )
     => ( ( bij_betw_complex_a @ D @ C @ E )
        = ( bij_betw_complex_a @ ( comp_c274302683omplex @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_bij__betw__comp__iff) ).

thf(477,plain,
    ! [A: complex > complex,B: set_complex,C: set_complex,D: complex > a,E: set_a] :
      ( ( bij_be209634132omplex @ A @ B @ C )
     => ( ( bij_betw_complex_a @ D @ C @ E )
        = ( bij_betw_complex_a @ ( comp_c274302683omplex @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(141,axiom,
    ( ( comp_a_a_real @ id_a )
    = id_real_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_fun_Omap__id0) ).

thf(811,plain,
    ( ( comp_a_a_real @ id_a )
    = id_real_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(339,axiom,
    ! [A: real > a] :
      ( ( inj_on_a_complex @ poinca1910941596x_of_a @ top_top_set_a )
     => ( ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ A ) )
        = ( path_simple_path_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103__092_060open_062_092_060And_062g_O_Ainj_Acomplex__of_A_092_060Longrightarrow_062_Asimple__path_A_Icomplex__of_A_092_060circ_062_Ag_J_A_061_Asimple__path_Ag_092_060close_062) ).

thf(1471,plain,
    ! [A: real > a] :
      ( ( inj_on_a_complex @ poinca1910941596x_of_a @ top_top_set_a )
     => ( ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ A ) )
        = ( path_simple_path_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(123,axiom,
    ! [A: complex > complex] :
      ( ( ! [B: complex] :
            ( ( A @ B )
            = B ) )
      = ( A = id_complex ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_eq__id__iff) ).

thf(758,plain,
    ! [A: complex > complex] :
      ( ( ! [B: complex] :
            ( ( A @ B )
            = B ) )
      = ( A = id_complex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(56,axiom,
    ! [A: complex > a,B: complex > complex] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( ( inj_on94911183omplex @ B @ top_top_set_complex )
       => ( inj_on_complex_a @ ( comp_c274302683omplex @ A @ B ) @ top_top_set_complex ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_inj__compose) ).

thf(535,plain,
    ! [A: complex > a,B: complex > complex] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( ( inj_on94911183omplex @ B @ top_top_set_complex )
       => ( inj_on_complex_a @ ( comp_c274302683omplex @ A @ B ) @ top_top_set_complex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(79,axiom,
    ! [A: set_complex,B: complex > a,C: complex > a] :
      ( ! [D: complex] :
          ( ( member_complex @ D @ A )
         => ( ( B @ D )
            = ( C @ D ) ) )
     => ( ( inj_on_complex_a @ B @ A )
        = ( inj_on_complex_a @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_inj__on__cong) ).

thf(609,plain,
    ! [A: set_complex,B: complex > a,C: complex > a] :
      ( ! [D: complex] :
          ( ( member_complex @ D @ A )
         => ( ( B @ D )
            = ( C @ D ) ) )
     => ( ( inj_on_complex_a @ B @ A )
        = ( inj_on_complex_a @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(246,axiom,
    ! [A: a > a,B: set_a,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_a_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
        = ( bij_betw_a_complex @ ( comp_a_complex_a @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_bij__betw__comp__iff) ).

thf(1162,plain,
    ! [A: a > a,B: set_a,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_a_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
        = ( bij_betw_a_complex @ ( comp_a_complex_a @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(152,axiom,
    ! [A: complex > a,B: a > complex,C: a,D: a > a,E: real > a,F: real] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_complex_a_a @ A @ B @ C )
        = ( comp_a_a_real @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_comp__cong) ).

thf(848,plain,
    ! [A: complex > a,B: a > complex,C: a,D: a > a,E: real > a,F: real] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_complex_a_a @ A @ B @ C )
        = ( comp_a_a_real @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(167,axiom,
    ! [A: real > a,B: real > real] :
      ( ( path_pathstart_a @ ( comp_real_a_real @ A @ B ) )
      = ( A @ ( path_pathstart_real @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_pathstart__compose) ).

thf(895,plain,
    ! [A: real > a,B: real > real] :
      ( ( path_pathstart_a @ ( comp_real_a_real @ A @ B ) )
      = ( A @ ( path_pathstart_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(187,axiom,
    ( id_a
    = ( ^ [A: a] : A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_id__def) ).

thf(964,plain,
    ( id_a
    = ( ^ [A: a] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(83,axiom,
    ! [A: set_a] : ( bij_betw_a_a @ id_a @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_bij__betw__id) ).

thf(626,plain,
    ! [A: set_a] : ( bij_betw_a_a @ id_a @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(302,axiom,
    ! [A: a > complex,B: real > a] :
      ( ( path_p769714271omplex @ ( comp_a_complex_real @ A @ B ) )
      = ( A @ ( path_pathfinish_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_pathfinish__compose) ).

thf(1344,plain,
    ! [A: a > complex,B: real > a] :
      ( ( path_p769714271omplex @ ( comp_a_complex_real @ A @ B ) )
      = ( A @ ( path_pathfinish_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(127,axiom,
    ! [A: complex > a,B: a > complex,C: a,D: real > a,E: real > real,F: real] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_complex_a_a @ A @ B @ C )
        = ( comp_real_a_real @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_comp__cong) ).

thf(769,plain,
    ! [A: complex > a,B: a > complex,C: a,D: real > a,E: real > real,F: real] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_complex_a_a @ A @ B @ C )
        = ( comp_real_a_real @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(35,axiom,
    ! [A: a > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( inj_on1576005937plex_a @ ( comp_a_a_complex @ A ) @ top_to525076535plex_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_fun_Oinj__map) ).

thf(462,plain,
    ! [A: a > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( inj_on1576005937plex_a @ ( comp_a_a_complex @ A ) @ top_to525076535plex_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(232,axiom,
    ! [A: real > real,B: real > real,C: a > real,D: real > a,E: real > a,F: a > a] :
      ( ( ( comp_real_real_real @ A @ B )
        = ( comp_a_real_real @ C @ D ) )
     => ( ( ( comp_real_a_a @ E @ C )
          = F )
       => ( ( comp_real_a_real @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_a_a_real @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_rewriteR__comp__comp2) ).

thf(1112,plain,
    ! [A: real > real,B: real > real,C: a > real,D: real > a,E: real > a,F: a > a] :
      ( ( ( comp_real_real_real @ A @ B )
        = ( comp_a_real_real @ C @ D ) )
     => ( ( ( comp_real_a_a @ E @ C )
          = F )
       => ( ( comp_real_a_real @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_a_a_real @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(44,axiom,
    ! [A: complex > a] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
      = ( ! [B: complex,C: complex] :
            ( ( ( A @ B )
              = ( A @ C ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_inj__def) ).

thf(494,plain,
    ! [A: complex > a] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
      = ( ! [B: complex,C: complex] :
            ( ( ( A @ B )
              = ( A @ C ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(222,axiom,
    ! [A: a > complex,B: complex] :
      ( ( bij_betw_a_complex @ A @ top_top_set_a @ top_top_set_complex )
     => ~ ! [C: a] :
            ( ( B
              = ( A @ C ) )
           => ~ ! [D: a] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_bij__pointE) ).

thf(1080,plain,
    ! [A: a > complex,B: complex] :
      ( ( bij_betw_a_complex @ A @ top_top_set_a @ top_top_set_complex )
     => ~ ! [C: a] :
            ( ( B
              = ( A @ C ) )
           => ~ ! [D: a] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(250,axiom,
    ! [A: real > a,B: real > real,C: real > a,D: real] :
      ( ( ( comp_real_a_real @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_comp__eq__dest__lhs) ).

thf(1177,plain,
    ! [A: real > a,B: real > real,C: real > a,D: real] :
      ( ( ( comp_real_a_real @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(311,axiom,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
       => ( ( path_path_complex @ ( comp_a_complex_real @ A @ B ) )
          = ( path_path_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_path__linear__image__eq) ).

thf(1381,plain,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
       => ( ( path_path_complex @ ( comp_a_complex_real @ A @ B ) )
          = ( path_path_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(53,axiom,
    ( comp_a_a_a
    = ( ^ [A: a > a,B: a > a,C: a] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_comp__apply) ).

thf(521,plain,
    ( comp_a_a_a
    = ( ^ [A: a > a,B: a > a,C: a] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(193,axiom,
    ! [A: a > a,B: real > a,C: real > a,D: real] :
      ( ( ( comp_a_a_real @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comp__eq__dest__lhs) ).

thf(983,plain,
    ! [A: a > a,B: real > a,C: real > a,D: real] :
      ( ( ( comp_a_a_real @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(145,axiom,
    ! [A: real > a] :
      ( ( comp_a_a_real @ id_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_fun_Omap__id) ).

thf(827,plain,
    ! [A: real > a] :
      ( ( comp_a_a_real @ id_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(347,axiom,
    ! [A: a > complex,B: real > a,C: complex > real] :
      ( ( comp_a1063143865omplex @ A @ ( comp_real_a_complex @ B @ C ) )
      = ( comp_r667767405omplex @ ( comp_a_complex_real @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_fun_Omap__comp) ).

thf(1496,plain,
    ! [A: a > complex,B: real > a,C: complex > real] :
      ( ( comp_a1063143865omplex @ A @ ( comp_real_a_complex @ B @ C ) )
      = ( comp_r667767405omplex @ ( comp_a_complex_real @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(153,axiom,
    ! [A: a > complex,B: complex > a,C: a > complex,D: complex > a,E: complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = ( comp_a1063143865omplex @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_comp__eq__dest) ).

thf(851,plain,
    ! [A: a > complex,B: complex > a,C: a > complex,D: complex > a,E: complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = ( comp_a1063143865omplex @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(198,axiom,
    ! [A: complex > a,B: a > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( real_V1477106445omplex @ B )
       => ( real_V670066493omplex @ ( comp_a1063143865omplex @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_linear__compose) ).

thf(1000,plain,
    ! [A: complex > a,B: a > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( real_V1477106445omplex @ B )
       => ( real_V670066493omplex @ ( comp_a1063143865omplex @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(327,axiom,
    ! [A: a > complex,B: a > a,C: real > a] :
      ( ( comp_a_complex_real @ A @ ( comp_a_a_real @ B @ C ) )
      = ( comp_a_complex_real @ ( comp_a_complex_a @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_fun_Omap__comp) ).

thf(1435,plain,
    ! [A: a > complex,B: a > a,C: real > a] :
      ( ( comp_a_complex_real @ A @ ( comp_a_a_real @ B @ C ) )
      = ( comp_a_complex_real @ ( comp_a_complex_a @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(38,axiom,
    ! [A: complex > a,B: set_complex,C: complex,D: complex] :
      ( ( inj_on_complex_a @ A @ B )
     => ( ( member_complex @ C @ B )
       => ( ( member_complex @ D @ B )
         => ( ( ( A @ C )
              = ( A @ D ) )
            = ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_inj__on__eq__iff) ).

thf(473,plain,
    ! [A: complex > a,B: set_complex,C: complex,D: complex] :
      ( ( inj_on_complex_a @ A @ B )
     => ( ( member_complex @ C @ B )
       => ( ( member_complex @ D @ B )
         => ( ( ( A @ C )
              = ( A @ D ) )
            = ( C = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(247,axiom,
    ! [A: a > a,B: set_a,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_a_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
       => ( bij_betw_a_complex @ ( comp_a_complex_a @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_bij__betw__trans) ).

thf(1166,plain,
    ! [A: a > a,B: set_a,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_a_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
       => ( bij_betw_a_complex @ ( comp_a_complex_a @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(181,axiom,
    ! [A: a > a,B: real > a,C: set_real] :
      ( ( inj_on_real_a @ ( comp_a_a_real @ A @ B ) @ C )
     => ( inj_on_real_a @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_inj__on__imageI2) ).

thf(944,plain,
    ! [A: a > a,B: real > a,C: set_real] :
      ( ( inj_on_real_a @ ( comp_a_a_real @ A @ B ) @ C )
     => ( inj_on_real_a @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(322,axiom,
    ( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a )
    = id_complex ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_complex__of__real__of) ).

thf(1420,plain,
    ( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a )
    = id_complex ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(10,axiom,
    ! [A: set_a,B: a > complex,C: a > complex] :
      ( ! [D: a] :
          ( ( member_a @ D @ A )
         => ( ( B @ D )
            = ( C @ D ) ) )
     => ( ( inj_on_a_complex @ B @ A )
        = ( inj_on_a_complex @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_inj__on__cong) ).

thf(374,plain,
    ! [A: set_a,B: a > complex,C: a > complex] :
      ( ! [D: a] :
          ( ( member_a @ D @ A )
         => ( ( B @ D )
            = ( C @ D ) ) )
     => ( ( inj_on_a_complex @ B @ A )
        = ( inj_on_a_complex @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(282,axiom,
    ! [A: complex > a,B: real > complex] :
      ( ( path_pathstart_a @ ( comp_complex_a_real @ A @ B ) )
      = ( A @ ( path_p797330068omplex @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_pathstart__compose) ).

thf(1277,plain,
    ! [A: complex > a,B: real > complex] :
      ( ( path_pathstart_a @ ( comp_complex_a_real @ A @ B ) )
      = ( A @ ( path_p797330068omplex @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(203,axiom,
    ( ( (=) @ complex )
    = ( ^ [A: complex,B: complex] :
        ? [C: complex] :
          ( ( member_complex @ C @ top_top_set_complex )
          & ( ( id_complex @ C )
            = A )
          & ( ( id_complex @ C )
            = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_DEADID_Oin__rel) ).

thf(1018,plain,
    ( ( (=) @ complex )
    = ( ^ [A: complex,B: complex] :
        ? [C: complex] :
          ( ( member_complex @ C @ top_top_set_complex )
          & ( ( id_complex @ C )
            = A )
          & ( ( id_complex @ C )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(61,axiom,
    ! [A: set_a,B: set_a] :
      ( ( bij_betw_a_a @ id_a @ A @ B )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_bij__betw__id__iff) ).

thf(553,plain,
    ! [A: set_a,B: set_a] :
      ( ( bij_betw_a_a @ id_a @ A @ B )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(34,axiom,
    ! [A: complex > a,B: a > complex,C: a > a,D: a > a,E: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_a_a_a @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_comp__eq__dest) ).

thf(458,plain,
    ! [A: complex > a,B: a > complex,C: a > a,D: a > a,E: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_a_a_a @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(148,axiom,
    ! [A: a > complex,B: a > a,C: a > complex,D: a > a,E: a] :
      ( ( ( comp_a_complex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_comp__eq__dest) ).

thf(836,plain,
    ! [A: a > complex,B: a > a,C: a > complex,D: a > a,E: a] :
      ( ( ( comp_a_complex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(213,axiom,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: a > a,E: complex > a,F: complex > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ( ( ( comp_a_a_complex @ D @ E )
          = F )
       => ( ( comp_c130555887omplex @ A @ ( comp_a1063143865omplex @ B @ E ) )
          = ( comp_a1063143865omplex @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_rewriteL__comp__comp2) ).

thf(1049,plain,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: a > a,E: complex > a,F: complex > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = ( comp_a_complex_a @ C @ D ) )
     => ( ( ( comp_a_a_complex @ D @ E )
          = F )
       => ( ( comp_c130555887omplex @ A @ ( comp_a1063143865omplex @ B @ E ) )
          = ( comp_a1063143865omplex @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(43,axiom,
    ! [A: a > complex,B: set_a,C: a,D: a] :
      ( ( inj_on_a_complex @ A @ B )
     => ( ( C != D )
       => ( ( member_a @ C @ B )
         => ( ( member_a @ D @ B )
           => ( ( A @ C )
             != ( A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_inj__on__contraD) ).

thf(490,plain,
    ! [A: a > complex,B: set_a,C: a,D: a] :
      ( ( inj_on_a_complex @ A @ B )
     => ( ( C != D )
       => ( ( member_a @ C @ B )
         => ( ( member_a @ D @ B )
           => ( ( A @ C )
             != ( A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(97,axiom,
    ! [A: complex > a,B: a > complex,C: a > a,D: a > a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_a_a_a @ C @ D ) )
     => ! [E: a] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_comp__eq__elim) ).

thf(675,plain,
    ! [A: complex > a,B: a > complex,C: a > a,D: a > a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_a_a_a @ C @ D ) )
     => ! [E: a] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(258,axiom,
    ! [A: a > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( inj_on_real_a_real_a @ ( comp_a_a_real @ A ) @ top_top_set_real_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_fun_Oinj__map) ).

thf(1203,plain,
    ! [A: a > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( inj_on_real_a_real_a @ ( comp_a_a_real @ A ) @ top_top_set_real_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(260,axiom,
    ! [A: a > a,B: real > a,C: a > a,D: real > a,E: real] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_comp__eq__dest) ).

thf(1208,plain,
    ! [A: a > a,B: real > a,C: a > a,D: real > a,E: real] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(72,axiom,
    ( bij_betw_a_complex
    = ( ^ [A: a > complex,B: set_a,C: set_complex] :
        ? [D: complex > a] :
          ( ! [E: a] :
              ( ( member_a @ E @ B )
             => ( ( member_complex @ ( A @ E ) @ C )
                & ( ( D @ ( A @ E ) )
                  = E ) ) )
          & ! [E: complex] :
              ( ( member_complex @ E @ C )
             => ( ( member_a @ ( D @ E ) @ B )
                & ( ( A @ ( D @ E ) )
                  = E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_bij__betw__iff__bijections) ).

thf(589,plain,
    ( bij_betw_a_complex
    = ( ^ [A: a > complex,B: set_a,C: set_complex] :
        ? [D: complex > a] :
          ( ! [E: a] :
              ( ( member_a @ E @ B )
             => ( ( member_complex @ ( A @ E ) @ C )
                & ( ( D @ ( A @ E ) )
                  = E ) ) )
          & ! [E: complex] :
              ( ( member_complex @ E @ C )
             => ( ( member_a @ ( D @ E ) @ B )
                & ( ( A @ ( D @ E ) )
                  = E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(94,axiom,
    ! [A: a > complex,B: set_a,C: a,D: a] :
      ( ( inj_on_a_complex @ A @ B )
     => ( ( member_a @ C @ B )
       => ( ( member_a @ D @ B )
         => ( ( ( A @ C )
              = ( A @ D ) )
            = ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_inj__on__eq__iff) ).

thf(663,plain,
    ! [A: a > complex,B: set_a,C: a,D: a] :
      ( ( inj_on_a_complex @ A @ B )
     => ( ( member_a @ C @ B )
       => ( ( member_a @ D @ B )
         => ( ( ( A @ C )
              = ( A @ D ) )
            = ( C = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(59,axiom,
    ! [A: complex > a,B: set_complex,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
       => ( bij_be209634132omplex @ ( comp_a1063143865omplex @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_bij__betw__trans) ).

thf(548,plain,
    ! [A: complex > a,B: set_complex,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
       => ( bij_be209634132omplex @ ( comp_a1063143865omplex @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(179,axiom,
    ! [A: a > a,B: real > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( ( inj_on_real_a @ B @ top_top_set_real )
       => ( inj_on_real_a @ ( comp_a_a_real @ A @ B ) @ top_top_set_real ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_inj__compose) ).

thf(939,plain,
    ! [A: a > a,B: real > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( ( inj_on_real_a @ B @ top_top_set_real )
       => ( inj_on_real_a @ ( comp_a_a_real @ A @ B ) @ top_top_set_real ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(301,axiom,
    ! [A: real > a,B: complex > real,C: complex,D: a > a,E: complex > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F @ A ) @ B @ C )
        = ( comp_a1063143865omplex @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_type__copy__map__cong0) ).

thf(1340,plain,
    ! [A: real > a,B: complex > real,C: complex,D: a > a,E: complex > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F @ A ) @ B @ C )
        = ( comp_a1063143865omplex @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(129,axiom,
    ! [A: a > complex] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( inj_on_a_a_a_complex @ ( comp_a_complex_a @ A ) @ top_top_set_a_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_fun_Oinj__map) ).

thf(776,plain,
    ! [A: a > complex] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( inj_on_a_a_a_complex @ ( comp_a_complex_a @ A ) @ top_top_set_a_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(154,axiom,
    bij_be209634132omplex @ id_complex @ top_top_set_complex @ top_top_set_complex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_bij__id) ).

thf(855,plain,
    bij_be209634132omplex @ id_complex @ top_top_set_complex @ top_top_set_complex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(87,axiom,
    ! [A: complex > a,B: set_complex,C: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ! [D: complex] :
          ( ( member_complex @ D @ B )
         => ( member_a @ ( A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_bij__betwE) ).

thf(640,plain,
    ! [A: complex > a,B: set_complex,C: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ! [D: complex] :
          ( ( member_complex @ D @ B )
         => ( member_a @ ( A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(205,axiom,
    ! [A: complex > a,B: complex > complex,C: complex > a,D: a > complex] :
      ( ( ( comp_c274302683omplex @ A @ B )
        = C )
     => ( ( comp_complex_a_a @ A @ ( comp_c124850173plex_a @ B @ D ) )
        = ( comp_complex_a_a @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_rewriteL__comp__comp) ).

thf(1025,plain,
    ! [A: complex > a,B: complex > complex,C: complex > a,D: a > complex] :
      ( ( ( comp_c274302683omplex @ A @ B )
        = C )
     => ( ( comp_complex_a_a @ A @ ( comp_c124850173plex_a @ B @ D ) )
        = ( comp_complex_a_a @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(22,axiom,
    ! [A: complex > a,B: complex,C: complex] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( ( ( A @ B )
          = ( A @ C ) )
        = ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_inj__eq) ).

thf(414,plain,
    ! [A: complex > a,B: complex,C: complex] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( ( ( A @ B )
          = ( A @ C ) )
        = ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(308,axiom,
    ! [A: a > complex,B: real > a,C: a > complex,D: real > a,E: complex > real,F: complex > a] :
      ( ( ( comp_a_complex_real @ A @ B )
        = ( comp_a_complex_real @ C @ D ) )
     => ( ( ( comp_real_a_complex @ D @ E )
          = F )
       => ( ( comp_a1063143865omplex @ A @ ( comp_real_a_complex @ B @ E ) )
          = ( comp_a1063143865omplex @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_rewriteL__comp__comp2) ).

thf(1368,plain,
    ! [A: a > complex,B: real > a,C: a > complex,D: real > a,E: complex > real,F: complex > a] :
      ( ( ( comp_a_complex_real @ A @ B )
        = ( comp_a_complex_real @ C @ D ) )
     => ( ( ( comp_real_a_complex @ D @ E )
          = F )
       => ( ( comp_a1063143865omplex @ A @ ( comp_real_a_complex @ B @ E ) )
          = ( comp_a1063143865omplex @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(110,axiom,
    ! [A: complex,B: complex] : ( path_path_complex @ ( path_rectpath @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_path__rectpath) ).

thf(712,plain,
    ! [A: complex,B: complex] : ( path_path_complex @ ( path_rectpath @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(199,axiom,
    ! [A: a > a,B: real > a] :
      ( ( path_pathstart_a @ ( comp_a_a_real @ A @ B ) )
      = ( A @ ( path_pathstart_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_pathstart__compose) ).

thf(1003,plain,
    ! [A: a > a,B: real > a] :
      ( ( path_pathstart_a @ ( comp_a_a_real @ A @ B ) )
      = ( A @ ( path_pathstart_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(102,axiom,
    ! [A: a > a] :
      ( ( comp_a_a_a @ A @ id_a )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_comp__id) ).

thf(690,plain,
    ! [A: a > a] :
      ( ( comp_a_a_a @ A @ id_a )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(353,axiom,
    ! [A: complex > a,B: real > complex,C: real,D: a > a,E: real > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F @ A ) @ B @ C )
        = ( comp_a_complex_real @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_type__copy__map__cong0) ).

thf(1516,plain,
    ! [A: complex > a,B: real > complex,C: real,D: a > a,E: real > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F @ A ) @ B @ C )
        = ( comp_a_complex_real @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(265,axiom,
    ( comp_real_a_real
    = ( ^ [A: real > a,B: real > real,C: real] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_comp__def) ).

thf(1225,plain,
    ( comp_real_a_real
    = ( ^ [A: real > a,B: real > real,C: real] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(108,axiom,
    ! [A: a > complex] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
        = ( ! [B: a] :
              ( ( ( A @ B )
                = zero_zero_complex )
             => ( B = zero_zero_a ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_linear__inj__iff__eq__0) ).

thf(707,plain,
    ! [A: a > complex] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
        = ( ! [B: a] :
              ( ( ( A @ B )
                = zero_zero_complex )
             => ( B = zero_zero_a ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(20,axiom,
    ! [A: a > a,B: a > a] :
      ( ( ( comp_a_a_a @ A @ B )
        = id_a )
     => ( ( ( comp_a_a_a @ B @ A )
          = id_a )
       => ( bij_betw_a_a @ B @ top_top_set_a @ top_top_set_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_o__bij) ).

thf(409,plain,
    ! [A: a > a,B: a > a] :
      ( ( ( comp_a_a_a @ A @ B )
        = id_a )
     => ( ( ( comp_a_a_a @ B @ A )
          = id_a )
       => ( bij_betw_a_a @ B @ top_top_set_a @ top_top_set_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(267,axiom,
    ! [A: a > complex,B: a,C: a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( ( A @ B )
          = ( A @ C ) )
       => ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_injD) ).

thf(1230,plain,
    ! [A: a > complex,B: a,C: a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( ( A @ B )
          = ( A @ C ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(343,axiom,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
       => ( ( path_s36253918omplex @ ( comp_a_complex_real @ A @ B ) )
          = ( path_simple_path_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_simple__path__linear__image__eq) ).

thf(1484,plain,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( inj_on_a_complex @ A @ top_top_set_a )
       => ( ( path_s36253918omplex @ ( comp_a_complex_real @ A @ B ) )
          = ( path_simple_path_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(348,axiom,
    ! [A: complex > complex,B: real > complex] :
      ( ( path_p797330068omplex @ ( comp_c595887981x_real @ A @ B ) )
      = ( A @ ( path_p797330068omplex @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_pathstart__compose) ).

thf(1499,plain,
    ! [A: complex > complex,B: real > complex] :
      ( ( path_p797330068omplex @ ( comp_c595887981x_real @ A @ B ) )
      = ( A @ ( path_p797330068omplex @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(326,axiom,
    ! [A: a > complex,B: real > a,C: a > complex,D: real > a] :
      ( ( ( comp_a_complex_real @ A @ B )
        = ( comp_a_complex_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_comp__eq__elim) ).

thf(1432,plain,
    ! [A: a > complex,B: real > a,C: a > complex,D: real > a] :
      ( ( ( comp_a_complex_real @ A @ B )
        = ( comp_a_complex_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(333,axiom,
    ! [A: a > complex,B: real > a,C: complex > real] :
      ( ( comp_r667767405omplex @ ( comp_a_complex_real @ A @ B ) @ C )
      = ( comp_a1063143865omplex @ A @ ( comp_real_a_complex @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_comp__assoc) ).

thf(1452,plain,
    ! [A: a > complex,B: real > a,C: complex > real] :
      ( ( comp_r667767405omplex @ ( comp_a_complex_real @ A @ B ) @ C )
      = ( comp_a1063143865omplex @ A @ ( comp_real_a_complex @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(47,axiom,
    ( ( comp_a_a_a @ id_a )
    = id_a_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_fun_Omap__id0) ).

thf(502,plain,
    ( ( comp_a_a_a @ id_a )
    = id_a_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(149,axiom,
    bij_betw_a_a @ id_a @ top_top_set_a @ top_top_set_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_bij__id) ).

thf(840,plain,
    bij_betw_a_a @ id_a @ top_top_set_a @ top_top_set_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(276,axiom,
    ! [A: real > a] :
      ( ( path_arc_a @ A )
     => ( path_simple_path_a @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_arc__imp__simple__path) ).

thf(1262,plain,
    ! [A: real > a] :
      ( ( path_arc_a @ A )
     => ( path_simple_path_a @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(68,axiom,
    ( inj_on_a_complex
    = ( ^ [A: a > complex,B: set_a] :
        ! [C: a] :
          ( ( member_a @ C @ B )
         => ! [D: a] :
              ( ( member_a @ D @ B )
             => ( ( ( A @ C )
                  = ( A @ D ) )
               => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_inj__on__def) ).

thf(576,plain,
    ( inj_on_a_complex
    = ( ^ [A: a > complex,B: set_a] :
        ! [C: a] :
          ( ( member_a @ C @ B )
         => ! [D: a] :
              ( ( member_a @ D @ B )
             => ( ( ( A @ C )
                  = ( A @ D ) )
               => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(140,axiom,
    ! [A: real > a] :
      ( ( path_simple_path_a @ A )
     => ( ( path_arc_a @ A )
        | ( ( path_pathfinish_a @ A )
          = ( path_pathstart_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_simple__path__cases) ).

thf(808,plain,
    ! [A: real > a] :
      ( ( path_simple_path_a @ A )
     => ( ( path_arc_a @ A )
        | ( ( path_pathfinish_a @ A )
          = ( path_pathstart_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(4,axiom,
    ! [A: a > complex,B: complex > a,C: set_complex] :
      ( ( inj_on94911183omplex @ ( comp_a1063143865omplex @ A @ B ) @ C )
     => ( inj_on_complex_a @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_inj__on__imageI2) ).

thf(359,plain,
    ! [A: a > complex,B: complex > a,C: set_complex] :
      ( ( inj_on94911183omplex @ ( comp_a1063143865omplex @ A @ B ) @ C )
     => ( inj_on_complex_a @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(171,axiom,
    real_V762982918plex_a @ poinca837721858l_of_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_real__of__bounded__linear) ).

thf(907,plain,
    real_V762982918plex_a @ poinca837721858l_of_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(275,axiom,
    ! [A: real > a,B: complex > real,C: a > a,D: complex > a,E: real > complex,F: real > a] :
      ( ( ( comp_real_a_complex @ A @ B )
        = ( comp_a_a_complex @ C @ D ) )
     => ( ( ( comp_complex_a_real @ D @ E )
          = F )
       => ( ( comp_real_a_real @ A @ ( comp_c819638635l_real @ B @ E ) )
          = ( comp_a_a_real @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_rewriteL__comp__comp2) ).

thf(1257,plain,
    ! [A: real > a,B: complex > real,C: a > a,D: complex > a,E: real > complex,F: real > a] :
      ( ( ( comp_real_a_complex @ A @ B )
        = ( comp_a_a_complex @ C @ D ) )
     => ( ( ( comp_complex_a_real @ D @ E )
          = F )
       => ( ( comp_real_a_real @ A @ ( comp_c819638635l_real @ B @ E ) )
          = ( comp_a_a_real @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(240,axiom,
    ! [A: real > a,B: a > real,C: a > a,D: real > a] :
      ( ( ( comp_real_a_a @ A @ B )
        = C )
     => ( ( comp_real_a_real @ A @ ( comp_a_real_real @ B @ D ) )
        = ( comp_a_a_real @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_rewriteL__comp__comp) ).

thf(1141,plain,
    ! [A: real > a,B: a > real,C: a > a,D: real > a] :
      ( ( ( comp_real_a_a @ A @ B )
        = C )
     => ( ( comp_real_a_real @ A @ ( comp_a_real_real @ B @ D ) )
        = ( comp_a_a_real @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(92,axiom,
    ! [A: complex > a,B: complex,C: complex] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( ( ( A @ B )
          = ( A @ C ) )
       => ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_injD) ).

thf(656,plain,
    ! [A: complex > a,B: complex,C: complex] :
      ( ( inj_on_complex_a @ A @ top_top_set_complex )
     => ( ( ( A @ B )
          = ( A @ C ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(284,axiom,
    ! [A: complex > a,B: real > complex,C: real > a,D: a > complex] :
      ( ( ( comp_complex_a_real @ A @ B )
        = C )
     => ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ D @ A ) @ B )
        = ( comp_a_complex_real @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_rewriteR__comp__comp) ).

thf(1284,plain,
    ! [A: complex > a,B: real > complex,C: real > a,D: a > complex] :
      ( ( ( comp_complex_a_real @ A @ B )
        = C )
     => ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ D @ A ) @ B )
        = ( comp_a_complex_real @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(115,axiom,
    ! [A: complex > a,B: a > complex,C: complex > a,D: a > complex,E: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_complex_a_a @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_comp__eq__dest) ).

thf(727,plain,
    ! [A: complex > a,B: a > complex,C: complex > a,D: a > complex,E: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = ( comp_complex_a_a @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(192,axiom,
    ! [A: real > real,B: real > real,C: real > real,D: real > a] :
      ( ( ( comp_real_real_real @ A @ B )
        = C )
     => ( ( comp_real_a_real @ ( comp_real_a_real @ D @ A ) @ B )
        = ( comp_real_a_real @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_rewriteR__comp__comp) ).

thf(978,plain,
    ! [A: real > real,B: real > real,C: real > real,D: real > a] :
      ( ( ( comp_real_real_real @ A @ B )
        = C )
     => ( ( comp_real_a_real @ ( comp_real_a_real @ D @ A ) @ B )
        = ( comp_real_a_real @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(31,axiom,
    ! [A: a > a,B: a > a,C: a] :
      ( ( ( comp_a_a_a @ A @ B )
        = id_a )
     => ( ( A @ ( B @ C ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_pointfree__idE) ).

thf(446,plain,
    ! [A: a > a,B: a > a,C: a] :
      ( ( ( comp_a_a_a @ A @ B )
        = id_a )
     => ( ( A @ ( B @ C ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(74,axiom,
    ! [A: complex > a] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
        = ( ! [B: complex] :
              ( ( ( A @ B )
                = zero_zero_a )
             => ( B = zero_zero_complex ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_linear__inj__iff__eq__0) ).

thf(595,plain,
    ! [A: complex > a] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
        = ( ! [B: complex] :
              ( ( ( A @ B )
                = zero_zero_a )
             => ( B = zero_zero_complex ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(45,axiom,
    ! [A: a > a,B: complex > a,C: set_complex] :
      ( ( inj_on_complex_a @ ( comp_a_a_complex @ A @ B ) @ C )
     => ( inj_on_complex_a @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_inj__on__imageI2) ).

thf(497,plain,
    ! [A: a > a,B: complex > a,C: set_complex] :
      ( ( inj_on_complex_a @ ( comp_a_a_complex @ A @ B ) @ C )
     => ( inj_on_complex_a @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(270,axiom,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( path_pathfinish_a @ ( comp_real_a_real @ A @ B ) )
        = ( A @ ( path_pathfinish_real @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_pathfinish__linear__image) ).

thf(1240,plain,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( path_pathfinish_a @ ( comp_real_a_real @ A @ B ) )
        = ( A @ ( path_pathfinish_real @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(320,axiom,
    ! [A: real > a,B: a > real,C: a,D: a > a,E: a > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_real_complex_a @ ( comp_a_complex_real @ F @ A ) @ B @ C )
        = ( comp_a_complex_a @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_type__copy__map__cong0) ).

thf(1412,plain,
    ! [A: real > a,B: a > real,C: a,D: a > a,E: a > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_real_complex_a @ ( comp_a_complex_real @ F @ A ) @ B @ C )
        = ( comp_a_complex_a @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(236,axiom,
    ( comp_a_complex_a
    = ( ^ [A: a > complex,B: a > a,C: a] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_comp__apply) ).

thf(1126,plain,
    ( comp_a_complex_a
    = ( ^ [A: a > complex,B: a > a,C: a] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(314,axiom,
    ! [A: real > a,B: complex > real,C: complex > a,D: a > complex] :
      ( ( ( comp_real_a_complex @ A @ B )
        = C )
     => ( ( comp_r667767405omplex @ ( comp_a_complex_real @ D @ A ) @ B )
        = ( comp_a1063143865omplex @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_rewriteR__comp__comp) ).

thf(1390,plain,
    ! [A: real > a,B: complex > real,C: complex > a,D: a > complex] :
      ( ( ( comp_real_a_complex @ A @ B )
        = C )
     => ( ( comp_r667767405omplex @ ( comp_a_complex_real @ D @ A ) @ B )
        = ( comp_a1063143865omplex @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(285,axiom,
    ! [A: a > complex,B: complex > a,C: real > complex] :
      ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ A @ B ) @ C )
      = ( comp_a_complex_real @ A @ ( comp_complex_a_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_comp__assoc) ).

thf(1289,plain,
    ! [A: a > complex,B: complex > a,C: real > complex] :
      ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ A @ B ) @ C )
      = ( comp_a_complex_real @ A @ ( comp_complex_a_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(230,axiom,
    ! [A: complex > a,B: a > complex,C: set_a] :
      ( ( inj_on_a_a @ ( comp_complex_a_a @ A @ B ) @ C )
     => ( inj_on_a_complex @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_inj__on__imageI2) ).

thf(1108,plain,
    ! [A: complex > a,B: a > complex,C: set_a] :
      ( ( inj_on_a_a @ ( comp_complex_a_a @ A @ B ) @ C )
     => ( inj_on_a_complex @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(294,axiom,
    ! [A: real > a,B: real > real,C: real,D: a > a,E: real > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_r701421291x_real @ ( comp_a_complex_real @ F @ A ) @ B @ C )
        = ( comp_a_complex_real @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_type__copy__map__cong0) ).

thf(1316,plain,
    ! [A: real > a,B: real > real,C: real,D: a > a,E: real > a,F: a > complex] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_r701421291x_real @ ( comp_a_complex_real @ F @ A ) @ B @ C )
        = ( comp_a_complex_real @ ( comp_a_complex_a @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(32,axiom,
    ! [A: set_a,B: complex > a,C: a > complex] :
      ( ! [D: a] :
          ( ( member_a @ D @ A )
         => ( ( B @ ( C @ D ) )
            = D ) )
     => ( inj_on_a_complex @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_inj__on__inverseI) ).

thf(450,plain,
    ! [A: set_a,B: complex > a,C: a > complex] :
      ( ! [D: a] :
          ( ( member_a @ D @ A )
         => ( ( B @ ( C @ D ) )
            = D ) )
     => ( inj_on_a_complex @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(6,axiom,
    ! [A: a > a,B: a > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( real_V202220639ar_a_a @ B )
       => ( real_V202220639ar_a_a @ ( comp_a_a_a @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_linear__compose) ).

thf(363,plain,
    ! [A: a > a,B: a > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( real_V202220639ar_a_a @ B )
       => ( real_V202220639ar_a_a @ ( comp_a_a_a @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(62,axiom,
    ! [A: a] : ( member_a @ A @ top_top_set_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_UNIV__I) ).

thf(556,plain,
    ! [A: a] : ( member_a @ A @ top_top_set_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(262,axiom,
    ! [A: complex > complex,B: a > complex,C: complex > a] :
      ( ( comp_c130555887omplex @ A @ ( comp_a1063143865omplex @ B @ C ) )
      = ( comp_a1063143865omplex @ ( comp_c124850173plex_a @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_fun_Omap__comp) ).

thf(1216,plain,
    ! [A: complex > complex,B: a > complex,C: complex > a] :
      ( ( comp_c130555887omplex @ A @ ( comp_a1063143865omplex @ B @ C ) )
      = ( comp_a1063143865omplex @ ( comp_c124850173plex_a @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(166,axiom,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( inj_on_a_a @ A @ top_top_set_a )
       => ( ( path_simple_path_a @ ( comp_a_a_real @ A @ B ) )
          = ( path_simple_path_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_simple__path__linear__image__eq) ).

thf(891,plain,
    ! [A: a > a,B: real > a] :
      ( ( real_V202220639ar_a_a @ A )
     => ( ( inj_on_a_a @ A @ top_top_set_a )
       => ( ( path_simple_path_a @ ( comp_a_a_real @ A @ B ) )
          = ( path_simple_path_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(281,axiom,
    path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_a1) ).

thf(1276,plain,
    path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(297,axiom,
    ! [A: a > complex,B: real > a,C: real,D: a > complex,E: real > a,F: real] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a_complex_real @ A @ B @ C )
        = ( comp_a_complex_real @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_comp__cong) ).

thf(1326,plain,
    ! [A: a > complex,B: real > a,C: real,D: a > complex,E: real > a,F: real] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a_complex_real @ A @ B @ C )
        = ( comp_a_complex_real @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(105,axiom,
    ! [A: real > complex] :
      ( ( path_arc_complex @ A )
     => ( path_s36253918omplex @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_arc__imp__simple__path) ).

thf(699,plain,
    ! [A: real > complex] :
      ( ( path_arc_complex @ A )
     => ( path_s36253918omplex @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(51,axiom,
    ! [A: a > complex,B: set_a,C: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ! [D: a] :
          ( ( member_a @ D @ B )
         => ( member_complex @ ( A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_bij__betwE) ).

thf(517,plain,
    ! [A: a > complex,B: set_a,C: set_complex] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ! [D: a] :
          ( ( member_a @ D @ B )
         => ( member_complex @ ( A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(216,axiom,
    ( comp_complex_a_a
    = ( ^ [A: complex > a,B: a > complex,C: a] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_comp__apply) ).

thf(1062,plain,
    ( comp_complex_a_a
    = ( ^ [A: complex > a,B: a > complex,C: a] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(15,axiom,
    ! [A: complex > a] :
      ( ( comp_a_a_complex @ id_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_id__comp) ).

thf(390,plain,
    ! [A: complex > a] :
      ( ( comp_a_a_complex @ id_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(85,axiom,
    ! [A: a > real,B: a > a,C: real > real,D: a > real,E: real > a,F: real > a] :
      ( ( ( comp_a_real_a @ A @ B )
        = ( comp_real_real_a @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_a_a_a @ ( comp_real_a_a @ E @ A ) @ B )
          = ( comp_real_a_a @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_rewriteR__comp__comp2) ).

thf(632,plain,
    ! [A: a > real,B: a > a,C: real > real,D: a > real,E: real > a,F: real > a] :
      ( ( ( comp_a_real_a @ A @ B )
        = ( comp_real_real_a @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_a_a_a @ ( comp_real_a_a @ E @ A ) @ B )
          = ( comp_real_a_a @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(271,axiom,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( inj_on_real_a @ A @ top_top_set_real )
       => ( ( path_path_a @ ( comp_real_a_real @ A @ B ) )
          = ( path_path_real @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_path__linear__image__eq) ).

thf(1244,plain,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( inj_on_real_a @ A @ top_top_set_real )
       => ( ( path_path_a @ ( comp_real_a_real @ A @ B ) )
          = ( path_path_real @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(131,axiom,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( path_pathstart_a @ ( comp_real_a_real @ A @ B ) )
        = ( A @ ( path_pathstart_real @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_pathstart__linear__image__eq) ).

thf(781,plain,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( path_pathstart_a @ ( comp_real_a_real @ A @ B ) )
        = ( A @ ( path_pathstart_real @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(186,axiom,
    ! [A: a > a,B: real > a,C: a > a,D: real > a] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_comp__eq__elim) ).

thf(961,plain,
    ! [A: a > a,B: real > a,C: a > a,D: real > a] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_a_a_real @ C @ D ) )
     => ! [E: real] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(142,axiom,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: complex > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = C )
     => ( ( comp_complex_a_a @ ( comp_c274302683omplex @ D @ A ) @ B )
        = ( comp_complex_a_a @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_rewriteR__comp__comp) ).

thf(813,plain,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: complex > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = C )
     => ( ( comp_complex_a_a @ ( comp_c274302683omplex @ D @ A ) @ B )
        = ( comp_complex_a_a @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(312,axiom,
    ! [A: real > a,B: set_real,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_real_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
        = ( bij_be122140626omplex @ ( comp_a_complex_real @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_bij__betw__comp__iff) ).

thf(1385,plain,
    ! [A: real > a,B: set_real,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_real_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
        = ( bij_be122140626omplex @ ( comp_a_complex_real @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(182,axiom,
    ! [A: complex > a] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
       => ? [B: a > complex] :
            ( ( real_V1477106445omplex @ B )
            & ( ( comp_a1063143865omplex @ B @ A )
              = id_complex ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_linear__injective__left__inverse) ).

thf(946,plain,
    ! [A: complex > a] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
       => ? [B: a > complex] :
            ( ( real_V1477106445omplex @ B )
            & ( ( comp_a1063143865omplex @ B @ A )
              = id_complex ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(227,axiom,
    ! [A: a > complex,B: complex > a,C: complex,D: a > complex,E: a > a,F: a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a1063143865omplex @ A @ B @ C )
        = ( comp_a_complex_a @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_comp__cong) ).

thf(1101,plain,
    ! [A: a > complex,B: complex > a,C: complex,D: a > complex,E: a > a,F: a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a1063143865omplex @ A @ B @ C )
        = ( comp_a_complex_a @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(116,axiom,
    ! [A: complex > a,B: a > complex,C: a > a,D: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_comp__eq__dest__lhs) ).

thf(731,plain,
    ! [A: complex > a,B: a > complex,C: a > a,D: a] :
      ( ( ( comp_complex_a_a @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(23,axiom,
    ! [A: real > real,B: a > real,C: a > real,D: a > a,E: real > a,F: a > a] :
      ( ( ( comp_real_real_a @ A @ B )
        = ( comp_a_real_a @ C @ D ) )
     => ( ( ( comp_real_a_a @ E @ C )
          = F )
       => ( ( comp_real_a_a @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_a_a_a @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_rewriteR__comp__comp2) ).

thf(418,plain,
    ! [A: real > real,B: a > real,C: a > real,D: a > a,E: real > a,F: a > a] :
      ( ( ( comp_real_real_a @ A @ B )
        = ( comp_a_real_a @ C @ D ) )
     => ( ( ( comp_real_a_a @ E @ C )
          = F )
       => ( ( comp_real_a_a @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_a_a_a @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(221,axiom,
    ! [A: a > complex,B: complex > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( real_V1327653935plex_a @ B )
       => ( real_V202220639ar_a_a @ ( comp_complex_a_a @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_linear__compose) ).

thf(1077,plain,
    ! [A: a > complex,B: complex > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( real_V1327653935plex_a @ B )
       => ( real_V202220639ar_a_a @ ( comp_complex_a_a @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(261,axiom,
    ! [A: complex > complex,B: real > complex] :
      ( ( real_V670066493omplex @ A )
     => ( ( inj_on94911183omplex @ A @ top_top_set_complex )
       => ( ( path_path_complex @ ( comp_c595887981x_real @ A @ B ) )
          = ( path_path_complex @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_path__linear__image__eq) ).

thf(1212,plain,
    ! [A: complex > complex,B: real > complex] :
      ( ( real_V670066493omplex @ A )
     => ( ( inj_on94911183omplex @ A @ top_top_set_complex )
       => ( ( path_path_complex @ ( comp_c595887981x_real @ A @ B ) )
          = ( path_path_complex @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(291,axiom,
    ( comp_a_complex_real
    = ( ^ [A: a > complex,B: real > a,C: real] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_comp__apply) ).

thf(1309,plain,
    ( comp_a_complex_real
    = ( ^ [A: a > complex,B: real > a,C: real] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(329,axiom,
    real_V1477106445omplex @ poinca1910941596x_of_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_complex__of__linear) ).

thf(1442,plain,
    real_V1477106445omplex @ poinca1910941596x_of_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(211,axiom,
    ( ( (=) @ a )
    = ( ^ [A: a,B: a] :
        ? [C: a] :
          ( ( member_a @ C @ top_top_set_a )
          & ( ( id_a @ C )
            = A )
          & ( ( id_a @ C )
            = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_DEADID_Oin__rel) ).

thf(1045,plain,
    ( ( (=) @ a )
    = ( ^ [A: a,B: a] :
        ? [C: a] :
          ( ( member_a @ C @ top_top_set_a )
          & ( ( id_a @ C )
            = A )
          & ( ( id_a @ C )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(206,axiom,
    ! [A: a > complex,B: complex > a,C: a > complex,D: complex > a] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = ( comp_a1063143865omplex @ C @ D ) )
     => ! [E: complex] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_comp__eq__elim) ).

thf(1030,plain,
    ! [A: a > complex,B: complex > a,C: a > complex,D: complex > a] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = ( comp_a1063143865omplex @ C @ D ) )
     => ! [E: complex] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(346,axiom,
    ! [A: real > complex,B: real > real,C: a > complex,D: real > a,E: complex > a,F: a > a] :
      ( ( ( comp_r701421291x_real @ A @ B )
        = ( comp_a_complex_real @ C @ D ) )
     => ( ( ( comp_complex_a_a @ E @ C )
          = F )
       => ( ( comp_real_a_real @ ( comp_complex_a_real @ E @ A ) @ B )
          = ( comp_a_a_real @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_rewriteR__comp__comp2) ).

thf(1491,plain,
    ! [A: real > complex,B: real > real,C: a > complex,D: real > a,E: complex > a,F: a > a] :
      ( ( ( comp_r701421291x_real @ A @ B )
        = ( comp_a_complex_real @ C @ D ) )
     => ( ( ( comp_complex_a_a @ E @ C )
          = F )
       => ( ( comp_real_a_real @ ( comp_complex_a_real @ E @ A ) @ B )
          = ( comp_a_a_real @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(27,axiom,
    ! [A: complex > a,B: set_complex,C: set_a,D: complex] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( member_complex @ D @ B )
       => ( member_a @ ( A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_bij__betw__apply) ).

thf(433,plain,
    ! [A: complex > a,B: set_complex,C: set_a,D: complex] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ( ( member_complex @ D @ B )
       => ( member_a @ ( A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(50,axiom,
    ! [A: a > a,B: a] :
      ( ( bij_betw_a_a @ A @ top_top_set_a @ top_top_set_a )
     => ~ ! [C: a] :
            ( ( B
              = ( A @ C ) )
           => ~ ! [D: a] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_bij__pointE) ).

thf(510,plain,
    ! [A: a > a,B: a] :
      ( ( bij_betw_a_a @ A @ top_top_set_a @ top_top_set_a )
     => ~ ! [C: a] :
            ( ( B
              = ( A @ C ) )
           => ~ ! [D: a] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(95,axiom,
    ! [A: a > a,B: complex > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( ( inj_on_complex_a @ B @ top_top_set_complex )
       => ( inj_on_complex_a @ ( comp_a_a_complex @ A @ B ) @ top_top_set_complex ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_inj__compose) ).

thf(667,plain,
    ! [A: a > a,B: complex > a] :
      ( ( inj_on_a_a @ A @ top_top_set_a )
     => ( ( inj_on_complex_a @ B @ top_top_set_complex )
       => ( inj_on_complex_a @ ( comp_a_a_complex @ A @ B ) @ top_top_set_complex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(287,axiom,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: real > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = C )
     => ( ( comp_c595887981x_real @ A @ ( comp_a_complex_real @ B @ D ) )
        = ( comp_a_complex_real @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_rewriteL__comp__comp) ).

thf(1294,plain,
    ! [A: complex > complex,B: a > complex,C: a > complex,D: real > a] :
      ( ( ( comp_c124850173plex_a @ A @ B )
        = C )
     => ( ( comp_c595887981x_real @ A @ ( comp_a_complex_real @ B @ D ) )
        = ( comp_a_complex_real @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(13,axiom,
    ! [A: complex > a,B: set_complex,C: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ? [D: a > complex] : ( bij_betw_a_complex @ D @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_bij__betw__inv) ).

thf(383,plain,
    ! [A: complex > a,B: set_complex,C: set_a] :
      ( ( bij_betw_complex_a @ A @ B @ C )
     => ? [D: a > complex] : ( bij_betw_a_complex @ D @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(352,axiom,
    ! [A: real > a,B: set_real,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_real_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
       => ( bij_be122140626omplex @ ( comp_a_complex_real @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_bij__betw__trans) ).

thf(1513,plain,
    ! [A: real > a,B: set_real,C: set_a,D: a > complex,E: set_complex] :
      ( ( bij_betw_real_a @ A @ B @ C )
     => ( ( bij_betw_a_complex @ D @ C @ E )
       => ( bij_be122140626omplex @ ( comp_a_complex_real @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(238,axiom,
    ! [A: a > complex,B: a,C: a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( ( A @ B )
          = ( A @ C ) )
        = ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_inj__eq) ).

thf(1133,plain,
    ! [A: a > complex,B: a,C: a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( ( A @ B )
          = ( A @ C ) )
        = ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(283,axiom,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( path_p769714271omplex @ ( comp_a_complex_real @ A @ B ) )
        = ( A @ ( path_pathfinish_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_pathfinish__linear__image) ).

thf(1280,plain,
    ! [A: a > complex,B: real > a] :
      ( ( real_V1477106445omplex @ A )
     => ( ( path_p769714271omplex @ ( comp_a_complex_real @ A @ B ) )
        = ( A @ ( path_pathfinish_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(147,axiom,
    ! [A: a > a] :
      ( ( ! [B: a] :
            ( ( A @ B )
            = B ) )
      = ( A = id_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_eq__id__iff) ).

thf(833,plain,
    ! [A: a > a] :
      ( ( ! [B: a] :
            ( ( A @ B )
            = B ) )
      = ( A = id_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(183,axiom,
    ! [A: a > complex] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
      = ( ! [B: a,C: a] :
            ( ( ( A @ B )
              = ( A @ C ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_inj__def) ).

thf(950,plain,
    ! [A: a > complex] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
      = ( ! [B: a,C: a] :
            ( ( ( A @ B )
              = ( A @ C ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(315,axiom,
    ! [A: a > complex] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( inj_on319905617omplex @ ( comp_a_complex_real @ A ) @ top_top_set_real_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_fun_Oinj__map) ).

thf(1395,plain,
    ! [A: a > complex] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( inj_on319905617omplex @ ( comp_a_complex_real @ A ) @ top_top_set_real_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(143,axiom,
    ! [A: real > real,B: complex > real,C: complex,D: a > real,E: complex > a,F: real > a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_real_a_complex @ ( comp_real_a_real @ F @ A ) @ B @ C )
        = ( comp_a_a_complex @ ( comp_real_a_a @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_type__copy__map__cong0) ).

thf(818,plain,
    ! [A: real > real,B: complex > real,C: complex,D: a > real,E: complex > a,F: real > a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_real_a_complex @ ( comp_real_a_real @ F @ A ) @ B @ C )
        = ( comp_a_a_complex @ ( comp_real_a_a @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(272,axiom,
    ! [A: a > complex,B: complex > a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( inj_on_complex_a @ B @ top_top_set_complex )
       => ( inj_on94911183omplex @ ( comp_a1063143865omplex @ A @ B ) @ top_top_set_complex ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_inj__compose) ).

thf(1248,plain,
    ! [A: a > complex,B: complex > a] :
      ( ( inj_on_a_complex @ A @ top_top_set_a )
     => ( ( inj_on_complex_a @ B @ top_top_set_complex )
       => ( inj_on94911183omplex @ ( comp_a1063143865omplex @ A @ B ) @ top_top_set_complex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(158,axiom,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
       => ( ( path_path_a @ ( comp_complex_a_real @ A @ B ) )
          = ( path_path_complex @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_path__linear__image__eq) ).

thf(865,plain,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( inj_on_complex_a @ A @ top_top_set_complex )
       => ( ( path_path_a @ ( comp_complex_a_real @ A @ B ) )
          = ( path_path_complex @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(126,axiom,
    ! [A: real > a] :
      ( ( inj_on_real_a @ A @ top_top_set_real )
     => ( inj_on958237983real_a @ ( comp_real_a_real @ A ) @ top_to1446257885l_real ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_fun_Oinj__map) ).

thf(767,plain,
    ! [A: real > a] :
      ( ( inj_on_real_a @ A @ top_top_set_real )
     => ( inj_on958237983real_a @ ( comp_real_a_real @ A ) @ top_to1446257885l_real ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(165,axiom,
    ! [A: real > real,B: real > real,C: real > real,D: real > real,E: real > a,F: real > a] :
      ( ( ( comp_real_real_real @ A @ B )
        = ( comp_real_real_real @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_real_a_real @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_real_a_real @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_rewriteR__comp__comp2) ).

thf(886,plain,
    ! [A: real > real,B: real > real,C: real > real,D: real > real,E: real > a,F: real > a] :
      ( ( ( comp_real_real_real @ A @ B )
        = ( comp_real_real_real @ C @ D ) )
     => ( ( ( comp_real_a_real @ E @ C )
          = F )
       => ( ( comp_real_a_real @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_real_a_real @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(174,axiom,
    ! [A: real > real,B: a > real,C: complex > real,D: a > complex,E: real > a,F: complex > a] :
      ( ( ( comp_real_real_a @ A @ B )
        = ( comp_complex_real_a @ C @ D ) )
     => ( ( ( comp_real_a_complex @ E @ C )
          = F )
       => ( ( comp_real_a_a @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_complex_a_a @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_rewriteR__comp__comp2) ).

thf(918,plain,
    ! [A: real > real,B: a > real,C: complex > real,D: a > complex,E: real > a,F: complex > a] :
      ( ( ( comp_real_real_a @ A @ B )
        = ( comp_complex_real_a @ C @ D ) )
     => ( ( ( comp_real_a_complex @ E @ C )
          = F )
       => ( ( comp_real_a_a @ ( comp_real_a_real @ E @ A ) @ B )
          = ( comp_complex_a_a @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(138,axiom,
    ! [A: complex > a,B: a > complex] :
      ( ( ( comp_complex_a_a @ A @ B )
        = id_a )
     => ( ( ( comp_a1063143865omplex @ B @ A )
          = id_complex )
       => ( bij_betw_a_complex @ B @ top_top_set_a @ top_top_set_complex ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_o__bij) ).

thf(801,plain,
    ! [A: complex > a,B: a > complex] :
      ( ( ( comp_complex_a_a @ A @ B )
        = id_a )
     => ( ( ( comp_a1063143865omplex @ B @ A )
          = id_complex )
       => ( bij_betw_a_complex @ B @ top_top_set_a @ top_top_set_complex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(307,axiom,
    ! [A: a > complex,B: complex > a,C: complex > complex,D: real > complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = C )
     => ( ( comp_a_complex_real @ A @ ( comp_complex_a_real @ B @ D ) )
        = ( comp_c595887981x_real @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_rewriteL__comp__comp) ).

thf(1363,plain,
    ! [A: a > complex,B: complex > a,C: complex > complex,D: real > complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = C )
     => ( ( comp_a_complex_real @ A @ ( comp_complex_a_real @ B @ D ) )
        = ( comp_c595887981x_real @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(293,axiom,
    ( ( path_pathfinish_a @ c )
    = ( path_pathstart_a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).

thf(1314,plain,
    ( ( path_pathfinish_a @ c )
    = ( path_pathstart_a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(207,axiom,
    ! [A: complex > a,B: a > complex,C: a > a] :
      ( ( comp_a_a_a @ ( comp_complex_a_a @ A @ B ) @ C )
      = ( comp_complex_a_a @ A @ ( comp_a_complex_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_comp__assoc) ).

thf(1033,plain,
    ! [A: complex > a,B: a > complex,C: a > a] :
      ( ( comp_a_a_a @ ( comp_complex_a_a @ A @ B ) @ C )
      = ( comp_complex_a_a @ A @ ( comp_a_complex_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(18,axiom,
    ! [A: set_a,B: a > complex,C: a > complex,D: set_complex] :
      ( ! [E: a] :
          ( ( member_a @ E @ A )
         => ( ( B @ E )
            = ( C @ E ) ) )
     => ( ( bij_betw_a_complex @ B @ A @ D )
        = ( bij_betw_a_complex @ C @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_bij__betw__cong) ).

thf(400,plain,
    ! [A: set_a,B: a > complex,C: a > complex,D: set_complex] :
      ( ! [E: a] :
          ( ( member_a @ E @ A )
         => ( ( B @ E )
            = ( C @ E ) ) )
     => ( ( bij_betw_a_complex @ B @ A @ D )
        = ( bij_betw_a_complex @ C @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(17,axiom,
    ! [A: complex > a,B: complex > complex,C: complex > a,D: a > complex] :
      ( ( ( comp_c274302683omplex @ A @ B )
        = C )
     => ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ D @ A ) @ B )
        = ( comp_a1063143865omplex @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_rewriteR__comp__comp) ).

thf(395,plain,
    ! [A: complex > a,B: complex > complex,C: complex > a,D: a > complex] :
      ( ( ( comp_c274302683omplex @ A @ B )
        = C )
     => ( ( comp_c130555887omplex @ ( comp_a1063143865omplex @ D @ A ) @ B )
        = ( comp_a1063143865omplex @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(118,axiom,
    ( comp_real_a_real
    = ( ^ [A: real > a,B: real > real,C: real] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_comp__apply) ).

thf(740,plain,
    ( comp_real_a_real
    = ( ^ [A: real > a,B: real > real,C: real] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(269,axiom,
    ! [A: a > a,B: real > a,C: real > a,D: real] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_a_a_real @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_comp__eq__id__dest) ).

thf(1236,plain,
    ! [A: a > a,B: real > a,C: real > a,D: real] :
      ( ( ( comp_a_a_real @ A @ B )
        = ( comp_a_a_real @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(278,axiom,
    ( comp_a1063143865omplex
    = ( ^ [A: a > complex,B: complex > a,C: complex] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_comp__def) ).

thf(1268,plain,
    ( comp_a1063143865omplex
    = ( ^ [A: a > complex,B: complex > a,C: complex] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(25,axiom,
    ! [A: a > a,B: set_a,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_a_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
       => ( bij_betw_a_a @ ( comp_a_a_a @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_bij__betw__trans) ).

thf(427,plain,
    ! [A: a > a,B: set_a,C: set_a,D: a > a,E: set_a] :
      ( ( bij_betw_a_a @ A @ B @ C )
     => ( ( bij_betw_a_a @ D @ C @ E )
       => ( bij_betw_a_a @ ( comp_a_a_a @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(156,axiom,
    ! [A: a > complex] :
      ( ( real_V912435428omplex @ A )
     => ( real_V451440129omplex @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_bounded__linear_Oaxioms_I2_J) ).

thf(860,plain,
    ! [A: a > complex] :
      ( ( real_V912435428omplex @ A )
     => ( real_V451440129omplex @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(89,axiom,
    ? [A: complex] : ( member_complex @ A @ top_top_set_complex ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_UNIV__witness) ).

thf(644,plain,
    ? [A: complex] : ( member_complex @ A @ top_top_set_complex ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(172,axiom,
    ! [A: a > complex,B: a > a,C: a > complex,D: a] :
      ( ( ( comp_a_complex_a @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_comp__eq__dest__lhs) ).

thf(908,plain,
    ! [A: a > complex,B: a > a,C: a > complex,D: a] :
      ( ( ( comp_a_complex_a @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(113,axiom,
    ( comp_a1063143865omplex
    = ( ^ [A: a > complex,B: complex > a,C: complex] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_comp__apply) ).

thf(723,plain,
    ( comp_a1063143865omplex
    = ( ^ [A: a > complex,B: complex > a,C: complex] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(144,axiom,
    ! [A: a > complex] :
      ( ! [B: a,C: a] :
          ( ( ( A @ B )
            = ( A @ C ) )
         => ( B = C ) )
     => ( inj_on_a_complex @ A @ top_top_set_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_injI) ).

thf(822,plain,
    ! [A: a > complex] :
      ( ! [B: a,C: a] :
          ( ( ( A @ B )
            = ( A @ C ) )
         => ( B = C ) )
     => ( inj_on_a_complex @ A @ top_top_set_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(288,axiom,
    ! [A: a > complex,B: real > a,C: real > real] :
      ( ( comp_r701421291x_real @ ( comp_a_complex_real @ A @ B ) @ C )
      = ( comp_a_complex_real @ A @ ( comp_real_a_real @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_comp__assoc) ).

thf(1299,plain,
    ! [A: a > complex,B: real > a,C: real > real] :
      ( ( comp_r701421291x_real @ ( comp_a_complex_real @ A @ B ) @ C )
      = ( comp_a_complex_real @ A @ ( comp_real_a_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(350,axiom,
    ! [A: a > complex,B: real > a,C: real > complex,D: complex > real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = C )
     => ( ( comp_a1063143865omplex @ A @ ( comp_real_a_complex @ B @ D ) )
        = ( comp_r667767405omplex @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_rewriteL__comp__comp) ).

thf(1505,plain,
    ! [A: a > complex,B: real > a,C: real > complex,D: complex > real] :
      ( ( ( comp_a_complex_real @ A @ B )
        = C )
     => ( ( comp_a1063143865omplex @ A @ ( comp_real_a_complex @ B @ D ) )
        = ( comp_r667767405omplex @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(304,axiom,
    ! [A: a > complex,B: real > a,C: real,D: a > complex,E: a > a,F: a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a_complex_real @ A @ B @ C )
        = ( comp_a_complex_a @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_comp__cong) ).

thf(1352,plain,
    ! [A: a > complex,B: real > a,C: real,D: a > complex,E: a > a,F: a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_a_complex_real @ A @ B @ C )
        = ( comp_a_complex_a @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(36,axiom,
    ! [A: a > complex,B: complex > a,C: complex > complex,D: complex > complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = C )
     => ( ( comp_a1063143865omplex @ A @ ( comp_c274302683omplex @ B @ D ) )
        = ( comp_c130555887omplex @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_rewriteL__comp__comp) ).

thf(464,plain,
    ! [A: a > complex,B: complex > a,C: complex > complex,D: complex > complex] :
      ( ( ( comp_a1063143865omplex @ A @ B )
        = C )
     => ( ( comp_a1063143865omplex @ A @ ( comp_c274302683omplex @ B @ D ) )
        = ( comp_c130555887omplex @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(8,axiom,
    ! [A: complex > a] :
      ( ( comp_a_a_complex @ id_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_fun_Omap__id) ).

thf(369,plain,
    ! [A: complex > a] :
      ( ( comp_a_a_complex @ id_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(78,axiom,
    ( ( comp_a_a_complex @ id_a )
    = id_complex_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_fun_Omap__id0) ).

thf(607,plain,
    ( ( comp_a_a_complex @ id_a )
    = id_complex_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(295,axiom,
    ! [A: complex > a,B: real > complex] :
      ( ( path_pathfinish_a @ ( comp_complex_a_real @ A @ B ) )
      = ( A @ ( path_p769714271omplex @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_pathfinish__compose) ).

thf(1320,plain,
    ! [A: complex > a,B: real > complex] :
      ( ( path_pathfinish_a @ ( comp_complex_a_real @ A @ B ) )
      = ( A @ ( path_p769714271omplex @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(37,axiom,
    ! [A: a > complex,B: set_a,C: set_complex,D: complex > a,E: set_a] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( bij_betw_complex_a @ D @ C @ E )
        = ( bij_betw_a_a @ ( comp_complex_a_a @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_bij__betw__comp__iff) ).

thf(469,plain,
    ! [A: a > complex,B: set_a,C: set_complex,D: complex > a,E: set_a] :
      ( ( bij_betw_a_complex @ A @ B @ C )
     => ( ( bij_betw_complex_a @ D @ C @ E )
        = ( bij_betw_a_a @ ( comp_complex_a_a @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(1,conjecture,
    ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
    = ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
   != ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(354,plain,
    ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
   != ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(175,axiom,
    ! [A: complex > a,B: a] :
      ( ( bij_betw_complex_a @ A @ top_top_set_complex @ top_top_set_a )
     => ~ ! [C: complex] :
            ( ( B
              = ( A @ C ) )
           => ~ ! [D: complex] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_bij__pointE) ).

thf(923,plain,
    ! [A: complex > a,B: a] :
      ( ( bij_betw_complex_a @ A @ top_top_set_complex @ top_top_set_a )
     => ~ ! [C: complex] :
            ( ( B
              = ( A @ C ) )
           => ~ ! [D: complex] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(345,axiom,
    bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ top_top_set_complex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_complex__of__bij) ).

thf(1490,plain,
    bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ top_top_set_complex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(321,axiom,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( path_pathstart_a @ ( comp_complex_a_real @ A @ B ) )
        = ( A @ ( path_p797330068omplex @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_pathstart__linear__image__eq) ).

thf(1416,plain,
    ! [A: complex > a,B: real > complex] :
      ( ( real_V1327653935plex_a @ A )
     => ( ( path_pathstart_a @ ( comp_complex_a_real @ A @ B ) )
        = ( A @ ( path_p797330068omplex @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(122,axiom,
    ! [A: real > a,B: a > a] :
      ( ( real_V779700657real_a @ A )
     => ( ( real_V202220639ar_a_a @ B )
       => ( real_V779700657real_a @ ( comp_a_a_real @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_linear__compose) ).

thf(755,plain,
    ! [A: real > a,B: a > a] :
      ( ( real_V779700657real_a @ A )
     => ( ( real_V202220639ar_a_a @ B )
       => ( real_V779700657real_a @ ( comp_a_a_real @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(338,axiom,
    ! [A: real > complex] :
      ( ( path_arc_complex @ A )
     => ( ( path_p769714271omplex @ A )
       != ( path_p797330068omplex @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_arc__distinct__ends) ).

thf(1468,plain,
    ! [A: real > complex] :
      ( ( path_arc_complex @ A )
     => ( ( path_p769714271omplex @ A )
       != ( path_p797330068omplex @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(33,axiom,
    ! [A: a > a,B: a > a,C: a > a,D: a] :
      ( ( ( comp_a_a_a @ A @ B )
        = ( comp_a_a_a @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_comp__eq__id__dest) ).

thf(454,plain,
    ! [A: a > a,B: a > a,C: a > a,D: a] :
      ( ( ( comp_a_a_a @ A @ B )
        = ( comp_a_a_a @ id_a @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(164,axiom,
    ! [A: complex > a,B: real > complex,C: real,D: real > a,E: real > real,F: a > a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_complex_a_real @ ( comp_a_a_complex @ F @ A ) @ B @ C )
        = ( comp_real_a_real @ ( comp_a_a_real @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_type__copy__map__cong0) ).

thf(882,plain,
    ! [A: complex > a,B: real > complex,C: real,D: real > a,E: real > real,F: a > a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp_complex_a_real @ ( comp_a_a_complex @ F @ A ) @ B @ C )
        = ( comp_real_a_real @ ( comp_a_a_real @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(190,axiom,
    ! [A: complex > a,B: a > complex,C: a,D: complex > a,E: a > complex,F: a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_complex_a_a @ A @ B @ C )
        = ( comp_complex_a_a @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_comp__cong) ).

thf(972,plain,
    ! [A: complex > a,B: a > complex,C: a,D: complex > a,E: a > complex,F: a] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ F ) ) )
     => ( ( comp_complex_a_a @ A @ B @ C )
        = ( comp_complex_a_a @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(178,axiom,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( inj_on_real_a @ A @ top_top_set_real )
       => ( ( path_arc_a @ ( comp_real_a_real @ A @ B ) )
          = ( path_arc_real @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_arc__linear__image__eq) ).

thf(935,plain,
    ! [A: real > a,B: real > real] :
      ( ( real_V779700657real_a @ A )
     => ( ( inj_on_real_a @ A @ top_top_set_real )
       => ( ( path_arc_a @ ( comp_real_a_real @ A @ B ) )
          = ( path_arc_real @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(201,axiom,
    ! [A: real > real,B: set_real,C: set_real,D: real > a,E: set_a] :
      ( ( bij_betw_real_real @ A @ B @ C )
     => ( ( bij_betw_real_a @ D @ C @ E )
        = ( bij_betw_real_a @ ( comp_real_a_real @ D @ A ) @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_bij__betw__comp__iff) ).

thf(1009,plain,
    ! [A: real > real,B: set_real,C: set_real,D: real > a,E: set_a] :
      ( ( bij_betw_real_real @ A @ B @ C )
     => ( ( bij_betw_real_a @ D @ C @ E )
        = ( bij_betw_real_a @ ( comp_real_a_real @ D @ A ) @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(6638,plain,
    $false,
    inference(cvc4,[status(thm)],[1036,1337,1190,846,628,1110,481,683,1068,1443,994,1422,379,614,1173,523,1158,582,873,1205,1426,385,1137,797,913,538,1458,670,1222,930,1095,1196,898,841,1475,436,1254,719,785,372,504,1264,1455,1323,619,1087,1479,1347,1013,881,1100,1302,789,1450,591,1040,646,966,1373,443,1020,574,1377,877,956,1072,1119,660,988,1405,1201,1104,527,1169,687,678,1438,1199,761,381,366,1311,714,942,439,1047,798,778,1042,1355,862,598,1502,561,693,484,361,879,830,710,1106,551,1128,1402,1360,1270,1064,1227,725,1006,356,869,499,1397,519,742,578,697,1234,1329,1160,1182,1461,901,642,637,489,1446,970,1292,933,622,393,997,701,654,1150,1478,569,1429,792,508,586,765,1054,558,1071,953,1185,412,1251,1219,1273,856,745,601,750,1510,1146,430,1154,423,1389,772,904,975,545,1488,787,1058,1332,1090,804,704,1464,604,1194,406,1117,736,990,567,1122,1307,681,1408,477,811,1471,758,535,609,1162,848,895,964,626,1344,769,462,1112,494,1080,1177,1381,521,983,827,1496,851,1000,1435,473,1166,944,1420,374,1277,1018,553,458,836,1049,490,675,1203,1208,589,663,548,939,1340,776,855,640,1025,414,1368,712,1003,690,1516,1225,707,409,1230,1484,1499,1432,1452,502,840,1262,576,808,359,907,1257,1141,656,1284,727,978,446,595,497,1240,1412,1126,1390,1289,1108,1316,450,363,556,1216,891,1276,1326,699,517,1062,390,632,1244,781,961,813,1385,946,1101,731,418,1077,1212,1309,1442,1045,1030,1491,433,510,667,1294,383,1513,1133,1280,833,950,1395,818,1248,865,767,886,918,801,1363,1314,1033,400,395,740,1236,1268,427,860,644,908,723,822,1299,1505,1352,464,369,607,1320,469,354,923,1490,1416,755,1468,454,882,972,935,1009]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ITP148^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n025.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Sat May 18 18:32:54 EDT 2024
% 0.17/0.39  % CPUTime  : 
% 1.02/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.07/1.18  % [INFO] 	 Parsing done (268ms). 
% 2.07/1.19  % [INFO] 	 Running in sequential loop mode. 
% 2.78/1.42  % [INFO] 	 eprover registered as external prover. 
% 2.78/1.42  % [INFO] 	 cvc4 registered as external prover. 
% 2.78/1.43  % [INFO] 	 Scanning for conjecture ... 
% 3.15/1.53  % [INFO] 	 Found a conjecture (or negated_conjecture) and 354 axioms. Running axiom selection ... 
% 3.61/1.64  % [INFO] 	 Axiom selection finished. Selected 351 axioms (removed 3 axioms). 
% 4.18/1.84  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.26/1.86  % [INFO] 	 Type checking passed. 
% 4.26/1.86  % [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 ... 
% 69.24/27.01  % External prover 'cvc4' found a proof!
% 69.24/27.01  % [INFO] 	 Killing All external provers ... 
% 69.24/27.01  % Time passed: 26461ms (effective reasoning time: 25820ms)
% 69.24/27.01  % 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)>
% 69.24/27.02  % Axioms used in derivation (351): fact_312_bij__pointE, fact_108_rewriteR__comp__comp2, fact_131_rewriteR__comp__comp, fact_128_rewriteR__comp__comp, fact_117_rewriteR__comp__comp2, fact_158_inj__onI, fact_8_comp__apply, fact_87_pathfinish__linear__image, fact_33_comp__assoc, fact_345_comp__eq__id__dest, fact_25_comp__def, fact_15_pathfinish__compose, fact_219_arc__imp__simple__path, fact_273_path__rectpath, fact_339_pointfree__idE, fact_56_comp__eq__elim, fact_298_bij__betw__inv, fact_255_path__linear__image__eq, fact_22_complex__of__linear, fact_0_assms_I2_J, fact_42_comp__eq__dest, fact_306_bij__betw__iff__bijections, fact_163_inj__on__cong, fact_195_fun_Oinj__map, fact_199_fun_Oinj__map, fact_183_inj__on__imageI2, fact_311_o__bij, fact_61_comp__cong, fact_39_comp__assoc, fact_318_bij__betw__trans, fact_300_bij__betw__cong, fact_177_inj__compose, fact_164_inj__on__eq__iff, fact_16_pathstart__compose, fact_190_simple__path__linear__image__eq, fact_156_inj__onD, fact_63_comp__cong, fact_52_comp__eq__elim, fact_352_simple__path__imp__path, fact_45_comp__eq__dest, fact_244_fun_Omap__comp, fact_27_comp__def, fact_235_arc__simple__path, fact_78_comp__eq__dest__lhs, fact_173_inj__compose, fact_263_type__copy__map__cong0, fact_307_bij__betw__iff__bijections, fact_292_id__def, fact_230_simple__path__imp__arc, fact_222_arc__distinct__ends, fact_168_inj__on__inverseI, fact_40_comp__assoc, fact_148_injD, fact_157_inj__onD, fact_73_comp__eq__dest__lhs, fact_270_type__copy__map__cong0, fact_150_injI, fact_212_arc__linear__image__eq, fact_246_fun_Omap__comp, fact_334_bij__betw__comp__iff, fact_285_bij__id, fact_225_UNIV__eq__I, fact_134_rewriteR__comp__comp, fact_284_bij__betw__id, fact_79_pathstart__linear__image__eq, fact_105_pathstart__rectpath, fact_309_o__bij, fact_101_linear__compose, fact_259_linear__inj__iff__eq__0, fact_250_complex__of__bij, fact_99_linear__compose, fact_310_o__bij, fact_186_inj__on__imageI2, fact_248_real__of__complex__of, fact_17_pathstart__compose, fact_144_rewriteL__comp__comp, fact_239_fun_Omap__comp, fact_146_rewriteL__comp__comp, fact_49_comp__eq__dest, fact_340_pointfree__idE, fact_226_UNIV__eq__I, fact_1_assms_I1_J, fact_12_pathfinish__compose, fact_114_rewriteR__comp__comp2, fact_66_comp__cong, fact_44_comp__eq__dest, fact_319_bij__betw__trans, fact_80_pathstart__linear__image__eq, fact_123_rewriteL__comp__comp2, fact_32_comp__assoc, fact_2_a1, fact_338_pointfree__idE, fact_238_fun_Omap__comp, fact_314_bij__pointE, fact_193_simple__path__linear__image__eq, fact_95_linear__compose, fact_139_rewriteL__comp__comp, fact_137_rewriteR__comp__comp, fact_85_pathfinish__linear__image, fact_228_UNIV__witness, fact_107_bounded__linear_Obounded__linear, fact_220_arc__imp__simple__path, fact_315_bij__pointE, fact_264_type__copy__map__cong0, fact_41_comp__eq__dest, fact_133_rewriteR__comp__comp, fact_332_bij__betw__comp__iff, fact_54_comp__eq__elim, fact_267_type__copy__map__cong0, fact_308_o__bij, fact_141_rewriteL__comp__comp, fact_77_comp__eq__dest__lhs, fact_109_rewriteR__comp__comp2, fact_323_bij__betw__trans, fact_301_bij__betw__cong, fact_29_comp__def, fact_26_comp__def, fact_342_comp__eq__id__dest, fact_258_path__linear__image__eq, fact_43_comp__eq__dest, fact_69_comp__cong, fact_30_comp__def, fact_322_bij__betw__trans, fact_280_fun_Omap__id, fact_94_linear__compose, fact_236_arc__simple__path, fact_58_comp__eq__elim, fact_210_bounded__linear__def, fact_205_iso__tuple__UNIV__I, fact_348_comp__eq__id__dest, fact_81_pathstart__linear__image__eq, fact_47_comp__eq__dest, fact_132_rewriteR__comp__comp, fact_160_inj__on__def, fact_192_simple__path__linear__image__eq, fact_6_comp__apply, fact_90_bounded__linear_Olinear, fact_281_fun_Omap__id, fact_282_fun_Omap__id, fact_286_bij__id, fact_126_rewriteL__comp__comp2, fact_276_comp__id, fact_38_comp__assoc, fact_278_id__comp, fact_216_real__of__inj, fact_237_fun_Omap__comp, fact_179_inj__compose, fact_89_bounded__linear_Olinear, fact_295_bij__betwE, fact_213_arc__linear__image__eq, fact_337_bij__betw__imp__inj__on, fact_351_inj__on__id, fact_198_fun_Oinj__map, fact_175_inj__compose, fact_257_path__linear__image__eq, fact_70_comp__cong, fact_320_bij__betw__trans, fact_227_UNIV__witness, fact_3_comp__apply, fact_249_real__of__bij, fact_196_fun_Oinj__map, fact_83_pathstart__linear__image__eq, fact_135_rewriteR__comp__comp, fact_289_fun_Omap__id0, fact_271_id__apply, fact_313_bij__pointE, fact_59_comp__eq__elim, fact_82_pathstart__linear__image__eq, fact_71_comp__eq__dest__lhs, fact_151_injI, fact_119_rewriteL__comp__comp2, fact_221_arc__distinct__ends, fact_169_inj__on__inverseI, fact_232_simple__path__eq__arc, fact_321_bij__betw__trans, fact_13_pathfinish__compose, fact_120_rewriteL__comp__comp2, fact_50_comp__eq__dest, fact_229_simple__path__imp__arc, fact_19_pathstart__compose, fact_149_injD, fact_353_simple__path__imp__path, fact_191_simple__path__linear__image__eq, fact_4_comp__apply, fact_140_rewriteL__comp__comp, fact_272_id__apply, fact_241_fun_Omap__comp, fact_188_inj__on__imageI2, fact_265_type__copy__map__cong0, fact_302_bij__betw__apply, fact_53_comp__eq__elim, fact_324_bij__betw__trans, fact_116_rewriteR__comp__comp2, fact_274_comp__id, fact_176_inj__compose, fact_103__092_060open_062_092_060And_062g_O_Ainj_Acomplex__of_A_092_060Longrightarrow_062_Asimple__path_A_Icomplex__of_A_092_060circ_062_Ag_J_A_061_Asimple__path_Ag_092_060close_062, fact_279_id__comp, fact_336_bij__betw__imp__inj__on, fact_118_rewriteL__comp__comp2, fact_62_comp__cong, fact_287_DEADID_Oin__rel, fact_268_type__copy__map__cong0, fact_100_linear__compose, fact_142_rewriteL__comp__comp, fact_189_simple__path__linear__image__eq, fact_171_inj__compose, fact_31_comp__assoc, fact_296_eq__id__iff, fact_65_comp__cong, fact_165_inj__on__eq__iff, fact_294_bij__betwE, fact_187_inj__on__imageI2, fact_167_inj__on__contraD, fact_111_rewriteR__comp__comp2, fact_283_bij__betw__id, fact_178_inj__compose, fact_204_iso__tuple__UNIV__I, fact_181_inj__on__imageI2, fact_251_linear__injective__left__inverse, fact_145_rewriteL__comp__comp, fact_143_rewriteL__comp__comp, fact_124_rewriteL__comp__comp2, fact_76_comp__eq__dest__lhs, fact_288_DEADID_Oin__rel, fact_37_comp__assoc, fact_344_comp__eq__id__dest, fact_247_complex__of__real__of, fact_303_bij__betw__apply, fact_347_comp__eq__id__dest, fact_84_pathfinish__linear__image, fact_106_bounded__linear_Obounded__linear, fact_93_linear__compose, fact_115_rewriteR__comp__comp2, fact_215_arc__linear__image__eq, fact_88_pathfinish__linear__image, fact_327_bij__betw__comp__iff, fact_125_rewriteL__comp__comp2, fact_64_comp__cong, fact_35_comp__assoc, fact_86_pathfinish__linear__image, fact_253_linear__injective__left__inverse, fact_252_linear__injective__left__inverse, fact_55_comp__eq__elim, fact_28_comp__def, fact_113_rewriteR__comp__comp2, fact_233_simple__path__cases, fact_24_comp__def, fact_60_comp__eq__elim, fact_21_complex__of__bounded__linear, fact_9_comp__apply, fact_5_comp__apply, fact_152_inj__eq, fact_208_bounded__linear_Ointro, fact_98_linear__compose, fact_317_bij__betw__trans, fact_74_comp__eq__dest__lhs, fact_153_inj__eq, fact_346_comp__eq__id__dest, fact_68_comp__cong, fact_207_UNIV__I, fact_129_rewriteR__comp__comp, fact_217_top__set__def, fact_23_comp__def, fact_46_comp__eq__dest, fact_67_comp__cong, fact_201_fun_Oinj__map, fact_194_fun_Oinj__map, fact_174_inj__compose, fact_166_inj__on__contraD, fact_234_simple__path__cases, fact_102_linear__compose, fact_14_pathfinish__compose, fact_260_linear__inj__iff__eq__0, fact_127_rewriteL__comp__comp2, fact_316_bij__betw__trans, fact_20_pathstart__compose, fact_243_fun_Omap__comp, fact_130_rewriteR__comp__comp, fact_138_rewriteL__comp__comp, fact_214_arc__linear__image__eq, fact_333_bij__betw__comp__iff, fact_48_comp__eq__dest, fact_172_inj__compose, fact_277_id__comp, fact_291_fun_Omap__id0, fact_290_fun_Omap__id0, fact_72_comp__eq__dest__lhs, fact_223_bounded__linear_Oaxioms_I2_J, fact_155_inj__def, fact_266_type__copy__map__cong0, fact_36_comp__assoc, fact_122_rewriteL__comp__comp2, fact_154_inj__def, fact_197_fun_Oinj__map, fact_343_comp__eq__id__dest, fact_262_type__copy__map__cong0, fact_254_path__linear__image__eq, fact_231_simple__path__eq__arc, fact_305_bij__betw__id__iff, fact_34_comp__assoc, fact_97_linear__compose, fact_269_type__copy__map__cong0, fact_104_pathfinish__rectpath, fact_256_path__linear__image__eq, fact_96_linear__compose, fact_57_comp__eq__elim, fact_161_inj__on__def, fact_11_pathfinish__compose, fact_335_bij__betw__comp__iff, fact_293_id__def, fact_299_bij__betw__inv, fact_182_inj__on__imageI2, fact_325_bij__betw__trans, fact_328_bij__betw__comp__iff, fact_18_pathstart__compose, fact_218_top__set__def, fact_185_inj__on__imageI2, fact_275_comp__id, fact_7_comp__apply, fact_121_rewriteL__comp__comp2, fact_136_rewriteR__comp__comp, fact_297_eq__id__iff, fact_203_real__of__linear, fact_240_fun_Omap__comp, fact_184_inj__on__imageI2, fact_51_comp__eq__elim, fact_112_rewriteR__comp__comp2, fact_75_comp__eq__dest__lhs, fact_242_fun_Omap__comp, fact_326_bij__betw__comp__iff, fact_304_bij__betw__id__iff, fact_206_UNIV__I, fact_349_arc__imp__path, fact_331_bij__betw__comp__iff, fact_10_comp__apply, fact_245_fun_Omap__comp, fact_350_inj__on__id, fact_329_bij__betw__comp__iff, fact_341_comp__eq__id__dest, fact_261_type__copy__map__cong0, fact_202_real__of__bounded__linear, fact_91_linear__conv__bounded__linear, fact_180_inj__on__imageI2, fact_92_linear__conv__bounded__linear, fact_330_bij__betw__comp__iff, fact_200_fun_Oinj__map, fact_162_inj__on__cong, fact_110_rewriteR__comp__comp2, fact_147_rewriteL__comp__comp, fact_159_inj__onI, fact_170_inj__compose
% 69.24/27.02  % No. of inferences in proof: 706
% 69.24/27.02  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 26461 ms resp. 25820 ms w/o parsing
% 70.76/27.40  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 70.76/27.40  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------