%------------------------------------------------------------------------------
% File     : SYP118^1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Syntactic
% Problem  : Associativity of function composition
% Version  : Especial.
% English  :

% Refs     :
% Source   : [TPTP]
% Names    : 001 [TPTP]

% Status   : Theorem
% Rating   : 0.25 v9.3.0
% Syntax   : Number of formulae    :    3 (   2 unt;   1 typ;   0 def)
%            Number of atoms       :    2 (   2 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   27 (   0   ~;   0   |;   0   &;  27   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   7 avg)
%            Number of types       :    0 (   0 usr)
%            Number of type decls  :    1 (   1 !>P;   0 !>D)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   1 usr;   0 con; 2-6 aty)
%            Number of variables   :   16 (   1   ^;  12   !;   0   ?;  16   :)
%                                         (   3  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR_NDT

% Comments : Originally from HOL Light
%------------------------------------------------------------------------------
thf(o,type,
    o: 
      !>[B: $tType,A: $tType,C: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).

thf('trivia/o_DEF_',axiom,
    ! [C: $tType,B: $tType,A: $tType,F: B > C,G: A > B] :
      ( ( o @ B @ A @ C @ F @ G )
      = ( ^ [X: A] : ( F @ ( G @ X ) ) ) ) ).

thf('trivia/o_ASSOC_',conjecture,
    ! [D: $tType,C: $tType,A: $tType,B: $tType,F: C > D,G: B > C,H: A > B] :
      ( ( o @ C @ A @ D @ F @ ( o @ B @ A @ C @ G @ H ) )
      = ( o @ B @ A @ D @ ( o @ C @ B @ D @ F @ G ) @ H ) ) ).

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