## TPTP Problem File: SEU912^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU912^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from SET-TOP-CATEGORY-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1244 [Bro09]

% Status   : Theorem
% Rating   : 0.89 v7.2.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    9 (   0 unit;   8 type;   0 defn)
%            Number of atoms       :  220 (   6 equality; 168 variable)
%            Maximal formula depth :   23 (   5 average)
%            Number of connectives :  207 (   0   ~;   6   |;  37   &; 112   @)
%                                         (   0 <=>;  52  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   51 (  51   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8   :;   0   =)
%            Number of variables   :   69 (   6 sgn;  51   !;   6   ?;  12   ^)
%                                         (  69   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          :
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(b_type,type,(
b: \$tType )).

thf(c_type,type,(
c: \$tType )).

thf(f,type,(
f: ( a > \$o ) > b > \$o )).

thf(g,type,(
g: ( b > \$o ) > c > \$o )).

thf(cA,type,(
cA: ( a > \$o ) > \$o )).

thf(cC,type,(
cC: ( c > \$o ) > \$o )).

thf(cB,type,(
cB: ( b > \$o ) > \$o )).

thf(cDOMTHM9_pme,conjecture,
( ( ! [Xx: a > \$o] :
( ( cA @ Xx )
=> ( cB @ ( f @ Xx ) ) )
& ! [Xe: b > \$o] :
( ( ! [X: ( b > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: b] : \$false )
& ! [Xx: b > \$o] :
( ( X @ Xx )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx: b] :
( ( Xe @ Xx )
=> ? [S: b > \$o] :
( ( cB @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: a > \$o] :
( ( ( cA @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( f @ Xx @ Xx0 ) ) )
=> ( cA @ Xx ) )
& ! [Xx: a > \$o] :
( ( ( cA @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( f @ Xx @ Xx0 ) ) )
=> ? [Xe0: a > \$o] :
( ! [X: ( a > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: a] : \$false )
& ! [Xx0: a > \$o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx0: a] :
( ( Xe0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > \$o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cA @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( f @ Xy @ Xx0 ) ) ) ) ) ) ) )
& ! [Xx: b > \$o] :
( ( cB @ Xx )
=> ( cC @ ( g @ Xx ) ) )
& ! [Xe: c > \$o] :
( ( ! [X: ( c > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: c] : \$false )
& ! [Xx: c > \$o] :
( ( X @ Xx )
=> ! [Xt: c] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: c] :
( ( Xx @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx: c] :
( ( Xe @ Xx )
=> ? [S: c > \$o] :
( ( cC @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: b > \$o] :
( ( ( cB @ Xx )
& ! [Xx0: c] :
( ( Xe @ Xx0 )
=> ( g @ Xx @ Xx0 ) ) )
=> ( cB @ Xx ) )
& ! [Xx: b > \$o] :
( ( ( cB @ Xx )
& ! [Xx0: c] :
( ( Xe @ Xx0 )
=> ( g @ Xx @ Xx0 ) ) )
=> ? [Xe0: b > \$o] :
( ! [X: ( b > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: b] : \$false )
& ! [Xx0: b > \$o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx0: b] :
( ( Xe0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: b > \$o] :
( ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cB @ Xy )
& ! [Xx0: c] :
( ( Xe @ Xx0 )
=> ( g @ Xy @ Xx0 ) ) ) ) ) ) ) ) )
=> ( ! [Xx: a > \$o] :
( ( cA @ Xx )
=> ( cC @ ( g @ ( f @ Xx ) ) ) )
& ! [Xe: c > \$o] :
( ( ! [X: ( c > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: c] : \$false )
& ! [Xx: c > \$o] :
( ( X @ Xx )
=> ! [Xt: c] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: c] :
( ( Xx @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx: c] :
( ( Xe @ Xx )
=> ? [S: c > \$o] :
( ( cC @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: a > \$o] :
( ( ( cA @ Xx )
& ! [Xx0: c] :
( ( Xe @ Xx0 )
=> ( g @ ( f @ Xx ) @ Xx0 ) ) )
=> ( cA @ Xx ) )
& ! [Xx: a > \$o] :
( ( ( cA @ Xx )
& ! [Xx0: c] :
( ( Xe @ Xx0 )
=> ( g @ ( f @ Xx ) @ Xx0 ) ) )
=> ? [Xe0: a > \$o] :
( ! [X: ( a > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: a] : \$false )
& ! [Xx0: a > \$o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx0: a] :
( ( Xe0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > \$o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cA @ Xy )
& ! [Xx0: c] :
( ( Xe @ Xx0 )
=> ( g @ ( f @ Xy ) @ Xx0 ) ) ) ) ) ) ) ) ) )).

%------------------------------------------------------------------------------
```