## TPTP Problem File: SEV183^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV183^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from SET-TOP-ACS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1240 [Bro09]

% Status   : Theorem
% Rating   : 1.00 v6.2.0, 0.86 v6.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    7 (   0 unit;   6 type;   0 defn)
%            Number of atoms       :  183 (   5 equality; 146 variable)
%            Maximal formula depth :   24 (   6 average)
%            Number of connectives :  172 (   0   ~;   4   |;  32   &;  92   @)
%                                         (   0 <=>;  44  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   52 (  52   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6   :;   0   =)
%            Number of variables   :   63 (   4 sgn;  45   !;   8   ?;  10   ^)
%                                         (  63   :;   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(f,type,(
f: ( a > \$o ) > b > \$o )).

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

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

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

thf(cDOMTHM7_pme,conjecture,
( ( ! [Xx: a > \$o] :
( ( cA @ Xx )
=> ( cB @ Xx ) )
& ! [X: ( b > \$o ) > \$o] :
( ! [Xx: b > \$o] :
( ( X @ Xx )
=> ( cC @ Xx ) )
=> ( cC
@ ^ [Xx: b] :
! [S: b > \$o] :
( ( X @ S )
=> ( S @ Xx ) ) ) )
& ! [D: ( b > \$o ) > \$o] :
( ( ! [Xx: b > \$o] :
( ( D @ Xx )
=> ( cC @ Xx ) )
& ? [Xy: b > \$o] :
( D @ Xy )
& ! [Xy: b > \$o,Xz: b > \$o] :
? [Xw: b > \$o] :
( ! [Xx: b] :
( ( Xy @ Xx )
=> ( Xw @ Xx ) )
& ! [Xx: b] :
( ( Xz @ Xx )
=> ( Xw @ Xx ) ) ) )
=> ( cC
@ ^ [Xx: b] :
? [S: b > \$o] :
( ( D @ S )
& ( S @ Xx ) ) ) )
& ! [Xx: a > \$o] :
( ( cA @ Xx )
=> ( cC @ ( 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] :
( ( cC @ 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 ) ) ) ) ) ) ) ) )
=> ? [Xg: ( a > \$o ) > b > \$o] :
( ! [Xx: a > \$o] :
( ( cB @ Xx )
=> ( cC @ ( Xg @ 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] :
( ( cC @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: a > \$o] :
( ( ( cB @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xg @ Xx @ Xx0 ) ) )
=> ( cB @ Xx ) )
& ! [Xx: a > \$o] :
( ( ( cB @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xg @ 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] :
( ( ( cB @ Xy )
& ! [Xx0: a] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xg @ Xy @ Xx0 ) ) ) ) ) ) ) )
& ! [Xx: a > \$o] :
( ( cA @ Xx )
=> ( ( f @ Xx )
= ( Xg @ Xx ) ) ) ) )).

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