## TPTP Problem File: SEV253^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV253^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from SETS-OF-SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1102 [Bro09]

% Status   : Theorem
% Rating   : 1.00 v5.2.0, 0.75 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   43 (   0 equality;  34 variable)
%            Maximal formula depth :   12 (   6 average)
%            Number of connectives :   44 (   2   ~;   0   |;   9   &;  23   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :   19 (   0 sgn;  11   !;   5   ?;   3   ^)
%                                         (  19   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%------------------------------------------------------------------------------
thf(cL,type,(
cL: ( \$i > \$o ) > \$o )).

thf(cG,type,(
cG: ( \$i > \$o ) > \$o )).

thf(cF,type,(
cF: ( ( \$i > \$o ) > \$o ) > \$o )).

thf(cTHM630_pme,conjecture,
( ( ! [C: ( \$i > \$o ) > \$o] :
( ( ! [Xx: \$i > \$o] :
( ( C @ Xx )
=> ( cG @ Xx ) )
& ! [Xx: \$i] :
? [Y: \$i > \$o] :
( ( C @ Y )
& ( Y @ Xx ) ) )
=> ? [D: ( \$i > \$o ) > \$o] :
( ( cF @ D )
& ! [Xx: \$i > \$o] :
( ( D @ Xx )
=> ( C @ Xx ) )
& ! [Xx: \$i] :
? [Y: \$i > \$o] :
( ( D @ Y )
& ( Y @ Xx ) ) ) )
& ! [C: ( \$i > \$o ) > \$o] :
( ( cF @ C )
=> ( cF
@ ^ [U: \$i > \$o] :
( C
@ ^ [Xx: \$i] :
~ ( U @ Xx ) ) ) )
& ! [B: ( \$i > \$o ) > \$o] :
( ( ( cF @ B )
& ! [Xx: \$i > \$o] :
( ( B @ Xx )
=> ( cL @ Xx ) ) )
=> ? [Xm: \$i] :
! [Z: \$i > \$o] :
( ( B @ Z )
=> ( Z @ Xm ) ) )
& ! [Z: \$i > \$o] :
( ( cL @ Z )
=> ( cG
@ ^ [Xx: \$i] :
~ ( Z @ Xx ) ) ) )
=> ? [Xa: \$i] :
! [Z: \$i > \$o] :
( ( cL @ Z )
=> ( Z @ Xa ) ) )).

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