## TPTP Problem File: SEV049^5.p

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```%------------------------------------------------------------------------------
% File     : SEV049^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM120A
% Version  : Especial.
% English  : Variant of THM120 designed to eliminate trivial proof. Subset is
%            one such relation.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0137 [Bro09]
%          : THM120A [TPS]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   12 (   0 equality;  10 variable)
%            Maximal formula depth :   10 (  10 average)
%            Number of connectives :   12 (   1   ~;   0   |;   2   &;   8   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   0   :;   0   =)
%            Number of variables   :    6 (   2 sgn;   3   !;   1   ?;   2   ^)
%                                         (   6   :;   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
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(cTHM120A_pme,conjecture,(
? [R: ( \$i > \$o ) > ( \$i > \$o ) > \$o] :
( ~ ( R
@ ^ [Xx: \$i] : \$true
@ ^ [Xx: \$i] : \$false )
& ! [Xx: \$i > \$o,Xy: \$i > \$o,Xz: \$i > \$o] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) ) )).

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