## TPTP Problem File: SYO222^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO222^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM115A
% Version  : Especial.
% English  : Sunil's example.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0352 [Bro09]
%          : THM115 [TPS]
%          : THM115A [TPS]

% Status   : Theorem
% Rating   : 0.67 v7.2.0, 0.62 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   17 (   2 equality;   9 variable)
%            Maximal formula depth :   10 (   4 average)
%            Number of connectives :   12 (   0   ~;   0   |;   2   &;   7   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :    5 (   0 sgn;   3   !;   2   ?;   0   ^)
%                                         (   5   :;   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(f,type,(
f: \$i > \$i )).

thf(a,type,(
a: \$i )).

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

thf(cTHM115A,conjecture,(
? [A: \$i > \$o] :
( ! [Xx: \$i] :
( ( A @ ( f @ Xx ) )
=> ( cP @ Xx ) )
& ( ( ( cP @ a )
& ! [Xx: \$i,Xy: \$i] :
( ( ( f @ Xx )
= ( f @ Xy ) )
=> ( Xx = Xy ) ) )
=> ? [Xz: \$i] :
( A @ Xz ) ) ) )).

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