## TPTP Problem File: SEU966^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU966^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Functions)
% Problem  : TPS problem from FUNCTION-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1054 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v4.1.0, 0.00 v4.0.1, 0.50 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   38 (   4 equality;  28 variable)
%            Maximal formula depth :   15 (   6 average)
%            Number of connectives :   31 (   2   ~;   0   |;   4   &;  18   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :   14 (   0 sgn;   9   !;   0   ?;   5   ^)
%                                         (  14   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_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,(
a: \$i )).

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

thf(h,type,(
h: \$i > \$i )).

thf(cTHM196A_pme,conjecture,
( ( ( ( h @ a )
= a )
& ( ( h @ b )
!= a )
& ! [Xf: \$i > \$i,Xg: \$i > \$i] :
( ! [Xx: \$i] :
( ( Xf @ Xx )
= ( Xg @ Xx ) )
=> ( Xf = Xg ) ) )
=> ~ ( ! [Xj: \$i > \$i,Xk: \$i > \$i] :
( ! [Xp: ( \$i > \$i ) > \$o] :
( ( ( Xp
@ ^ [Xu: \$i] : Xu )
& ! [Xj_4: \$i > \$i] :
( ( Xp @ Xj_4 )
=> ( Xp
@ ^ [Xx: \$i] :
( Xj @ ( Xj_4 @ Xx ) ) ) ) )
=> ( Xp
@ ^ [Xx: \$i] :
( Xk @ ( Xj @ Xx ) ) ) )
=> ! [Xp: ( \$i > \$i ) > \$o] :
( ( ( Xp
@ ^ [Xu: \$i] : Xu )
& ! [Xj_5: \$i > \$i] :
( ( Xp @ Xj_5 )
=> ( Xp
@ ^ [Xx: \$i] :
( Xj @ ( Xj_5 @ Xx ) ) ) ) )
=> ( Xp @ Xk ) ) ) ) )).

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