## TPTP Problem File: SYO339^5.p

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```%------------------------------------------------------------------------------
% File     : SYO339^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1155 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   79 (   0 equality;  73 variable)
%            Maximal formula depth :   17 (   7 average)
%            Number of connectives :   78 (   0   ~;   0   |;  14   &;  54   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   18 (   0 sgn;  12   !;   6   ?;   0   ^)
%                                         (  18   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_NEQ_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          :
%------------------------------------------------------------------------------
thf(b,type,(
b: \$i )).

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

thf(cBLEDSOE_FENG_SV_IMV_SOL,conjecture,(
! [Xr: \$i > \$i > \$o,Xf: \$i > \$i,X0: \$i] :
( ( ! [A: \$i > \$o] :
( ( ? [Xl: \$i] :
( A @ Xl )
& ? [Xu: \$i] :
! [Xx: \$i] :
( ( A @ Xx )
=> ( Xr @ Xx @ Xu ) ) )
=> ? [Xl: \$i] :
( ! [Xx: \$i] :
( ( A @ Xx )
=> ( Xr @ Xx @ Xl ) )
& ! [Xy: \$i] :
( ! [Xx: \$i] :
( ( A @ Xx )
=> ( Xr @ Xx @ Xy ) )
=> ( Xr @ Xl @ Xy ) ) ) )
& ! [Xx: \$i] :
( ( Xr @ X0 @ ( Xf @ Xx ) )
=> ? [Xt: \$i] :
( ( Xr @ Xt @ Xx )
& ! [Xs: \$i] :
( ( ( Xr @ Xt @ Xs )
& ( Xr @ Xs @ Xx ) )
=> ( Xr @ X0 @ ( Xf @ Xs ) ) ) ) )
& ! [Xx: \$i] :
( ( Xr @ ( Xf @ Xx ) @ X0 )
=> ? [Xt: \$i] :
( ( Xr @ Xx @ Xt )
& ! [Xs: \$i] :
( ( ( Xr @ Xs @ Xt )
& ( Xr @ Xx @ Xs ) )
=> ( Xr @ ( Xf @ Xs ) @ X0 ) ) ) )
& ( Xr @ a @ b )
& ( Xr @ ( Xf @ a ) @ X0 )
& ( Xr @ X0 @ ( Xf @ b ) ) )
=> ? [Xx: \$i] :
( ( Xr @ a @ Xx )
& ( Xr @ Xx @ b )
& ( Xr @ ( Xf @ Xx ) @ X0 )
& ( Xr @ X0 @ ( Xf @ Xx ) ) ) ) )).

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