## TPTP Problem File: ALG290^5.p

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%------------------------------------------------------------------------------
% File     : ALG290^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : General Algebra (Domain theory)
% Problem  : TPS problem from PU-LAMBDA-MODEL-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1190 [Bro09]

% Status   : Theorem
% Rating   : 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    9 (   0 unit;   8 type;   0 defn)
%            Number of atoms       :  101 (  10 equality;  58 variable)
%            Maximal formula depth :   16 (   4 average)
%            Number of connectives :   81 (   1   ~;   2   |;  15   &;  50   @)
%                                         (   1 <=>;  12  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8   :;   0   =)
%            Number of variables   :   25 (   0 sgn;  16   !;   7   ?;   2   ^)
%                                         (  25   :;   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(a_type,type,(
a: \$tType )).

thf(cP,type,(
cP: a > a > a )).

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

thf(cX,type,(
cX: a > \$o )).

thf(cR,type,(
cR: a > a )).

thf(cL,type,(
cL: a > a )).

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

thf(cZ,type,(
cZ: a )).

thf(cPU_X2310A_pme,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [Xx: a,Xy: a] :
( ( cL @ ( cP @ Xx @ Xy ) )
= Xx )
& ! [Xx: a,Xy: a] :
( ( cR @ ( cP @ Xx @ Xy ) )
= Xy )
& ! [Xt: a] :
( ( Xt != cZ )
<=> ( Xt
= ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
& ! [X0: a > \$o] :
( ? [Xt: a] :
( ( X0 @ Xt )
& ! [Xu: a] :
( ( X0 @ Xu )
=> ( X0 @ ( cL @ Xu ) ) ) )
=> ( X0 @ cZ ) ) )
=> ( ( ^ [Xy: a] :
? [Xx: a] :
( ! [Xx_17: a] :
( ! [X0: a > \$o] :
( ( ( X0 @ Xx )
& ! [Xz: a] :
( ( X0 @ Xz )
=> ( X0 @ ( cL @ Xz ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xx_17 ) ) )
=> ( cX @ Xx_17 ) )
& ( ( cF @ ( cP @ Xx @ Xy ) )
| ( cG @ ( cP @ Xx @ Xy ) ) ) ) )
= ( ^ [Xz: a] :
( ? [Xx: a] :
( ! [Xx_18: a] :
( ! [X0: a > \$o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xx_18 ) ) )
=> ( cX @ Xx_18 ) )
& ( cF @ ( cP @ Xx @ Xz ) ) )
| ? [Xx: a] :
( ! [Xx_19: a] :
( ! [X0: a > \$o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xx_19 ) ) )
=> ( cX @ Xx_19 ) )
& ( cG @ ( cP @ Xx @ Xz ) ) ) ) ) ) )).

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