## TPTP Problem File: ALG294^5.p

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```%------------------------------------------------------------------------------
% File     : ALG294^5 : TPTP v8.0.0. 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_1238 [Bro09]

% Status   : Theorem
% Rating   : 0.55 v7.5.0, 0.71 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    8 (   0 unt;   7 typ;   0 def)
%            Number of atoms       :   29 (  21 equ;   0 cnn)
%            Maximal formula atoms :   15 (  29 avg)
%            Number of connectives :  148 (   1   ~;   5   |;  29   &;  89   @)
%                                         (   3 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  24 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   54 (   8   ^  29   !;  17   ?;  54   :)
% 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(cR,type,
cR: a > a ).

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

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

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

thf(cZ,type,
cZ: a ).

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

thf(cPU_X2310B_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 ) ) ) )
& ! [X: a > \$o] :
( ? [Xt: a] :
( ( X @ Xt )
& ! [Xu: a] :
( ( X @ Xu )
=> ( X @ ( cL @ Xu ) ) ) )
=> ( X @ cZ ) )
& ! [X: a > \$o,Xz: a] :
( ( cPHI @ X @ Xz )
<=> ? [Xx: a] :
( ! [Xx_14: a] :
( ! [X0: a > \$o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xx_14 ) ) )
=> ( X @ Xx_14 ) )
& ( cPHI
@ ^ [Xy: a] :
! [X0: a > \$o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xy ) ) )
@ Xz ) ) )
& ! [X: a > \$o,Xz: a] :
( ( cPSI @ X @ Xz )
<=> ? [Xx: a] :
( ! [Xx_15: a] :
( ! [X0: a > \$o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xx_15 ) ) )
=> ( X @ Xx_15 ) )
& ( cPSI
@ ^ [Xy: a] :
! [X0: a > \$o] :
( ( ( X0 @ Xx )
& ! [Xz0: a] :
( ( X0 @ Xz0 )
=> ( X0 @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X0 @ Xv )
& ( ( cR @ Xv )
= Xy ) ) )
@ Xz ) ) ) )
=> ( ( ^ [Xu: a] :
( ( Xu = cZ )
| ? [Xx: a,Xy: a] :
( ( Xu
= ( cP @ Xx @ Xy ) )
& ( ( cPHI
@ ^ [Xy0: a] :
! [X: a > \$o] :
( ( ( X @ Xx )
& ! [Xz: a] :
( ( X @ Xz )
=> ( X @ ( cL @ Xz ) ) ) )
=> ? [Xv: a] :
( ( X @ Xv )
& ( ( cR @ Xv )
= Xy0 ) ) )
@ Xy )
| ( cPSI
@ ^ [Xy0: a] :
! [X: a > \$o] :
( ( ( X @ Xx )
& ! [Xz: a] :
( ( X @ Xz )
=> ( X @ ( cL @ Xz ) ) ) )
=> ? [Xv: a] :
( ( X @ Xv )
& ( ( cR @ Xv )
= Xy0 ) ) )
@ Xy ) ) ) ) )
= ( ^ [Xz: a] :
( ( Xz = cZ )
| ? [Xx: a,Xy: a] :
( ( Xz
= ( cP @ Xx @ Xy ) )
& ( cPHI
@ ^ [Xy0: a] :
! [X: a > \$o] :
( ( ( X @ Xx )
& ! [Xz0: a] :
( ( X @ Xz0 )
=> ( X @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X @ Xv )
& ( ( cR @ Xv )
= Xy0 ) ) )
@ Xy ) )
| ( Xz = cZ )
| ? [Xx: a,Xy: a] :
( ( Xz
= ( cP @ Xx @ Xy ) )
& ( cPSI
@ ^ [Xy0: a] :
! [X: a > \$o] :
( ( ( X @ Xx )
& ! [Xz0: a] :
( ( X @ Xz0 )
=> ( X @ ( cL @ Xz0 ) ) ) )
=> ? [Xv: a] :
( ( X @ Xv )
& ( ( cR @ Xv )
= Xy0 ) ) )
@ Xy ) ) ) ) ) ) ).

%------------------------------------------------------------------------------
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