## TPTP Problem File: SEV314^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV314^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from CLOS-SYS-FP-THMS
% Version  : Especial.
% English  : Related to the Knaster-Tarski theorem.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1101 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   51 (   2 equality;  36 variable)
%            Maximal formula depth :   14 (   6 average)
%            Number of connectives :   46 (   0   ~;   0   |;   7   &;  29   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :   16 (   0 sgn;  13   !;   1   ?;   2   ^)
%                                         (  16   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_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(b_type,type,(
b: \$tType )).

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

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

thf(cFP_THM2_pme,conjecture,
( ( ! [S: ( a > b > \$o ) > \$o] :
( ! [Xx: a > b > \$o] :
( ( S @ Xx )
=> ( cCL @ Xx ) )
=> ( cCL
@ ^ [Xa: a,Xb: b] :
! [R: a > b > \$o] :
( ( S @ R )
=> ( R @ Xa @ Xb ) ) ) )
& ! [R: a > b > \$o] :
( ( cCL @ R )
=> ( cCL @ ( cF @ R ) ) )
& ! [R: a > b > \$o,S: a > b > \$o] :
( ( ( cCL @ R )
& ( cCL @ S )
& ! [Xa: a,Xb: b] :
( ( R @ Xa @ Xb )
=> ( S @ Xa @ Xb ) ) )
=> ! [Xa: a,Xb: b] :
( ( cF @ R @ Xa @ Xb )
=> ( cF @ S @ Xa @ Xb ) ) ) )
=> ? [X: a > b > \$o] :
( ( cCL @ X )
& ( ( cF @ X )
= X )
& ! [Y: a > b > \$o] :
( ( ( cCL @ Y )
& ( ( cF @ Y )
= Y ) )
=> ! [Xa: a,Xb: b] :
( ( X @ Xa @ Xb )
=> ( Y @ Xa @ Xb ) ) ) ) )).

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