## TPTP Problem File: SEV226^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV226^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from REALS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1194 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.60 v7.4.0, 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v5.4.0, 1.00 v5.0.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :  112 (   5 equality;  74 variable)
%            Maximal formula depth :   16 (   6 average)
%            Number of connectives :  104 (   3   ~;   6   |;  18   &;  66   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :   23 (   0 sgn;  17   !;   6   ?;   0   ^)
%                                         (  23   :;   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(c_less_,type,(
c_less_: \$i > \$i > \$o )).

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

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

thf(cBLEDSOE_FENG_SV_IMV_SOL_2_pme,conjecture,(
! [Xf: \$i > \$i,X0: \$i] :
( ( ! [A: \$i > \$o] :
( ( ? [Xl: \$i] :
( A @ Xl )
& ? [Xu: \$i] :
! [Xx: \$i] :
( ( A @ Xx )
=> ( ( c_less_ @ Xx @ Xu )
| ( Xx = Xu ) ) ) )
=> ? [Xl: \$i] :
( ! [Xx: \$i] :
( ( A @ Xx )
=> ( ( c_less_ @ Xx @ Xl )
| ( Xx = Xl ) ) )
& ! [Xy: \$i] :
( ! [Xx: \$i] :
( ( A @ Xx )
=> ( ( c_less_ @ Xx @ Xy )
| ( Xx = Xy ) ) )
=> ( ( c_less_ @ Xl @ Xy )
| ( Xl = Xy ) ) ) ) )
& ! [Xx: \$i] :
( ( c_less_ @ X0 @ ( Xf @ Xx ) )
=> ? [Xt: \$i] :
( ( c_less_ @ Xt @ Xx )
& ! [Xs: \$i] :
( ( ( c_less_ @ Xt @ Xs )
& ( c_less_ @ Xs @ Xx ) )
=> ( c_less_ @ X0 @ ( Xf @ Xs ) ) ) ) )
& ! [Xx: \$i] :
( ( c_less_ @ ( Xf @ Xx ) @ X0 )
=> ? [Xt: \$i] :
( ( c_less_ @ Xx @ Xt )
& ! [Xs: \$i] :
( ( ( c_less_ @ Xs @ Xt )
& ( c_less_ @ Xx @ Xs ) )
=> ( c_less_ @ ( Xf @ Xs ) @ X0 ) ) ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( c_less_ @ Xx @ Xy )
& ( c_less_ @ Xy @ Xz ) )
=> ( c_less_ @ Xx @ Xz ) )
& ! [Xx: \$i] :
~ ( c_less_ @ Xx @ Xx )
& ! [Xx: \$i,Xy: \$i] :
( ( c_less_ @ Xx @ Xy )
| ( c_less_ @ Xy @ Xx )
| ( Xx = Xy ) )
& ( c_less_ @ a @ b )
& ( c_less_ @ ( Xf @ a ) @ X0 )
& ( c_less_ @ X0 @ ( Xf @ b ) ) )
=> ? [Xx: \$i] :
( ( c_less_ @ a @ Xx )
& ( c_less_ @ Xx @ b )
& ~ ( c_less_ @ ( Xf @ Xx ) @ X0 )
& ~ ( c_less_ @ X0 @ ( Xf @ Xx ) ) ) ) )).

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