## TPTP Problem File: SEV184^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV184^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from SET-TOP-CAT-ACS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1249 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :  278 (  16 equality; 238 variable)
%            Maximal formula depth :   30 (   8 average)
%            Number of connectives :  245 (   0   ~;   8   |;  52   &; 123   @)
%                                         (   8 <=>;  54  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  152 ( 152   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4   :;   0   =)
%            Number of variables   :  116 (   8 sgn;  71   !;  25   ?;  20   ^)
%                                         ( 116   :;   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(b_type,type,(
b: \$tType )).

thf(a_type,type,(
a: \$tType )).

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

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

thf(cDOMTHM16_pme,conjecture,
( ( ! [X: ( a > \$o ) > \$o] :
( ! [Xx: a > \$o] :
( ( X @ Xx )
=> ( cA @ Xx ) )
=> ( cA
@ ^ [Xx: a] :
! [S: a > \$o] :
( ( X @ S )
=> ( S @ Xx ) ) ) )
& ! [D: ( a > \$o ) > \$o] :
( ( ! [Xx: a > \$o] :
( ( D @ Xx )
=> ( cA @ Xx ) )
& ? [Xy: a > \$o] :
( D @ Xy )
& ! [Xy: a > \$o,Xz: a > \$o] :
? [Xw: a > \$o] :
( ! [Xx: a] :
( ( Xy @ Xx )
=> ( Xw @ Xx ) )
& ! [Xx: a] :
( ( Xz @ Xx )
=> ( Xw @ Xx ) ) ) )
=> ( cA
@ ^ [Xx: a] :
? [S: a > \$o] :
( ( D @ S )
& ( S @ Xx ) ) ) )
& ! [X: ( b > \$o ) > \$o] :
( ! [Xx: b > \$o] :
( ( X @ Xx )
=> ( cB @ Xx ) )
=> ( cB
@ ^ [Xx: b] :
! [S: b > \$o] :
( ( X @ S )
=> ( S @ Xx ) ) ) )
& ! [D: ( b > \$o ) > \$o] :
( ( ! [Xx: b > \$o] :
( ( D @ Xx )
=> ( cB @ Xx ) )
& ? [Xy: b > \$o] :
( D @ Xy )
& ! [Xy: b > \$o,Xz: b > \$o] :
? [Xw: b > \$o] :
( ! [Xx: b] :
( ( Xy @ Xx )
=> ( Xw @ Xx ) )
& ! [Xx: b] :
( ( Xz @ Xx )
=> ( Xw @ Xx ) ) ) )
=> ( cB
@ ^ [Xx: b] :
? [S: b > \$o] :
( ( D @ S )
& ( S @ Xx ) ) ) ) )
=> ( ! [X: ( ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o ) > \$o] :
( ! [Xx: ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o] :
( ( X @ Xx )
=> ? [Xx0: a > \$o] :
( ( cA @ Xx0 )
& ? [Xy: b > \$o] :
( ( cB @ Xy )
& ! [Xr: ( a > \$o ) > ( b > \$o ) > \$o] :
( ( Xx @ Xr )
<=> ? [Xd: a > \$o,Xe: b > \$o] :
( ! [X0: ( a > \$o ) > \$o] :
( ( ( X0
@ ^ [Xy0: a] : \$false )
& ! [Xx1: a > \$o] :
( ( X0 @ Xx1 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X0
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X0 @ Xd ) )
& ! [Xx1: a] :
( ( Xd @ Xx1 )
=> ( Xx0 @ Xx1 ) )
& ! [X0: ( b > \$o ) > \$o] :
( ( ( X0
@ ^ [Xy0: b] : \$false )
& ! [Xx1: b > \$o] :
( ( X0 @ Xx1 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X0
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X0 @ Xe ) )
& ! [Xx1: b] :
( ( Xe @ Xx1 )
=> ( Xy @ Xx1 ) )
& ! [Xu: a > \$o,Xv: b > \$o] :
( ( Xr @ Xu @ Xv )
<=> ( ( Xd = Xu )
& ( Xe = Xv ) ) ) ) ) ) ) )
=> ? [Xx: a > \$o] :
( ( cA @ Xx )
& ? [Xy: b > \$o] :
( ( cB @ Xy )
& ! [Xr: ( a > \$o ) > ( b > \$o ) > \$o] :
( ! [S: ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o] :
( ( X @ S )
=> ( S @ Xr ) )
<=> ? [Xd: a > \$o,Xe: b > \$o] :
( ! [X0: ( a > \$o ) > \$o] :
( ( ( X0
@ ^ [Xy0: a] : \$false )
& ! [Xx0: a > \$o] :
( ( X0 @ Xx0 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X0
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X0 @ Xd ) )
& ! [Xx0: a] :
( ( Xd @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [X0: ( b > \$o ) > \$o] :
( ( ( X0
@ ^ [Xy0: b] : \$false )
& ! [Xx0: b > \$o] :
( ( X0 @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X0
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X0 @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) )
& ! [Xu: a > \$o,Xv: b > \$o] :
( ( Xr @ Xu @ Xv )
<=> ( ( Xd = Xu )
& ( Xe = Xv ) ) ) ) ) ) ) )
& ! [D: ( ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o ) > \$o] :
( ( ! [Xx: ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o] :
( ( D @ Xx )
=> ? [Xx0: a > \$o] :
( ( cA @ Xx0 )
& ? [Xy: b > \$o] :
( ( cB @ Xy )
& ! [Xr: ( a > \$o ) > ( b > \$o ) > \$o] :
( ( Xx @ Xr )
<=> ? [Xd: a > \$o,Xe: b > \$o] :
( ! [X: ( a > \$o ) > \$o] :
( ( ( X
@ ^ [Xy0: a] : \$false )
& ! [Xx1: a > \$o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xd ) )
& ! [Xx1: a] :
( ( Xd @ Xx1 )
=> ( Xx0 @ Xx1 ) )
& ! [X: ( b > \$o ) > \$o] :
( ( ( X
@ ^ [Xy0: b] : \$false )
& ! [Xx1: b > \$o] :
( ( X @ Xx1 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx1: b] :
( ( Xe @ Xx1 )
=> ( Xy @ Xx1 ) )
& ! [Xu: a > \$o,Xv: b > \$o] :
( ( Xr @ Xu @ Xv )
<=> ( ( Xd = Xu )
& ( Xe = Xv ) ) ) ) ) ) ) )
& ? [Xy: ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o] :
( D @ Xy )
& ! [Xy: ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o,Xz: ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o] :
? [Xw: ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o] :
( ! [Xx: ( a > \$o ) > ( b > \$o ) > \$o] :
( ( Xy @ Xx )
=> ( Xw @ Xx ) )
& ! [Xx: ( a > \$o ) > ( b > \$o ) > \$o] :
( ( Xz @ Xx )
=> ( Xw @ Xx ) ) ) )
=> ? [Xx: a > \$o] :
( ( cA @ Xx )
& ? [Xy: b > \$o] :
( ( cB @ Xy )
& ! [Xr: ( a > \$o ) > ( b > \$o ) > \$o] :
( ? [S: ( ( a > \$o ) > ( b > \$o ) > \$o ) > \$o] :
( ( D @ S )
& ( S @ Xr ) )
<=> ? [Xd: a > \$o,Xe: b > \$o] :
( ! [X: ( a > \$o ) > \$o] :
( ( ( X
@ ^ [Xy0: a] : \$false )
& ! [Xx0: a > \$o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xd ) )
& ! [Xx0: a] :
( ( Xd @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [X: ( b > \$o ) > \$o] :
( ( ( X
@ ^ [Xy0: b] : \$false )
& ! [Xx0: b > \$o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) )
& ! [Xu: a > \$o,Xv: b > \$o] :
( ( Xr @ Xu @ Xv )
<=> ( ( Xd = Xu )
& ( Xe = Xv ) ) ) ) ) ) ) ) ) )).

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