## TPTP Problem File: SEU911^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU911^5 : TPTP v7.0.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from SET-TOP-CATEGORY-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1241 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v4.1.0, 0.00 v4.0.1, 0.50 v4.0.0
% Syntax   : Number of formulae    :    9 (   0 unit;   8 type;   0 defn)
%            Number of atoms       :  201 (   9 equality; 157 variable)
%            Maximal formula depth :   27 (   6 average)
%            Number of connectives :  182 (   0   ~;   6   |;  33   &;  97   @)
%                                         (   1 <=>;  45  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   54 (  54   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8   :;   0   =)
%            Number of variables   :   67 (   7 sgn;  45   !;   8   ?;  14   ^)
%                                         (  67   :;   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_type,type,(
c: \$tType )).

thf(b_type,type,(
b: \$tType )).

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

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

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

thf(cC,type,(
cC: ( c > \$o ) > \$o )).

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

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

thf(cDOMTHM14_pme,conjecture,
( ( ! [Xx: c > \$o] :
( ( cC @ Xx )
=> ( cA @ ( f @ Xx ) ) )
& ! [Xe: a > \$o] :
( ( ! [X: ( a > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: a] : \$false )
& ! [Xx: a > \$o] :
( ( X @ Xx )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx: a] :
( ( Xe @ Xx )
=> ? [S: a > \$o] :
( ( cA @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: c > \$o] :
( ( ( cC @ Xx )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( f @ Xx @ Xx0 ) ) )
=> ( cC @ Xx ) )
& ! [Xx: c > \$o] :
( ( ( cC @ Xx )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( f @ Xx @ Xx0 ) ) )
=> ? [Xe0: c > \$o] :
( ! [X: ( c > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: c] : \$false )
& ! [Xx0: c > \$o] :
( ( X @ Xx0 )
=> ! [Xt: c] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: c] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: c > \$o] :
( ( ( cC @ Xy )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cC @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( f @ Xy @ Xx0 ) ) ) ) ) ) ) )
& ! [Xx: c > \$o] :
( ( cC @ Xx )
=> ( cB @ ( g @ Xx ) ) )
& ! [Xe: b > \$o] :
( ( ! [X: ( b > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: b] : \$false )
& ! [Xx: b > \$o] :
( ( X @ Xx )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx: b] :
( ( Xe @ Xx )
=> ? [S: b > \$o] :
( ( cB @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: c > \$o] :
( ( ( cC @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( g @ Xx @ Xx0 ) ) )
=> ( cC @ Xx ) )
& ! [Xx: c > \$o] :
( ( ( cC @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( g @ Xx @ Xx0 ) ) )
=> ? [Xe0: c > \$o] :
( ! [X: ( c > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: c] : \$false )
& ! [Xx0: c > \$o] :
( ( X @ Xx0 )
=> ! [Xt: c] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: c] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: c > \$o] :
( ( ( cC @ Xy )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cC @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( g @ Xy @ Xx0 ) ) ) ) ) ) ) ) )
=> ! [Xx: c > \$o] :
( ( cC @ Xx )
=> ( ( ^ [Xx0: b] :
? [S: b > \$o] :
( ? [Xr: ( a > \$o ) > ( b > \$o ) > \$o] :
( ? [Xd: a > \$o,Xe: b > \$o] :
( ( ! [X: ( a > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: a] : \$false )
& ! [Xx1: a > \$o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xd ) )
& ! [Xx1: a] :
( ( Xd @ Xx1 )
=> ( f @ Xx @ Xx1 ) )
& ! [X: ( b > \$o ) > \$o] :
( ( ( X
@ ^ [Xy: b] : \$false )
& ! [Xx1: b > \$o] :
( ( X @ Xx1 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx1: b] :
( ( Xe @ Xx1 )
=> ( g @ Xx @ Xx1 ) ) )
=> ! [Xu: a > \$o,Xv: b > \$o] :
( ( Xr @ Xu @ Xv )
<=> ( ( Xu = Xd )
& ( Xv = Xe ) ) ) )
& ( Xr
@ ^ [Xx1: a] : \$false
@ S ) )
& ( S @ Xx0 ) ) )
= ( g @ Xx ) ) ) )).

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