## TPTP Problem File: LCL636+1.001.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : LCL636+1.001 : TPTP v8.1.0. Released v4.0.0.
% Domain   : Logic Calculi (Modal Logic)
% Problem  : In K, the branching formula made provable, size 1
% Version  : Especial.
% English  : The branching formula plus a negation symbol in front and an
%            additional subformula to make the formula provable.

% Refs     : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
%          : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% Source   : [Kam08]
% Names    : k_branch_p [BHS00]

% Status   : Theorem
% Rating   : 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.12 v5.4.0, 0.09 v5.3.0, 0.17 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :   69 (   0 equ)
%            Maximal formula atoms :   69 (  69 avg)
%            Number of connectives :  129 (  61   ~;  41   |;  27   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (  19 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   6 usr;   0 prp; 1-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   15 (  14   !;   1   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments : A naive relational encoding of the modal logic problem into
%            first-order logic.
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
| ~ ( ! [Y] :
( ~ r1(X,Y)
| ( ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p2(X)
& ~ p102(X)
& p101(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
& ~ p102(X)
& p101(X) ) ) )
| ~ ( ~ p101(Y)
& p100(Y) ) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p2(X)
| ~ p101(X) )
| p2(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ p101(X) )
| ~ p2(Y) ) )
| ~ p101(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p1(X)
| ~ p100(X) )
| p1(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ p100(X) )
| ~ p1(Y) ) )
| ~ p100(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) )
& ( ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ p2(Y)
& ~ p102(Y)
& p101(Y) ) )
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
& ~ p102(Y)
& p101(Y) ) ) )
| ~ ( ~ p101(X)
& p100(X) ) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y)
| ~ p101(Y) )
| p2(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p2(Y)
| ~ p101(Y) )
| ~ p2(X) ) )
| ~ p101(X) )
& ( ( ( ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y)
| ~ p100(Y) )
| p1(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p1(Y)
| ~ p100(Y) )
| ~ p1(X) ) )
| ~ p100(X) )
& ( p101(X)
| ~ p102(X) )
& ( p100(X)
| ~ p101(X) )
& ~ p101(X)
& p100(X) ) ) ).

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