## TPTP Problem File: LCL685+1.001.p

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```%------------------------------------------------------------------------------
% File     : LCL685+1.001 : TPTP v8.1.0. Released v4.0.0.
% Domain   : Logic Calculi (Modal Logic)
% Problem  : In S4, pigeonhole formulae missing a conjunct, size 1
% Version  : Especial.
% English  :

% Refs     : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
%          : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% Source   : [Kam08]
% Names    : s4_ph_n [BHS00]

% Status   : CounterSatisfiable
% Rating   : 0.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   1 unt;   0 def)
%            Number of atoms       :   10 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   15 (   8   ~;   3   |;   3   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   3 usr;   0 prp; 1-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    7 (   6   !;   1   ?)
% SPC      : FOF_CSA_EPR_NEQ

% Comments : A naive relational encoding of the modal logic problem into
%            first-order logic.
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X) ).

fof(transitivity,axiom,
! [X,Y,Z] :
( ( r1(X,Y)
& r1(Y,Z) )
=> r1(X,Z) ) ).

fof(main,conjecture,
~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( p201(X)
& ~ p101(X) ) ) )
| ~ ( p201(X)
& p101(X) ) ) ).

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