%------------------------------------------------------------------------------
% File : LCL681+1.005 : TPTP v9.0.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In S4, in backwards search no way through box and dia, size 5
% 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_md_n [BHS00]
% Status : CounterSatisfiable
% Rating : 0.40 v9.0.0, 0.33 v8.2.0, 0.00 v7.4.0, 0.33 v7.3.0, 0.00 v7.0.0, 0.33 v6.4.0, 0.00 v6.2.0, 0.11 v6.1.0, 0.10 v6.0.0, 0.00 v5.5.0, 0.29 v5.4.0, 0.67 v5.3.0, 0.69 v5.2.0, 0.25 v5.0.0, 0.56 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax : Number of formulae : 3 ( 1 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 103 ( 35 avg)
% Number of connectives : 252 ( 148 ~; 98 |; 5 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 98 ( 35 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 : 59 ( 58 !; 1 ?)
% SPC : FOF_CSA_RFO_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] :
~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y) ) ) ) ) ) ) ) ) )
& ~ p1(Y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ p1(X) ) ) ) ) ) ) ) ) )
& ~ p1(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y) ) ) ) ) ) ) ) ) )
& ~ p1(Y) ) ) ) ) ) ) ) )
| ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ p1(X) ) ) ) ) ) ) ) ) )
& ~ p1(X) )
| p1(X) ) ).
%------------------------------------------------------------------------------