%------------------------------------------------------------------------------
% File : LCL640+1.001 : TPTP v8.2.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In K, formula with A4 and Dum leading to Dum, size 1
% Version : Especial.
% English : A4{box(p0->boxp0) -> p0/p0} & box A4 & Dum & Dum{p0->box p0/p0}
% -> Dum1.
% Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% Source : [Kam08]
% Names : k_dum_p [BHS00]
% Status : Theorem
% Rating : 0.00 v8.2.0, 0.07 v7.5.0, 0.00 v7.4.0, 0.12 v7.3.0, 0.00 v6.4.0, 0.07 v6.3.0, 0.08 v6.2.0, 0.09 v6.1.0, 0.24 v6.0.0, 0.50 v5.5.0, 0.38 v5.4.0, 0.39 v5.2.0, 0.21 v5.1.0, 0.29 v5.0.0, 0.40 v4.1.0, 0.44 v4.0.1, 0.42 v4.0.0
% Syntax : Number of formulae : 1 ( 0 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 62 ( 62 avg)
% Number of connectives : 123 ( 62 ~; 58 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 27 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 35 ( 34 !; 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)
| ( ( ! [X] :
( ~ r1(Y,X)
| p1(X) )
| ~ p1(Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| p1(X) )
| ~ p1(Y) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| p1(Y) )
| ~ p1(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| p1(Y) )
| ~ p1(X) )
| ~ ( ! [X] :
( ~ r1(Y,X)
| p1(X) )
| ~ p1(Y) ) ) ) )
& ( p1(Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| p1(X) )
| ~ p1(Y) ) ) )
& ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| p1(X) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
& ( ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| p1(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| p1(Y) )
| ~ p1(X) ) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| p1(X) )
| ~ p1(Y) ) ) ) ) )
| ~ ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| p1(X) )
| ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| p1(X) )
| ~ p1(Y) ) ) ) ) ).
%------------------------------------------------------------------------------