%------------------------------------------------------------------------------
% File : LCL653+1.001 : TPTP v8.2.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In K, dia box p0 not provable, size 1
% Version : Especial.
% English : dia box p0 not provable with instances of T, A4, and
% box(dia box dia p0 -> (p0 -> box p0)).
% Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% Source : [Kam08]
% Names : k_t4p_n [BHS00]
% Status : CounterSatisfiable
% Rating : 0.00 v7.0.0, 0.33 v6.4.0, 0.00 v5.5.0, 0.14 v5.4.0, 0.20 v5.3.0, 0.15 v5.2.0, 0.12 v5.0.0, 0.33 v4.1.0, 0.17 v4.0.1, 0.00 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 : 161 ( 93 ~; 61 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 31 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 5 usr; 0 prp; 1-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 47 ( 46 !; 1 ?)
% SPC : FOF_CSA_RFO_NEQ
% Comments : A naive relational encoding of the modal logic problem into
% first-order logic.
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ p4(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ p1(X) ) ) )
& ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y) ) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ! [X] :
( ~ r1(Y,X)
| p3(X) )
| ~ p2(Y) ) )
& p2(X)
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y) ) ) ) ) )
| ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
| ~ p2(X) ) ) )
& ! [X] :
( ~ r1(Y,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)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| p3(X) )
| ~ p2(Y) ) ) ) ) )
| ( ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
| ~ p2(X) )
& ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y) ) ) ) ) )
| ~ ! [Y] :
( ~ r1(X,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)
| ~ ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ! [X] :
( ~ r1(Y,X)
| p1(X) ) )
| ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ~ p1(Y) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ p1(X) ) ) ) ).
%------------------------------------------------------------------------------