%------------------------------------------------------------------------------
% File : LCL680+1.005 : TPTP v9.0.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In S4, in backward search find a 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_p [BHS00]
% Status : Theorem
% Rating : 0.80 v9.0.0, 0.75 v8.2.0, 0.80 v8.1.0, 0.79 v7.5.0, 0.86 v7.4.0, 0.81 v7.3.0, 0.57 v7.2.0, 0.67 v7.1.0, 0.50 v7.0.0, 0.93 v6.3.0, 0.92 v6.2.0, 0.82 v6.1.0, 1.00 v5.2.0, 0.93 v5.0.0, 0.95 v4.1.0, 0.94 v4.0.1, 0.95 v4.0.0
% Syntax : Number of formulae : 3 ( 1 unt; 0 def)
% Number of atoms : 348 ( 0 equ)
% Maximal formula atoms : 344 ( 116 avg)
% Number of connectives : 836 ( 491 ~; 331 |; 13 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 104 ( 37 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 : 187 ( 186 !; 1 ?)
% SPC : FOF_THM_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)
| ~ ( 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)
| 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)
| p1(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) ) ) ) ) ) ) ) ) )
& ~ p2(Y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| 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)
| ~ ( 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)
| ~ p2(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) ) ) ) ) ) ) ) ) )
& ~ p2(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)
| 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)
| ~ ( 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)
| ~ p2(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) ) ) ) ) ) ) ) ) )
& ~ p2(Y) ) ) ) ) ) ) ) )
| 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)
| ~ ! [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)
| ~ p2(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) ) ) ) ) ) ) ) ) )
& ~ 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)
| ~ ( p2(Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ p1(X) ) ) ) ) ) ) ) ) )
& ~ p1(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)
| ~ p2(X) ) ) ) ) ) ) ) ) )
& ~ p1(X) )
| p1(X) ) ).
%------------------------------------------------------------------------------