TPTP Problem File: LCL680+1.015.p
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%------------------------------------------------------------------------------
% File : LCL680+1.015 : TPTP v8.2.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In S4, in backward search find a way through box and dia, size 15
% 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 : 1.00 v4.0.0
% Syntax : Number of formulae : 3 ( 1 unt; 0 def)
% Number of atoms : 9673 ( 0 equ)
% Maximal formula atoms : 9669 (3224 avg)
% Number of connectives : 23986 (14316 ~;9626 |; 43 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1024 ( 344 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 : 4982 (4981 !; 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) ) ).