%------------------------------------------------------------------------------
% File : LCL678+1.005 : TPTP v9.0.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In S4, formula provable in intuitionistic logic, 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_ipc_p [BHS00]
% Status : Theorem
% Rating : 0.93 v9.0.0, 0.94 v8.2.0, 0.93 v7.5.0, 0.95 v7.4.0, 0.94 v7.3.0, 0.86 v7.2.0, 0.83 v7.1.0, 0.75 v7.0.0, 0.86 v6.4.0, 0.93 v6.3.0, 0.92 v6.2.0, 0.82 v6.1.0, 1.00 v6.0.0, 0.75 v5.5.0, 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 : 80 ( 0 equ)
% Maximal formula atoms : 76 ( 26 avg)
% Number of connectives : 130 ( 53 ~; 51 |; 25 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 11 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 45 ( 44 !; 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] :
~ ( $false
| ~ ( ! [Y] :
( ~ r1(X,Y)
| $false
| ~ ! [X] :
( ~ r1(Y,X)
| ( ! [Y] :
( ~ r1(X,Y)
| p5(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p4(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| p5(Y) ) ) )
& ! [Y] :
( ~ r1(X,Y)
| $false
| ~ ! [X] :
( ~ r1(Y,X)
| ( ! [Y] :
( ~ r1(X,Y)
| p5(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p4(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| p4(Y) ) ) )
& ! [Y] :
( ~ r1(X,Y)
| $false
| ~ ! [X] :
( ~ r1(Y,X)
| ( ! [Y] :
( ~ r1(X,Y)
| p5(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p4(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| p3(Y) ) ) )
& ! [Y] :
( ~ r1(X,Y)
| $false
| ~ ! [X] :
( ~ r1(Y,X)
| ( ! [Y] :
( ~ r1(X,Y)
| p5(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p4(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| p2(Y) ) ) )
& ! [Y] :
( ~ r1(X,Y)
| $false
| ~ ! [X] :
( ~ r1(Y,X)
| ( ! [Y] :
( ~ r1(X,Y)
| p5(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p4(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p2(Y) )
& ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| p1(Y) ) ) ) ) ) ).
%------------------------------------------------------------------------------