TPTP Problem File: LCL688+1.001.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : LCL688+1.001 : TPTP v8.2.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In S4, formula with T and A4, size 1
% Version : Especial.
% English : T{dia p0/p0} & box T{~box dia p0/p0} & A4{dia p0/p0} &
% box(dia box dia p0 -> (p0 -> box p0)) -> dia box p0 |
% dia box ~p0.
% Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% Source : [Kam08]
% Names : s4_t4p_p [BHS00]
% Status : Theorem
% Rating : 0.12 v8.2.0, 0.13 v8.1.0, 0.14 v7.5.0, 0.29 v7.4.0, 0.12 v7.3.0, 0.14 v7.2.0, 0.17 v7.1.0, 0.25 v7.0.0, 0.21 v6.4.0, 0.43 v6.3.0, 0.46 v6.2.0, 0.45 v6.1.0, 0.48 v6.0.0, 0.25 v5.5.0, 0.58 v5.4.0, 0.57 v5.3.0, 0.61 v5.2.0, 0.43 v5.1.0, 0.36 v5.0.0, 0.45 v4.1.0, 0.39 v4.0.1, 0.42 v4.0.0
% Syntax : Number of formulae : 3 ( 1 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 44 ( 16 avg)
% Number of connectives : 103 ( 58 ~; 38 |; 6 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 12 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 : 32 ( 31 !; 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] :
~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ~ p4(Y) )
| ~ ! [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)
| ~ ( ! [X] :
( ~ r1(Y,X)
| p3(X) )
| ~ p2(Y) ) )
& p2(X)
& ~ ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ p2(Y) ) ) ) ) ) ) )
| ( ~ p1(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) )
& 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) ) ) ) ).
%------------------------------------------------------------------------------