%------------------------------------------------------------------------------
% File : LCL686+1.005 : TPTP v8.2.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In S4, formula provable in S5 embedding, 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_s5_p [BHS00]
% Status : Theorem
% Rating : 0.00 v7.5.0, 0.05 v7.4.0, 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.12 v5.4.0, 0.13 v5.3.0, 0.22 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.11 v4.0.0
% Syntax : Number of formulae : 3 ( 1 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 140 ( 48 avg)
% Number of connectives : 257 ( 116 ~; 87 |; 53 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 55 ( 21 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 37 ( 36 !; 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)
| ~ p15(Y)
| ! [X] :
( ~ r1(Y,X)
| ~ p1(X) ) )
| ! [Y] :
( ~ r1(X,Y)
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| $false )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ( p14(Y)
& ~ p13(Y) )
| ( ~ p14(Y)
& p13(Y) ) ) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ( p13(X)
& ~ p12(X) )
| ( ~ p13(X)
& p12(X) ) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ( p12(Y)
& ~ p11(Y) )
| ( ~ p12(Y)
& p11(Y) ) ) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ( p11(X)
& ~ p10(X) )
| ( ~ p11(X)
& p10(X) ) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ( p10(Y)
& ~ p9(Y) )
| ( ~ p10(Y)
& p9(Y) ) ) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ( p9(X)
& ~ p8(X) )
| ( ~ p9(X)
& p8(X) ) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ( p8(Y)
& ~ p7(Y) )
| ( ~ p8(Y)
& p7(Y) ) ) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ( p7(X)
& ~ p6(X) )
| ( ~ p7(X)
& p6(X) ) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ( p6(Y)
& ~ p5(Y) )
| ( ~ p6(Y)
& p5(Y) ) ) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ( p5(X)
& ~ p4(X) )
| ( ~ p5(X)
& p4(X) ) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ( p4(Y)
& ~ p3(Y) )
| ( ~ p4(Y)
& p3(Y) ) ) ) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ( p3(X)
& ~ p2(X) )
| ( ~ p3(X)
& p2(X) ) ) ) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ( p2(Y)
& ~ p1(Y) )
| ( ~ p2(Y)
& p1(Y) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y] :
( ~ r1(X,Y)
| ( ~ p13(Y)
& ~ p14(Y) )
| ( p14(Y)
& p13(Y) )
| ( ~ p12(Y)
& ~ p13(Y) )
| ( p13(Y)
& p12(Y) )
| ( ~ p11(Y)
& ~ p12(Y) )
| ( p12(Y)
& p11(Y) )
| ( ~ p10(Y)
& ~ p11(Y) )
| ( p11(Y)
& p10(Y) )
| ( ~ p9(Y)
& ~ p10(Y) )
| ( p10(Y)
& p9(Y) )
| ( ~ p8(Y)
& ~ p9(Y) )
| ( p9(Y)
& p8(Y) )
| ( ~ p7(Y)
& ~ p8(Y) )
| ( p8(Y)
& p7(Y) )
| ( ~ p6(Y)
& ~ p7(Y) )
| ( p7(Y)
& p6(Y) )
| ( ~ p5(Y)
& ~ p6(Y) )
| ( p6(Y)
& p5(Y) )
| ( ~ p4(Y)
& ~ p5(Y) )
| ( p5(Y)
& p4(Y) )
| ( ~ p3(Y)
& ~ p4(Y) )
| ( p4(Y)
& p3(Y) )
| ( ~ p2(Y)
& ~ p3(Y) )
| ( p3(Y)
& p2(Y) )
| ( ~ p1(Y)
& ~ p2(Y) )
| ( p2(Y)
& p1(Y) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------