%------------------------------------------------------------------------------
% File : LCL657+1.005 : TPTP v8.2.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In KT, the branching formula, 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 : kt_branch_n [BHS00]
% Status : CounterSatisfiable
% Rating : 0.33 v8.2.0, 0.67 v8.1.0, 0.33 v7.4.0, 0.00 v7.3.0, 0.33 v6.4.0, 0.50 v6.2.0, 0.56 v6.1.0, 0.70 v6.0.0, 0.71 v5.4.0, 0.67 v5.3.0, 0.69 v5.2.0, 0.75 v5.0.0, 0.67 v4.0.1, 0.00 v4.0.0
% Syntax : Number of formulae : 2 ( 1 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 123 ( 62 avg)
% Number of connectives : 232 ( 110 ~; 68 |; 54 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 17 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 14 usr; 0 prp; 1-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 29 ( 28 !; 1 ?)
% SPC : FOF_CSA_RFO_NEQ
% Comments : A naive relational encoding of the modal logic problem into
% first-order logic.
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X) ).
fof(main,conjecture,
~ ? [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)
| ~ ( ~ p6(X)
& ~ p106(X)
& p105(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p6(X)
& ~ p106(X)
& p105(X) ) ) )
| ~ ( ~ p105(Y)
& p104(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p5(X)
& ~ p105(X)
& p104(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p5(X)
& ~ p105(X)
& p104(X) ) ) )
| ~ ( ~ p104(Y)
& p103(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p4(X)
& ~ p104(X)
& p103(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p4(X)
& ~ p104(X)
& p103(X) ) ) )
| ~ ( ~ p103(Y)
& p102(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p3(X)
& ~ p103(X)
& p102(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p3(X)
& ~ p103(X)
& p102(X) ) ) )
| ~ ( ~ p102(Y)
& p101(Y) ) )
& ( ( ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ p2(X)
& ~ p102(X)
& p101(X) ) )
& ~ ! [X] :
( ~ r1(Y,X)
| ~ ( p2(X)
& ~ p102(X)
& p101(X) ) ) )
| ~ ( ~ p101(Y)
& p100(Y) ) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p6(X)
| ~ p105(X) )
| p6(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p6(X)
| ~ p105(X) )
| ~ p6(Y) ) )
| ~ p105(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p5(X)
| ~ p104(X) )
| p5(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p5(X)
| ~ p104(X) )
| ~ p5(Y) ) )
| ~ p104(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p4(X)
| ~ p103(X) )
| p4(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p4(X)
| ~ p103(X) )
| ~ p4(Y) ) )
| ~ p103(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p3(X)
| ~ p102(X) )
| p3(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p3(X)
| ~ p102(X) )
| ~ p3(Y) ) )
| ~ p102(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p2(X)
| ~ p101(X) )
| p2(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p2(X)
| ~ p101(X) )
| ~ p2(Y) ) )
| ~ p101(Y) )
& ( ( ( ! [X] :
( ~ r1(Y,X)
| ~ p1(X)
| ~ p100(X) )
| p1(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p1(X)
| ~ p100(X) )
| ~ p1(Y) ) )
| ~ p100(Y) )
& ( p105(Y)
| ~ p106(Y) )
& ( p104(Y)
| ~ p105(Y) )
& ( p103(Y)
| ~ p104(Y) )
& ( p102(Y)
| ~ p103(Y) )
& ( p101(Y)
| ~ p102(Y) )
& ( p100(Y)
| ~ p101(Y) ) ) ) ) ) ) )
& ~ p101(X)
& p100(X) ) ).
%------------------------------------------------------------------------------