TPTP Problem File: GRA037^2.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : GRA037^2 : TPTP v8.2.0. Released v3.6.0.
% Domain : Graph Theory
% Problem : R(7,7) <= 256
% Version : Especial.
% English :
% Refs : [Rad06] Radziszowski (2006), Small Ramsey Numbers
% : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source : [Bro08]
% Names :
% Status : CounterSatisfiable
% Rating : 1.00 v8.1.0, 0.00 v7.4.0, 1.00 v3.7.0
% Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% Number of atoms : 0 ( 0 equ; 0 cnn)
% Maximal formula atoms : 0 ( 0 avg)
% Number of connectives : 392 ( 93 ~; 1 |; 124 &; 172 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 82 ( 82 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 29 ( 0 ^; 3 !; 26 ?; 29 :)
% SPC : TH0_OPN_NEQ_NAR
% Comments : If a type alpha has exactly n elements, then we can prove
% R(k,l) > n by finding a graph (symmetric binary relation) on type
% alpha with no k-cliques and no l-independent sets. Likewise, we
% can prove R(k,l) <= n by proving every graph (symmetric binary
% relation) on alpha must have a k-clique or l-independent set.
% There is one type with 4 elements: o > o. There are two types
% with 16 elements: o > o > o and (o > o) > o. There are two types
% with 256 elements: o > o > o > o and o > (o > o) > o. This means
% we always have two formulations of R(k,l) >/<= 16 and two
% formulations of R(k,l) >/<= 256.
% :
%------------------------------------------------------------------------------
thf(ramsey_u_7_7_256a,conjecture,
! [G: ( $o > ( $o > $o ) > $o ) > ( $o > ( $o > $o ) > $o ) > $o] :
( ! [Xx: $o > ( $o > $o ) > $o,Xy: $o > ( $o > $o ) > $o] :
( ( G @ Xx @ Xy )
=> ( G @ Xy @ Xx ) )
=> ( ? [Xx0: $o > ( $o > $o ) > $o,Xx1: $o > ( $o > $o ) > $o,Xx2: $o > ( $o > $o ) > $o,Xx3: $o > ( $o > $o ) > $o,Xx4: $o > ( $o > $o ) > $o,Xx5: $o > ( $o > $o ) > $o,Xx6: $o > ( $o > $o ) > $o,Xp0: ( $o > ( $o > $o ) > $o ) > $o,Xp1: ( $o > ( $o > $o ) > $o ) > $o,Xp2: ( $o > ( $o > $o ) > $o ) > $o,Xp3: ( $o > ( $o > $o ) > $o ) > $o,Xp4: ( $o > ( $o > $o ) > $o ) > $o,Xp5: ( $o > ( $o > $o ) > $o ) > $o] :
( ( Xp0 @ Xx0 )
& ~ ( Xp0 @ Xx1 )
& ~ ( Xp0 @ Xx2 )
& ~ ( Xp0 @ Xx3 )
& ~ ( Xp0 @ Xx4 )
& ~ ( Xp0 @ Xx5 )
& ~ ( Xp0 @ Xx6 )
& ~ ( Xp1 @ Xx0 )
& ( Xp1 @ Xx1 )
& ~ ( Xp1 @ Xx2 )
& ~ ( Xp1 @ Xx3 )
& ~ ( Xp1 @ Xx4 )
& ~ ( Xp1 @ Xx5 )
& ~ ( Xp1 @ Xx6 )
& ~ ( Xp2 @ Xx0 )
& ~ ( Xp2 @ Xx1 )
& ( Xp2 @ Xx2 )
& ~ ( Xp2 @ Xx3 )
& ~ ( Xp2 @ Xx4 )
& ~ ( Xp2 @ Xx5 )
& ~ ( Xp2 @ Xx6 )
& ~ ( Xp3 @ Xx0 )
& ~ ( Xp3 @ Xx1 )
& ~ ( Xp3 @ Xx2 )
& ( Xp3 @ Xx3 )
& ~ ( Xp3 @ Xx4 )
& ~ ( Xp3 @ Xx5 )
& ~ ( Xp3 @ Xx6 )
& ~ ( Xp4 @ Xx0 )
& ~ ( Xp4 @ Xx1 )
& ~ ( Xp4 @ Xx2 )
& ~ ( Xp4 @ Xx3 )
& ( Xp4 @ Xx4 )
& ~ ( Xp4 @ Xx5 )
& ~ ( Xp4 @ Xx6 )
& ~ ( Xp5 @ Xx0 )
& ~ ( Xp5 @ Xx1 )
& ~ ( Xp5 @ Xx2 )
& ~ ( Xp5 @ Xx3 )
& ~ ( Xp5 @ Xx4 )
& ( Xp5 @ Xx5 )
& ~ ( Xp5 @ Xx6 )
& ( G @ Xx1 @ Xx0 )
& ( G @ Xx2 @ Xx0 )
& ( G @ Xx2 @ Xx1 )
& ( G @ Xx3 @ Xx0 )
& ( G @ Xx3 @ Xx1 )
& ( G @ Xx3 @ Xx2 )
& ( G @ Xx4 @ Xx0 )
& ( G @ Xx4 @ Xx1 )
& ( G @ Xx4 @ Xx2 )
& ( G @ Xx4 @ Xx3 )
& ( G @ Xx5 @ Xx0 )
& ( G @ Xx5 @ Xx1 )
& ( G @ Xx5 @ Xx2 )
& ( G @ Xx5 @ Xx3 )
& ( G @ Xx5 @ Xx4 )
& ( G @ Xx6 @ Xx0 )
& ( G @ Xx6 @ Xx1 )
& ( G @ Xx6 @ Xx2 )
& ( G @ Xx6 @ Xx3 )
& ( G @ Xx6 @ Xx4 )
& ( G @ Xx6 @ Xx5 ) )
| ? [Xx0: $o > ( $o > $o ) > $o,Xx1: $o > ( $o > $o ) > $o,Xx2: $o > ( $o > $o ) > $o,Xx3: $o > ( $o > $o ) > $o,Xx4: $o > ( $o > $o ) > $o,Xx5: $o > ( $o > $o ) > $o,Xx6: $o > ( $o > $o ) > $o,Xp0: ( $o > ( $o > $o ) > $o ) > $o,Xp1: ( $o > ( $o > $o ) > $o ) > $o,Xp2: ( $o > ( $o > $o ) > $o ) > $o,Xp3: ( $o > ( $o > $o ) > $o ) > $o,Xp4: ( $o > ( $o > $o ) > $o ) > $o,Xp5: ( $o > ( $o > $o ) > $o ) > $o] :
( ( Xp0 @ Xx0 )
& ~ ( Xp0 @ Xx1 )
& ~ ( Xp0 @ Xx2 )
& ~ ( Xp0 @ Xx3 )
& ~ ( Xp0 @ Xx4 )
& ~ ( Xp0 @ Xx5 )
& ~ ( Xp0 @ Xx6 )
& ~ ( Xp1 @ Xx0 )
& ( Xp1 @ Xx1 )
& ~ ( Xp1 @ Xx2 )
& ~ ( Xp1 @ Xx3 )
& ~ ( Xp1 @ Xx4 )
& ~ ( Xp1 @ Xx5 )
& ~ ( Xp1 @ Xx6 )
& ~ ( Xp2 @ Xx0 )
& ~ ( Xp2 @ Xx1 )
& ( Xp2 @ Xx2 )
& ~ ( Xp2 @ Xx3 )
& ~ ( Xp2 @ Xx4 )
& ~ ( Xp2 @ Xx5 )
& ~ ( Xp2 @ Xx6 )
& ~ ( Xp3 @ Xx0 )
& ~ ( Xp3 @ Xx1 )
& ~ ( Xp3 @ Xx2 )
& ( Xp3 @ Xx3 )
& ~ ( Xp3 @ Xx4 )
& ~ ( Xp3 @ Xx5 )
& ~ ( Xp3 @ Xx6 )
& ~ ( Xp4 @ Xx0 )
& ~ ( Xp4 @ Xx1 )
& ~ ( Xp4 @ Xx2 )
& ~ ( Xp4 @ Xx3 )
& ( Xp4 @ Xx4 )
& ~ ( Xp4 @ Xx5 )
& ~ ( Xp4 @ Xx6 )
& ~ ( Xp5 @ Xx0 )
& ~ ( Xp5 @ Xx1 )
& ~ ( Xp5 @ Xx2 )
& ~ ( Xp5 @ Xx3 )
& ~ ( Xp5 @ Xx4 )
& ( Xp5 @ Xx5 )
& ~ ( Xp5 @ Xx6 )
& ~ ( G @ Xx1 @ Xx0 )
& ~ ( G @ Xx2 @ Xx0 )
& ~ ( G @ Xx2 @ Xx1 )
& ~ ( G @ Xx3 @ Xx0 )
& ~ ( G @ Xx3 @ Xx1 )
& ~ ( G @ Xx3 @ Xx2 )
& ~ ( G @ Xx4 @ Xx0 )
& ~ ( G @ Xx4 @ Xx1 )
& ~ ( G @ Xx4 @ Xx2 )
& ~ ( G @ Xx4 @ Xx3 )
& ~ ( G @ Xx5 @ Xx0 )
& ~ ( G @ Xx5 @ Xx1 )
& ~ ( G @ Xx5 @ Xx2 )
& ~ ( G @ Xx5 @ Xx3 )
& ~ ( G @ Xx5 @ Xx4 )
& ~ ( G @ Xx6 @ Xx0 )
& ~ ( G @ Xx6 @ Xx1 )
& ~ ( G @ Xx6 @ Xx2 )
& ~ ( G @ Xx6 @ Xx3 )
& ~ ( G @ Xx6 @ Xx4 )
& ~ ( G @ Xx6 @ Xx5 ) ) ) ) ).
%------------------------------------------------------------------------------