TPTP Problem File: GRA062^1.p
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%------------------------------------------------------------------------------
% File : GRA062^1 : TPTP v8.2.0. Released v3.6.0.
% Domain : Graph Theory
% Problem : R(6,12) > 256
% Version : Especial.
% English :
% Refs : [Rad06] Radziszowski (2006), Small Ramsey Numbers
% : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source : [Bro08]
% Names :
% Status : Theorem
% Rating : 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 : 733 ( 161 ~; 79 |; 162 &; 328 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 161 ( 161 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 37 ( 0 ^; 36 !; 1 ?; 37 :)
% SPC : TH0_THM_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.
% :
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thf(ramsey_l_6_12_256,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,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] :
( ( ( Xp0 @ Xx0 )
& ~ ( Xp0 @ Xx1 )
& ~ ( Xp0 @ Xx2 )
& ~ ( Xp0 @ Xx3 )
& ~ ( Xp0 @ Xx4 )
& ~ ( Xp0 @ Xx5 )
& ~ ( Xp1 @ Xx0 )
& ( Xp1 @ Xx1 )
& ~ ( Xp1 @ Xx2 )
& ~ ( Xp1 @ Xx3 )
& ~ ( Xp1 @ Xx4 )
& ~ ( Xp1 @ Xx5 )
& ~ ( Xp2 @ Xx0 )
& ~ ( Xp2 @ Xx1 )
& ( Xp2 @ Xx2 )
& ~ ( Xp2 @ Xx3 )
& ~ ( Xp2 @ Xx4 )
& ~ ( Xp2 @ Xx5 )
& ~ ( Xp3 @ Xx0 )
& ~ ( Xp3 @ Xx1 )
& ~ ( Xp3 @ Xx2 )
& ( Xp3 @ Xx3 )
& ~ ( Xp3 @ Xx4 )
& ~ ( Xp3 @ Xx5 )
& ~ ( Xp4 @ Xx0 )
& ~ ( Xp4 @ Xx1 )
& ~ ( Xp4 @ Xx2 )
& ~ ( Xp4 @ Xx3 )
& ( Xp4 @ Xx4 )
& ~ ( Xp4 @ Xx5 ) )
=> ( ~ ( 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 ) ) )
& ! [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,Xx7: $o > $o > $o > $o,Xx8: $o > $o > $o > $o,Xx9: $o > $o > $o > $o,Xx10: $o > $o > $o > $o,Xx11: $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,Xp6: ( $o > $o > $o > $o ) > $o,Xp7: ( $o > $o > $o > $o ) > $o,Xp8: ( $o > $o > $o > $o ) > $o,Xp9: ( $o > $o > $o > $o ) > $o,Xp10: ( $o > $o > $o > $o ) > $o] :
( ( ( Xp0 @ Xx0 )
& ~ ( Xp0 @ Xx1 )
& ~ ( Xp0 @ Xx2 )
& ~ ( Xp0 @ Xx3 )
& ~ ( Xp0 @ Xx4 )
& ~ ( Xp0 @ Xx5 )
& ~ ( Xp0 @ Xx6 )
& ~ ( Xp0 @ Xx7 )
& ~ ( Xp0 @ Xx8 )
& ~ ( Xp0 @ Xx9 )
& ~ ( Xp0 @ Xx10 )
& ~ ( Xp0 @ Xx11 )
& ~ ( Xp1 @ Xx0 )
& ( Xp1 @ Xx1 )
& ~ ( Xp1 @ Xx2 )
& ~ ( Xp1 @ Xx3 )
& ~ ( Xp1 @ Xx4 )
& ~ ( Xp1 @ Xx5 )
& ~ ( Xp1 @ Xx6 )
& ~ ( Xp1 @ Xx7 )
& ~ ( Xp1 @ Xx8 )
& ~ ( Xp1 @ Xx9 )
& ~ ( Xp1 @ Xx10 )
& ~ ( Xp1 @ Xx11 )
& ~ ( Xp2 @ Xx0 )
& ~ ( Xp2 @ Xx1 )
& ( Xp2 @ Xx2 )
& ~ ( Xp2 @ Xx3 )
& ~ ( Xp2 @ Xx4 )
& ~ ( Xp2 @ Xx5 )
& ~ ( Xp2 @ Xx6 )
& ~ ( Xp2 @ Xx7 )
& ~ ( Xp2 @ Xx8 )
& ~ ( Xp2 @ Xx9 )
& ~ ( Xp2 @ Xx10 )
& ~ ( Xp2 @ Xx11 )
& ~ ( Xp3 @ Xx0 )
& ~ ( Xp3 @ Xx1 )
& ~ ( Xp3 @ Xx2 )
& ( Xp3 @ Xx3 )
& ~ ( Xp3 @ Xx4 )
& ~ ( Xp3 @ Xx5 )
& ~ ( Xp3 @ Xx6 )
& ~ ( Xp3 @ Xx7 )
& ~ ( Xp3 @ Xx8 )
& ~ ( Xp3 @ Xx9 )
& ~ ( Xp3 @ Xx10 )
& ~ ( Xp3 @ Xx11 )
& ~ ( Xp4 @ Xx0 )
& ~ ( Xp4 @ Xx1 )
& ~ ( Xp4 @ Xx2 )
& ~ ( Xp4 @ Xx3 )
& ( Xp4 @ Xx4 )
& ~ ( Xp4 @ Xx5 )
& ~ ( Xp4 @ Xx6 )
& ~ ( Xp4 @ Xx7 )
& ~ ( Xp4 @ Xx8 )
& ~ ( Xp4 @ Xx9 )
& ~ ( Xp4 @ Xx10 )
& ~ ( Xp4 @ Xx11 )
& ~ ( Xp5 @ Xx0 )
& ~ ( Xp5 @ Xx1 )
& ~ ( Xp5 @ Xx2 )
& ~ ( Xp5 @ Xx3 )
& ~ ( Xp5 @ Xx4 )
& ( Xp5 @ Xx5 )
& ~ ( Xp5 @ Xx6 )
& ~ ( Xp5 @ Xx7 )
& ~ ( Xp5 @ Xx8 )
& ~ ( Xp5 @ Xx9 )
& ~ ( Xp5 @ Xx10 )
& ~ ( Xp5 @ Xx11 )
& ~ ( Xp6 @ Xx0 )
& ~ ( Xp6 @ Xx1 )
& ~ ( Xp6 @ Xx2 )
& ~ ( Xp6 @ Xx3 )
& ~ ( Xp6 @ Xx4 )
& ~ ( Xp6 @ Xx5 )
& ( Xp6 @ Xx6 )
& ~ ( Xp6 @ Xx7 )
& ~ ( Xp6 @ Xx8 )
& ~ ( Xp6 @ Xx9 )
& ~ ( Xp6 @ Xx10 )
& ~ ( Xp6 @ Xx11 )
& ~ ( Xp7 @ Xx0 )
& ~ ( Xp7 @ Xx1 )
& ~ ( Xp7 @ Xx2 )
& ~ ( Xp7 @ Xx3 )
& ~ ( Xp7 @ Xx4 )
& ~ ( Xp7 @ Xx5 )
& ~ ( Xp7 @ Xx6 )
& ( Xp7 @ Xx7 )
& ~ ( Xp7 @ Xx8 )
& ~ ( Xp7 @ Xx9 )
& ~ ( Xp7 @ Xx10 )
& ~ ( Xp7 @ Xx11 )
& ~ ( Xp8 @ Xx0 )
& ~ ( Xp8 @ Xx1 )
& ~ ( Xp8 @ Xx2 )
& ~ ( Xp8 @ Xx3 )
& ~ ( Xp8 @ Xx4 )
& ~ ( Xp8 @ Xx5 )
& ~ ( Xp8 @ Xx6 )
& ~ ( Xp8 @ Xx7 )
& ( Xp8 @ Xx8 )
& ~ ( Xp8 @ Xx9 )
& ~ ( Xp8 @ Xx10 )
& ~ ( Xp8 @ Xx11 )
& ~ ( Xp9 @ Xx0 )
& ~ ( Xp9 @ Xx1 )
& ~ ( Xp9 @ Xx2 )
& ~ ( Xp9 @ Xx3 )
& ~ ( Xp9 @ Xx4 )
& ~ ( Xp9 @ Xx5 )
& ~ ( Xp9 @ Xx6 )
& ~ ( Xp9 @ Xx7 )
& ~ ( Xp9 @ Xx8 )
& ( Xp9 @ Xx9 )
& ~ ( Xp9 @ Xx10 )
& ~ ( Xp9 @ Xx11 )
& ~ ( Xp10 @ Xx0 )
& ~ ( Xp10 @ Xx1 )
& ~ ( Xp10 @ Xx2 )
& ~ ( Xp10 @ Xx3 )
& ~ ( Xp10 @ Xx4 )
& ~ ( Xp10 @ Xx5 )
& ~ ( Xp10 @ Xx6 )
& ~ ( Xp10 @ Xx7 )
& ~ ( Xp10 @ Xx8 )
& ~ ( Xp10 @ Xx9 )
& ( Xp10 @ Xx10 )
& ~ ( Xp10 @ Xx11 ) )
=> ( ( 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 )
| ( G @ Xx7 @ Xx0 )
| ( G @ Xx7 @ Xx1 )
| ( G @ Xx7 @ Xx2 )
| ( G @ Xx7 @ Xx3 )
| ( G @ Xx7 @ Xx4 )
| ( G @ Xx7 @ Xx5 )
| ( G @ Xx7 @ Xx6 )
| ( G @ Xx8 @ Xx0 )
| ( G @ Xx8 @ Xx1 )
| ( G @ Xx8 @ Xx2 )
| ( G @ Xx8 @ Xx3 )
| ( G @ Xx8 @ Xx4 )
| ( G @ Xx8 @ Xx5 )
| ( G @ Xx8 @ Xx6 )
| ( G @ Xx8 @ Xx7 )
| ( G @ Xx9 @ Xx0 )
| ( G @ Xx9 @ Xx1 )
| ( G @ Xx9 @ Xx2 )
| ( G @ Xx9 @ Xx3 )
| ( G @ Xx9 @ Xx4 )
| ( G @ Xx9 @ Xx5 )
| ( G @ Xx9 @ Xx6 )
| ( G @ Xx9 @ Xx7 )
| ( G @ Xx9 @ Xx8 )
| ( G @ Xx10 @ Xx0 )
| ( G @ Xx10 @ Xx1 )
| ( G @ Xx10 @ Xx2 )
| ( G @ Xx10 @ Xx3 )
| ( G @ Xx10 @ Xx4 )
| ( G @ Xx10 @ Xx5 )
| ( G @ Xx10 @ Xx6 )
| ( G @ Xx10 @ Xx7 )
| ( G @ Xx10 @ Xx8 )
| ( G @ Xx10 @ Xx9 )
| ( G @ Xx11 @ Xx0 )
| ( G @ Xx11 @ Xx1 )
| ( G @ Xx11 @ Xx2 )
| ( G @ Xx11 @ Xx3 )
| ( G @ Xx11 @ Xx4 )
| ( G @ Xx11 @ Xx5 )
| ( G @ Xx11 @ Xx6 )
| ( G @ Xx11 @ Xx7 )
| ( G @ Xx11 @ Xx8 )
| ( G @ Xx11 @ Xx9 )
| ( G @ Xx11 @ Xx10 ) ) ) ) ).
%------------------------------------------------------------------------------