## TPTP Problem File: GRA020+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : GRA020+1 : TPTP v8.1.0. Released v3.2.0.
% Domain   : Graph Theory
% Problem  : 2-colored completed graph size 11 without subgraph of size 5
% Version  : Especial.
% English  : Find a 2-colored completed graph of size 11 without a complete
%            subgraph of size 5 which all the edges have the same color.

% Refs     : [Bez05] Bezem (2005), Email to Geoff Sutcliffe
% Source   : [Bez05]
% Names    : r5_11 [Bez05]

% Status   : CounterSatisfiable
% Rating   : 0.00 v5.5.0, 0.10 v5.4.0, 0.00 v5.3.0, 0.25 v5.0.0, 0.00 v4.1.0, 0.17 v4.0.1, 0.00 v3.4.0, 0.17 v3.3.0, 0.67 v3.2.0

% Syntax   : Number of formulae    :    7 (   1 unt;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :   11 (   6 avg)
%            Number of connectives :   35 (   0   ~;   1   |;  29   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;  11 con; 0-0 aty)
%            Number of variables   :   17 (  17   !;   0   ?)
% SPC      : FOF_CSA_EPR_NEQ

%------------------------------------------------------------------------------
fof(ordering,axiom,
( less_than(n1,n2)
& less_than(n2,n3)
& less_than(n3,n4)
& less_than(n4,n5)
& less_than(n5,n6)
& less_than(n6,n7)
& less_than(n7,n8)
& less_than(n8,n9)
& less_than(n9,n10)
& less_than(n10,n11) ) ).

fof(red_clique,axiom,
! [A,B,C,D,E] :
( ( red(A,B)
& red(A,C)
& red(B,C)
& red(A,D)
& red(B,D)
& red(C,D)
& red(A,E)
& red(B,E)
& red(C,E)
& red(D,E) )
=> goal ) ).

fof(green_clique,axiom,
! [A,B,C,D,E] :
( ( green(A,B)
& green(A,C)
& green(B,C)
& green(A,D)
& green(B,D)
& green(C,D)
& green(A,E)
& green(B,E)
& green(C,E)
& green(D,E) )
=> goal ) ).

fof(no_overlap,axiom,
! [A,B] :
( ( red(A,B)
& green(A,B) )
=> goal ) ).

fof(less_than_transitive,axiom,
! [A,B,C] :
( ( less_than(A,B)
& less_than(B,C) )
=> less_than(A,C) ) ).

fof(partition,axiom,
! [A,B] :
( less_than(A,B)
=> ( red(A,B)
| green(A,B) ) ) ).

fof(goal_to_be_proved,conjecture,
goal ).

%------------------------------------------------------------------------------
```