TPTP Problem File: GRA125^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : GRA125^1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Graph Theory
% Problem : Ramsey number r(4,4) = 18
% Version : Especial.
% English : The Ramsey property that if an undirected graph has at least
% R(m,n) vertices, then it must have either an m-clique or an
% n-anticlique.
% Refs : [Ram30] Ramsey (1930), On a Problem of Formal Logic
% : [Kal24] Kalizyk (2024), Email to G. Sutcliffe
% Source : [Kal24]
% Names : r_4_4_18 [Kal24]
% Status : Unsatisfiable
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 175 ( 153 unt; 19 typ; 0 def)
% Number of atoms : 179 ( 165 equ; 0 cnn)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 211 ( 160 ~; 23 |; 0 &; 28 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 19 usr; 18 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% SPC : TH0_UNS_EQU_NAR_NDT
% Comments :
%------------------------------------------------------------------------------
thf(rtp,type,
r: $i > $i > $o ).
thf(v0tp,type,
v0: $i ).
thf(v1tp,type,
v1: $i ).
thf(v2tp,type,
v2: $i ).
thf(v3tp,type,
v3: $i ).
thf(v4tp,type,
v4: $i ).
thf(v5tp,type,
v5: $i ).
thf(v6tp,type,
v6: $i ).
thf(v7tp,type,
v7: $i ).
thf(v8tp,type,
v8: $i ).
thf(v9tp,type,
v9: $i ).
thf(v10tp,type,
v10: $i ).
thf(v11tp,type,
v11: $i ).
thf(v12tp,type,
v12: $i ).
thf(v13tp,type,
v13: $i ).
thf(v14tp,type,
v14: $i ).
thf(v15tp,type,
v15: $i ).
thf(v16tp,type,
v16: $i ).
thf(v17tp,type,
v17: $i ).
thf(rsym,axiom,
! [X: $i,Y: $i] :
( ~ ( r @ X @ Y )
| ( r @ Y @ X ) ) ).
thf(rno4cl,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ( X = Y )
| ( X = Z )
| ( X = W )
| ( Y = Z )
| ( Y = W )
| ( Z = W )
| ~ ( r @ X @ Y )
| ~ ( r @ X @ Z )
| ~ ( r @ X @ W )
| ~ ( r @ Y @ Z )
| ~ ( r @ Y @ W )
| ~ ( r @ Z @ W ) ) ).
thf(rno4acl,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ( X = Y )
| ( X = Z )
| ( X = W )
| ( Y = Z )
| ( Y = W )
| ( Z = W )
| ( r @ X @ Y )
| ( r @ X @ Z )
| ( r @ X @ W )
| ( r @ Y @ Z )
| ( r @ Y @ W )
| ( r @ Z @ W ) ) ).
thf(v0nv1,axiom,
v0 != v1 ).
thf(v0nv2,axiom,
v0 != v2 ).
thf(v1nv2,axiom,
v1 != v2 ).
thf(v0nv3,axiom,
v0 != v3 ).
thf(v1nv3,axiom,
v1 != v3 ).
thf(v2nv3,axiom,
v2 != v3 ).
thf(v0nv4,axiom,
v0 != v4 ).
thf(v1nv4,axiom,
v1 != v4 ).
thf(v2nv4,axiom,
v2 != v4 ).
thf(v3nv4,axiom,
v3 != v4 ).
thf(v0nv5,axiom,
v0 != v5 ).
thf(v1nv5,axiom,
v1 != v5 ).
thf(v2nv5,axiom,
v2 != v5 ).
thf(v3nv5,axiom,
v3 != v5 ).
thf(v4nv5,axiom,
v4 != v5 ).
thf(v0nv6,axiom,
v0 != v6 ).
thf(v1nv6,axiom,
v1 != v6 ).
thf(v2nv6,axiom,
v2 != v6 ).
thf(v3nv6,axiom,
v3 != v6 ).
thf(v4nv6,axiom,
v4 != v6 ).
thf(v5nv6,axiom,
v5 != v6 ).
thf(v0nv7,axiom,
v0 != v7 ).
thf(v1nv7,axiom,
v1 != v7 ).
thf(v2nv7,axiom,
v2 != v7 ).
thf(v3nv7,axiom,
v3 != v7 ).
thf(v4nv7,axiom,
v4 != v7 ).
thf(v5nv7,axiom,
v5 != v7 ).
thf(v6nv7,axiom,
v6 != v7 ).
thf(v0nv8,axiom,
v0 != v8 ).
thf(v1nv8,axiom,
v1 != v8 ).
thf(v2nv8,axiom,
v2 != v8 ).
thf(v3nv8,axiom,
v3 != v8 ).
thf(v4nv8,axiom,
v4 != v8 ).
thf(v5nv8,axiom,
v5 != v8 ).
thf(v6nv8,axiom,
v6 != v8 ).
thf(v7nv8,axiom,
v7 != v8 ).
thf(v0nv9,axiom,
v0 != v9 ).
thf(v1nv9,axiom,
v1 != v9 ).
thf(v2nv9,axiom,
v2 != v9 ).
thf(v3nv9,axiom,
v3 != v9 ).
thf(v4nv9,axiom,
v4 != v9 ).
thf(v5nv9,axiom,
v5 != v9 ).
thf(v6nv9,axiom,
v6 != v9 ).
thf(v7nv9,axiom,
v7 != v9 ).
thf(v8nv9,axiom,
v8 != v9 ).
thf(v0nv10,axiom,
v0 != v10 ).
thf(v1nv10,axiom,
v1 != v10 ).
thf(v2nv10,axiom,
v2 != v10 ).
thf(v3nv10,axiom,
v3 != v10 ).
thf(v4nv10,axiom,
v4 != v10 ).
thf(v5nv10,axiom,
v5 != v10 ).
thf(v6nv10,axiom,
v6 != v10 ).
thf(v7nv10,axiom,
v7 != v10 ).
thf(v8nv10,axiom,
v8 != v10 ).
thf(v9nv10,axiom,
v9 != v10 ).
thf(v0nv11,axiom,
v0 != v11 ).
thf(v1nv11,axiom,
v1 != v11 ).
thf(v2nv11,axiom,
v2 != v11 ).
thf(v3nv11,axiom,
v3 != v11 ).
thf(v4nv11,axiom,
v4 != v11 ).
thf(v5nv11,axiom,
v5 != v11 ).
thf(v6nv11,axiom,
v6 != v11 ).
thf(v7nv11,axiom,
v7 != v11 ).
thf(v8nv11,axiom,
v8 != v11 ).
thf(v9nv11,axiom,
v9 != v11 ).
thf(v10nv11,axiom,
v10 != v11 ).
thf(v0nv12,axiom,
v0 != v12 ).
thf(v1nv12,axiom,
v1 != v12 ).
thf(v2nv12,axiom,
v2 != v12 ).
thf(v3nv12,axiom,
v3 != v12 ).
thf(v4nv12,axiom,
v4 != v12 ).
thf(v5nv12,axiom,
v5 != v12 ).
thf(v6nv12,axiom,
v6 != v12 ).
thf(v7nv12,axiom,
v7 != v12 ).
thf(v8nv12,axiom,
v8 != v12 ).
thf(v9nv12,axiom,
v9 != v12 ).
thf(v10nv12,axiom,
v10 != v12 ).
thf(v11nv12,axiom,
v11 != v12 ).
thf(v0nv13,axiom,
v0 != v13 ).
thf(v1nv13,axiom,
v1 != v13 ).
thf(v2nv13,axiom,
v2 != v13 ).
thf(v3nv13,axiom,
v3 != v13 ).
thf(v4nv13,axiom,
v4 != v13 ).
thf(v5nv13,axiom,
v5 != v13 ).
thf(v6nv13,axiom,
v6 != v13 ).
thf(v7nv13,axiom,
v7 != v13 ).
thf(v8nv13,axiom,
v8 != v13 ).
thf(v9nv13,axiom,
v9 != v13 ).
thf(v10nv13,axiom,
v10 != v13 ).
thf(v11nv13,axiom,
v11 != v13 ).
thf(v12nv13,axiom,
v12 != v13 ).
thf(v0nv14,axiom,
v0 != v14 ).
thf(v1nv14,axiom,
v1 != v14 ).
thf(v2nv14,axiom,
v2 != v14 ).
thf(v3nv14,axiom,
v3 != v14 ).
thf(v4nv14,axiom,
v4 != v14 ).
thf(v5nv14,axiom,
v5 != v14 ).
thf(v6nv14,axiom,
v6 != v14 ).
thf(v7nv14,axiom,
v7 != v14 ).
thf(v8nv14,axiom,
v8 != v14 ).
thf(v9nv14,axiom,
v9 != v14 ).
thf(v10nv14,axiom,
v10 != v14 ).
thf(v11nv14,axiom,
v11 != v14 ).
thf(v12nv14,axiom,
v12 != v14 ).
thf(v13nv14,axiom,
v13 != v14 ).
thf(v0nv15,axiom,
v0 != v15 ).
thf(v1nv15,axiom,
v1 != v15 ).
thf(v2nv15,axiom,
v2 != v15 ).
thf(v3nv15,axiom,
v3 != v15 ).
thf(v4nv15,axiom,
v4 != v15 ).
thf(v5nv15,axiom,
v5 != v15 ).
thf(v6nv15,axiom,
v6 != v15 ).
thf(v7nv15,axiom,
v7 != v15 ).
thf(v8nv15,axiom,
v8 != v15 ).
thf(v9nv15,axiom,
v9 != v15 ).
thf(v10nv15,axiom,
v10 != v15 ).
thf(v11nv15,axiom,
v11 != v15 ).
thf(v12nv15,axiom,
v12 != v15 ).
thf(v13nv15,axiom,
v13 != v15 ).
thf(v14nv15,axiom,
v14 != v15 ).
thf(v0nv16,axiom,
v0 != v16 ).
thf(v1nv16,axiom,
v1 != v16 ).
thf(v2nv16,axiom,
v2 != v16 ).
thf(v3nv16,axiom,
v3 != v16 ).
thf(v4nv16,axiom,
v4 != v16 ).
thf(v5nv16,axiom,
v5 != v16 ).
thf(v6nv16,axiom,
v6 != v16 ).
thf(v7nv16,axiom,
v7 != v16 ).
thf(v8nv16,axiom,
v8 != v16 ).
thf(v9nv16,axiom,
v9 != v16 ).
thf(v10nv16,axiom,
v10 != v16 ).
thf(v11nv16,axiom,
v11 != v16 ).
thf(v12nv16,axiom,
v12 != v16 ).
thf(v13nv16,axiom,
v13 != v16 ).
thf(v14nv16,axiom,
v14 != v16 ).
thf(v15nv16,axiom,
v15 != v16 ).
thf(v0nv17,axiom,
v0 != v17 ).
thf(v1nv17,axiom,
v1 != v17 ).
thf(v2nv17,axiom,
v2 != v17 ).
thf(v3nv17,axiom,
v3 != v17 ).
thf(v4nv17,axiom,
v4 != v17 ).
thf(v5nv17,axiom,
v5 != v17 ).
thf(v6nv17,axiom,
v6 != v17 ).
thf(v7nv17,axiom,
v7 != v17 ).
thf(v8nv17,axiom,
v8 != v17 ).
thf(v9nv17,axiom,
v9 != v17 ).
thf(v10nv17,axiom,
v10 != v17 ).
thf(v11nv17,axiom,
v11 != v17 ).
thf(v12nv17,axiom,
v12 != v17 ).
thf(v13nv17,axiom,
v13 != v17 ).
thf(v14nv17,axiom,
v14 != v17 ).
thf(v15nv17,axiom,
v15 != v17 ).
thf(v16nv17,axiom,
v16 != v17 ).
%------------------------------------------------------------------------------