TPTP Problem File: GRA135^1.p
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% File : GRA135^1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Graph Theory
% Problem : Ramsey-like (directed) graph theory problem a_n
% Version : Especial.
% English : Acyclic directed Ramsey graph with two colours, infinite domain.
% a: 4 vertices, edges 0-1,1-2,0-3,1-3
% b: 4 vertices, edges 0-1,0-2,1-2,2-3
% c: 4 vertices, edges 0-1,0-2,1-2,0-3,2-3
% d: 4 vertices, edges 0-1,0-2,1-2,1-3,2-3
% f: 5 vertices, edges 0-1,0-2,1-2,0-3,2-3,0-4,1-4,2-4
% g: 5 vertices, edges 0-1,0-2,1-2,1-3,2-3,0-4,1-4,2-4
% h: 5 vertices, edges 0-1,1-2,0-3,1-3,2-4,3-4
% i: 5 vertices, edges 0-1,1-2,0-3,1-3,0-4,2-4,3-4
% j: 5 vertices, edges 0-1,1-2,0-3,1-3,1-4,2-4,3-4
% k: 5 vertices, edges 0-1,1-2,0-3,1-3,0-4,1-4,2-4,3-4
% l: 5 vertices, edges 0-1,0-2,1-2,2-3,3-4}
% m: 5 vertices, edges 0-1,0-2,1-2,2-3,0-4,3-4
% n: 5 vertices, edges 0-1,0-2,1-2,2-3,1-4,3-4
% p: 5 vertices, edges 0-1,0-2,1-2,2-3,0-4,1-4,3-4
% q: 5 vertices, edges 0-1,0-2,1-2,2-3,2-4,3-4
% o3 : 3 vertices, edges 0-1,0-2,1-2
% Refs : [HH74] Harary & Hell (1974), Generalized Ramsey Theory for Gr
% : [BJ21] Brown & Janota (2021), First-Order Instantiation using
% : [Raw25] Rawson (2025), Email to Geoff Sutcliffe
% Source : [Raw25]
% Names : adr_a_n_rb_inf_th0.p [Raw25]
% Status : Unsatisfiable
% Rating : 0.33 v9.3.0
% Syntax : Number of formulae : 11 ( 3 unt; 4 typ; 0 def)
% Number of atoms : 18 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 14 ~; 11 |; 0 &; 31 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% SPC : TH0_UNS_EQU_NAR_NDT
% Comments :
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thf(ztp,type,
z: $i ).
thf(stp,type,
s: $i > $i ).
thf(rtp,type,
r: $i > $i > $o ).
thf(btp,type,
b: $i > $i > $o ).
thf(snz,axiom,
! [X: $i] :
( ( s @ X )
!= z ) ).
thf(sinj,axiom,
! [X: $i,Y: $i] :
( ( ( s @ X )
!= ( s @ Y ) )
| ( X = Y ) ) ).
thf(ri,axiom,
! [X: $i] :
~ ( r @ X @ X ) ).
thf(bi,axiom,
! [X: $i] :
~ ( b @ X @ X ) ).
thf(rb,axiom,
! [X: $i,Y: $i] :
( ( X = Y )
| ( r @ X @ Y )
| ( b @ X @ Y ) ) ).
thf(axr,axiom,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( r @ X0 @ X1 )
| ~ ( r @ X1 @ X2 )
| ~ ( r @ X0 @ X3 )
| ~ ( r @ X1 @ X3 ) ) ).
thf(axb,axiom,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( b @ X0 @ X1 )
| ~ ( b @ X0 @ X2 )
| ~ ( b @ X1 @ X2 )
| ~ ( b @ X2 @ X3 )
| ~ ( b @ X1 @ X4 )
| ~ ( b @ X3 @ X4 ) ) ).
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