TPTP Problem File: COM007+2.p
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% File : COM007+2 : TPTP v8.2.0. Released v3.2.0.
% Domain : Computing Theory
% Problem : Preservation of the Diamond Property under reflexive closure
% Version : Especial.
% English :
% Refs : [Bez05] Bezem (2005), Email to Geoff Sutcliffe
% Source : [Bez05]
% Names : dpe [Bez05]
% Status : Theorem
% Rating : 0.17 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.13 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.04 v6.2.0, 0.12 v6.1.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.0, 0.08 v3.7.0, 0.14 v3.5.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.00 v3.2.0
% Syntax : Number of formulae : 7 ( 1 unt; 0 def)
% Number of atoms : 17 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 10 ( 0 ~; 1 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 11 ( 10 !; 1 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
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fof(assumption,axiom,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ) ).
fof(goal_ax,axiom,
! [A] :
( ( reflexive_rewrite(b,A)
& reflexive_rewrite(c,A) )
=> goal ) ).
fof(equal_in_reflexive_rewrite,axiom,
! [A,B] :
( A = B
=> reflexive_rewrite(A,B) ) ).
fof(rewrite_in_reflexive_rewrite,axiom,
! [A,B] :
( rewrite(A,B)
=> reflexive_rewrite(A,B) ) ).
fof(equal_or_rewrite,axiom,
! [A,B] :
( reflexive_rewrite(A,B)
=> ( A = B
| rewrite(A,B) ) ) ).
fof(rewrite_diamond,axiom,
! [A,B,C] :
( ( rewrite(A,B)
& rewrite(A,C) )
=> ? [D] :
( rewrite(B,D)
& rewrite(C,D) ) ) ).
fof(goal_to_be_proved,conjecture,
goal ).
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