%--------------------------------------------------------------------------
% File     : COM004-1 : TPTP v9.0.0. Released v1.1.0.
% Domain   : Computing Theory
% Problem  : Part of completeness of resolution
% Version  : Especial.
% English  : Part of [Bun83]'s proof of the completeness of resolution uses
%            the notion of failure nodes. This proves a special case when a
%            parent is the empty failure node.

% Refs     : [Bun83] Bundy (1983), The Computer Modelling of Mathematical R
% Source   : [TPTP]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v3.3.0, 0.14 v3.1.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :    9 (   8 unt;   0 nHn;   6 RR)
%            Number of literals    :   13 (   2 equ;   5 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   0 prp; 2-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   10 (   1 sgn)
% SPC      : CNF_UNS_RFO_SEQ_HRN

% Comments :
%--------------------------------------------------------------------------
cnf(make_node,axiom,
    ( failure_node(parent_of(X,Y),or(C,D))
    | ~ failure_node(X,or(C,P))
    | ~ failure_node(Y,or(D,Q))
    | ~ contradictory(P,Q)
    | ~ siblings(X,Y) ) ).

cnf(not_x_contradicts_x,axiom,
    contradictory(negate(X),X) ).

cnf(x_contradicts_not_x,axiom,
    contradictory(X,negate(X)) ).

cnf(n_left_and_n_right_are_siblings,axiom,
    siblings(left_child_of(X),right_child_of(X)) ).

%----Stuff for the theorem
cnf(n_left_is_atom,hypothesis,
    failure_node(n_left,or(empty,atom)) ).

cnf(n_right_is_not_atom,hypothesis,
    failure_node(n_right,or(empty,negate(atom))) ).

cnf(n_left_equals_left_child_of_n,hypothesis,
    n_left = left_child_of(n) ).

cnf(n_right_equals_right_child_of_n,hypothesis,
    n_right = right_child_of(n) ).

%----The goal to be proved.
cnf(goal_is_there_an_empty_node,negated_conjecture,
    ~ failure_node(Z,or(empty,empty)) ).

%--------------------------------------------------------------------------