%--------------------------------------------------------------------------
% File     : BOO008-2 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Boolean Algebra
% Problem  : Sum is associative ( (X + Y) + Z = X + (Y + Z) )
% Version  : [ANL] (equality) axioms.
% English  :

% Refs     :
% Source   : [ANL]
% Names    : prob1.ver2.in [ANL]

% Status   : Unsatisfiable
% Rating   : 0.09 v8.2.0, 0.21 v8.1.0, 0.25 v7.5.0, 0.17 v7.4.0, 0.26 v7.3.0, 0.16 v7.1.0, 0.06 v7.0.0, 0.11 v6.4.0, 0.16 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.38 v6.0.0, 0.52 v5.5.0, 0.47 v5.4.0, 0.33 v5.3.0, 0.25 v5.2.0, 0.29 v5.1.0, 0.27 v5.0.0, 0.21 v4.1.0, 0.18 v4.0.1, 0.14 v4.0.0, 0.08 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.2.0, 0.07 v3.1.0, 0.00 v2.7.0, 0.09 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.44 v2.2.0, 0.57 v2.1.0, 0.75 v2.0.0
% Syntax   : Number of clauses     :   15 (  15 unt;   0 nHn;   1 RR)
%            Number of literals    :   15 (  15 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments :
%--------------------------------------------------------------------------
%----Include boolean algebra axioms for equality formulation
include('Axioms/BOO003-0.ax').
%--------------------------------------------------------------------------
%----The ANL version of this problem includes the idempotence lemmas

%input_clause(idempotence_of_add,axiom,
%    [++equal(add(X,X),X)]).
%input_clause(idempotence_of_multiply,axiom,
%    [++equal(multiply(X,X),X)]).

cnf(prove_associativity,negated_conjecture,
    add(a,add(b,c)) != add(add(a,b),c) ).

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