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% File     : LAT071-1 : TPTP v8.2.0. Released v2.6.0.
% Domain   : Lattice Theory (Orthomodularlattices)
% Problem  : Given single axiom OML-21C, prove associativity
% Version  : [MRV03] (equality) axioms.
% English  : Given a single axiom candidate OML-21C for orthomodular lattices
%            (OML) in terms of the Sheffer Stroke, prove a Sheffer stroke form
%            of associativity.

% Refs     : [MRV03] McCune et al. (2003), Sheffer Stroke Bases for Ortholatt
% Source   : [MRV03]
% Names    : OML-21C-associativity [MRV03]

% Status   : Open
% Rating   : 1.00 v2.6.0
% Syntax   : Number of clauses     :    2 (   2 unt;   0 nHn;   1 RR)
%            Number of literals    :    2 (   2 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :    4 (   2 sgn)
% SPC      : CNF_OPN_RFO_PEQ_UEQ

% Comments :
%--------------------------------------------------------------------------
%----Single axiom OML-21C
cnf(oml_21C,axiom,
    f(f(B,A),f(f(f(f(B,A),A),f(C,A)),f(f(A,A),D))) = A ).

%----Denial of Sheffer stroke associativity
cnf(associativity,negated_conjecture,
    f(a,f(f(b,c),f(b,c))) != f(c,f(f(b,a),f(b,a))) ).

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