%------------------------------------------------------------------------------
% File     : ALG002-0 : TPTP v9.0.0. Released v8.0.0.
% Domain   : Algebra (Median)
% Axioms   : Median algebra axioms
% Version  : [VM05] axioms.
% English  :

% Refs     : [VMURL] Veroff & McCune (URL), First-order Proof of a Median A
% Source   : [VMURL]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    4 (   4 unt;   0 nHn;   0 RR)
%            Number of literals    :    4 (   4 equ;   0 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 3-3 aty)
%            Number of variables   :   12 (   1 sgn)
% SPC      : 

% Comments : UEQ format.
%------------------------------------------------------------------------------
cnf(majority,axiom,
    f(X,X,Y) = X ).

cnf(permute1,axiom,
    f(X,Y,Z) = f(Z,X,Y) ).

cnf(permute2,axiom,
    f(X,Y,Z) = f(X,Z,Y) ).

cnf(associativity,axiom,
    f(f(X,W,Y),W,Z) = f(X,W,f(Y,W,Z)) ).

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