TPTP Axioms File: ALG002+0.ax


%------------------------------------------------------------------------------
% File     : ALG002+0 : TPTP v7.5.0. Released v3.2.0.
% 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 formulae    :    4 (   4 unit)
%            Number of atoms       :    4 (   4 equality)
%            Maximal formula depth :    5 (   4 average)
%            Number of connectives :    0 (   0 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   0 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :    1 (   0 constant; 3-3 arity)
%            Number of variables   :   12 (   0 singleton;  12 !;   0 ?)
%            Maximal term depth    :    3 (   2 average)
% SPC      : 

% Comments :
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fof(majority,axiom,(
    ! [X,Y] : f(X,X,Y) = X )).

fof(permute1,axiom,(
    ! [X,Y,Z] : f(X,Y,Z) = f(Z,X,Y) )).

fof(permute2,axiom,(
    ! [X,Y,Z] : f(X,Y,Z) = f(X,Z,Y) )).

fof(associativity,axiom,(
    ! [W,X,Y,Z] : f(f(X,W,Y),W,Z) = f(X,W,f(Y,W,Z)) )).

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