## TPTP Axioms File: BOO001-0.ax

```%--------------------------------------------------------------------------
% File     : BOO001-0 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Algebra (Ternary Boolean)
% Axioms   : Ternary Boolean algebra (equality) axioms
% Version  : [OTTER] (equality) axioms.
% English  :

% Refs     : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
%          : [Win82] Winker (1982), Generation and Verification of Finite M
% Source   : [OTTER]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    5 (   0 non-Horn;   5 unit;   0 RR)
%            Number of atoms      :    5 (   5 equality)
%            Maximal clause size  :    1 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    2 (   0 constant; 1-3 arity)
%            Number of variables  :   13 (   2 singleton)
%            Maximal term depth   :    3 (   2 average)
% SPC      :

% Comments : These axioms appear in [Win82], in which ternary_multiply_1 is
%            shown to be independant.
%          : These axioms are also used in [Wos88], p.222.
%--------------------------------------------------------------------------
cnf(associativity,axiom,
( multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)) )).

cnf(ternary_multiply_1,axiom,
( multiply(Y,X,X) = X )).

cnf(ternary_multiply_2,axiom,
( multiply(X,X,Y) = X )).

cnf(left_inverse,axiom,
( multiply(inverse(Y),Y,X) = X )).

cnf(right_inverse,axiom,
( multiply(X,Y,inverse(Y)) = X )).

%--------------------------------------------------------------------------
```