%--------------------------------------------------------------------------
% File     : RNG021-7 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Ring Theory (Alternative)
% Problem  : Third part of the linearised form of the associator
% Version  : [Ste87] (equality) axioms : Augmented.
% English  : The associator can be expressed in another form called
%            a linearised form. There are three clauses to be proved
%            to establish the equivalence of the two forms.

% Refs     : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin
% Source   : [TPTP]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.36 v9.0.0, 0.27 v8.2.0, 0.38 v8.1.0, 0.50 v7.5.0, 0.38 v7.4.0, 0.39 v7.3.0, 0.37 v7.1.0, 0.28 v7.0.0, 0.32 v6.4.0, 0.37 v6.3.0, 0.35 v6.2.0, 0.36 v6.1.0, 0.38 v6.0.0, 0.57 v5.5.0, 0.53 v5.4.0, 0.40 v5.3.0, 0.33 v5.2.0, 0.36 v5.1.0, 0.27 v5.0.0, 0.29 v4.1.0, 0.27 v4.0.1, 0.29 v4.0.0, 0.31 v3.7.0, 0.33 v3.4.0, 0.38 v3.3.0, 0.14 v3.2.0, 0.21 v3.1.0, 0.33 v2.7.0, 0.45 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.67 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.88 v2.0.0
% Syntax   : Number of clauses     :   23 (  23 unt;   0 nHn;   1 RR)
%            Number of literals    :   23 (  23 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :   45 (   2 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments :
%--------------------------------------------------------------------------
%----Include nonassociative ring axioms
include('Axioms/RNG003-0.ax').
%--------------------------------------------------------------------------
%----The next 7 clause are extra lemmas which Stevens found useful
cnf(product_of_inverses,axiom,
    multiply(additive_inverse(X),additive_inverse(Y)) = multiply(X,Y) ).

cnf(inverse_product1,axiom,
    multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ).

cnf(inverse_product2,axiom,
    multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ).

cnf(distributivity_of_difference1,axiom,
    multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) ).

cnf(distributivity_of_difference2,axiom,
    multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ).

cnf(distributivity_of_difference3,axiom,
    multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) ).

cnf(distributivity_of_difference4,axiom,
    multiply(add(X,Y),additive_inverse(Z)) = add(additive_inverse(multiply(X,Z)),additive_inverse(multiply(Y,Z))) ).

cnf(prove_linearised_form3,negated_conjecture,
    associator(add(u,v),x,y) != add(associator(u,x,y),associator(v,x,y)) ).

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