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%--------------------------------------------------------------------------
% File : RNG019-6 : TPTP v2.4.1. Released v1.0.0.
% Domain : Ring Theory (Alternative)
% Problem : First part of the linearised form of the associator
% Version : [Ste87] (equality) axioms.
% 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 : [Ste87]
% Names : c24 [Ste87]
% Status : unsatisfiable
% Rating : 0.25 v2.4.0, 0.67 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.50 v2.0.0
% Syntax : Number of clauses : 16 ( 0 non-Horn; 16 unit; 1 RR)
% Number of literals : 16 ( 16 equality)
% Maximal clause size : 1 ( 1 average)
% Number of predicates : 1 ( 0 propositional; 2-2 arity)
% Number of functors : 10 ( 5 constant; 0-3 arity)
% Number of variables : 27 ( 2 singleton)
% Maximal term depth : 5 ( 2 average)
% Comments :
% : tptp2X -f tptp -t rm_equality:rstfp RNG019-6.p
%--------------------------------------------------------------------------
input_clause(commutativity_for_addition,axiom,
[++ equal(add(X, Y), add(Y, X))]).
input_clause(associativity_for_addition,axiom,
[++ equal(add(X, add(Y, Z)), add(add(X, Y), Z))]).
input_clause(left_additive_identity,axiom,
[++ equal(add(additive_identity, X), X)]).
input_clause(right_additive_identity,axiom,
[++ equal(add(X, additive_identity), X)]).
input_clause(left_multiplicative_zero,axiom,
[++ equal(multiply(additive_identity, X), additive_identity)]).
input_clause(right_multiplicative_zero,axiom,
[++ equal(multiply(X, additive_identity), additive_identity)]).
input_clause(left_additive_inverse,axiom,
[++ equal(add(additive_inverse(X), X), additive_identity)]).
input_clause(right_additive_inverse,axiom,
[++ equal(add(X, additive_inverse(X)), additive_identity)]).
input_clause(distribute1,axiom,
[++ equal(multiply(X, add(Y, Z)), add(multiply(X, Y), multiply(X, Z)))]).
input_clause(distribute2,axiom,
[++ equal(multiply(add(X, Y), Z), add(multiply(X, Z), multiply(Y, Z)))]).
input_clause(additive_inverse_additive_inverse,axiom,
[++ equal(additive_inverse(additive_inverse(X)), X)]).
input_clause(right_alternative,axiom,
[++ equal(multiply(multiply(X, Y), Y), multiply(X, multiply(Y, Y)))]).
input_clause(left_alternative,axiom,
[++ equal(multiply(multiply(X, X), Y), multiply(X, multiply(X, Y)))]).
input_clause(associator,axiom,
[++ equal(associator(X, Y, Z), add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))))]).
input_clause(commutator,axiom,
[++ equal(commutator(X, Y), add(multiply(Y, X), additive_inverse(multiply(X, Y))))]).
input_clause(prove_linearised_form1,conjecture,
[-- equal(associator(x, y, add(u, v)), add(associator(x, y, u), associator(x, y, v)))]).
%--------------------------------------------------------------------------
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