%------------------------------------------------------------------------------
% File     : RNG132-1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Rings
% Problem  : Euler's four-square identity
% Version  : Especial
% English  :  

% Refs     : [Sai24] Saito (2024), Email to Geoff Sutcliffe
% Source   : [Sai24]
% Names    : eular.p [Sai24]

% Status   : Satisfiable
% Rating   : 0.00 v9.3.0
% Syntax   : Number of clauses     :   11 (  11 unt;   0 nHn;   1 RR)
%            Number of literals    :   11 (  11 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :   14 (  14 usr;   9 con; 0-4 aty)
%            Number of variables   :   23 (   0 sgn)
% SPC      : CNF_SAT_RFO_PEQ_UEQ

% Comments : The distributive laws should be used in the distributing way.
%------------------------------------------------------------------------------
% distributivities should be used in the distributing way
cnf(plus_comm,axiom,
    plus(X,Y) = plus(Y,X) ).

cnf(plus_assoc,axiom,
    plus(X,plus(Y,Z)) = plus(plus(X,Y),Z) ).

cnf(plus_zero,axiom,
    plus(zero,X) = X ).

cnf(plus_inv,axiom,
    plus(X,minus(X)) = zero ).

cnf(times_assoc,axiom,
    times(X,times(Y,Z)) = times(times(X,Y),Z) ).

cnf(times_com,axiom,
    times(X,Y) = times(Y,X) ).

cnf(square,axiom,
    sq(X) = times(X,X) ).

cnf(distrib,axiom,
    times(X,plus(Y,Z)) = plus(times(X,Y),times(X,Z)) ).

cnf(distrib_001,axiom,
    times(plus(X,Y),Z) = plus(times(X,Z),times(Y,Z)) ).

cnf(sum4,axiom,
    sum4(X,Y,Z,W) = plus(X,plus(Y,plus(Z,W))) ).

cnf(goals,negated_conjecture,
    times(sum4(sq(a1),sq(a2),sq(a3),sq(a4)),sum4(sq(a1),sq(a2),sq(a3),sq(a4))) != sum4(sq(sum4(times(a1,b1),times(minus(a2),b2),times(minus(a3),b3),times(minus(a4),b4))),sq(sum4(times(a1,b2),times(a2,b1),times(a3,b4),times(minus(a4),b3))),sq(sum4(times(a1,b3),times(minus(a2),b4),times(minus(a3),b1),times(a4,b2))),sq(sum4(times(a1,b4),times(a2,b3),times(minus(a3),b2),times(minus(a4),b1)))) ).

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