%------------------------------------------------------------------------------
% File     : RNG131-1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Rings
% Problem  : Brahmagupta Fibonacci identity
% Version  : Especial
% English  :  

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

% Status   : Unsatisfiable
% Rating   : 0.56 v9.3.0
% Syntax   : Number of clauses     :   10 (  10 unt;   0 nHn;   1 RR)
%            Number of literals    :   10 (  10 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    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   19 (   0 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : The distributive laws 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(distrib1,axiom,
    times(X,plus(Y,Z)) = plus(times(X,Y),times(X,Z)) ).

cnf(distrib2,axiom,
    times(plus(X,Y),Z) = plus(times(X,Z),times(Y,Z)) ).

cnf(goals,negated_conjecture,
    times(plus(sq(a),sq(b)),plus(sq(c),sq(d))) != plus(sq(plus(times(a,c),times(minus(b),d))),sq(plus(times(a,d),times(b,c)))) ).

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