TPTP Problem File: RNG007-1.p
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%--------------------------------------------------------------------------
% File : RNG007-1 : TPTP v9.0.0. Released v1.0.0.
% Domain : Ring Theory
% Problem : In Boolean rings, X is its own inverse
% Version : [MOW76] axioms.
% English : Given a ring in which for all x, x * x = x, prove that for
% all x, x + x = additive_identity
% Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source : [ANL]
% Names : lemma.ver3.in [ANL]
% : lemma.ver4.in [ANL]
% Status : Unsatisfiable
% Rating : 0.00 v8.1.0, 0.11 v7.5.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.31 v5.4.0, 0.27 v5.3.0, 0.42 v5.2.0, 0.12 v5.1.0, 0.00 v5.0.0, 0.14 v4.1.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.29 v2.5.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.50 v2.0.0
% Syntax : Number of clauses : 19 ( 8 unt; 0 nHn; 12 RR)
% Number of literals : 52 ( 2 equ; 34 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn)
% SPC : CNF_UNS_RFO_SEQ_HRN
% Comments :
%--------------------------------------------------------------------------
%----Include ring theory axioms
include('Axioms/RNG001-0.ax').
%--------------------------------------------------------------------------
cnf(x_squared_is_x,hypothesis,
product(X,X,X) ).
cnf(prove_a_plus_a_is_id,negated_conjecture,
~ sum(a,a,additive_identity) ).
%--------------------------------------------------------------------------