TPTP Problem File: BOO002-2.p
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%--------------------------------------------------------------------------
% File : BOO002-2 : TPTP v8.2.0. Released v1.1.0.
% Domain : Boolean Algebra (Ternary)
% Problem : In B3 algebra, X * X^-1 * Y = Y
% Version : [OTTER] (equality) axioms : Reduced & Augmented > Incomplete.
% English :
% Refs : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr
% Source : [Wos88]
% Names : Test Problem 13 [Wos88]
% : Lemma for Axiom Independence [Wos88]
% Status : Unsatisfiable
% Rating : 0.09 v8.2.0, 0.08 v8.1.0, 0.15 v7.5.0, 0.08 v7.4.0, 0.17 v7.3.0, 0.11 v7.1.0, 0.06 v7.0.0, 0.05 v6.3.0, 0.06 v6.2.0, 0.07 v6.1.0, 0.25 v6.0.0, 0.38 v5.5.0, 0.37 v5.4.0, 0.20 v5.3.0, 0.08 v5.2.0, 0.14 v5.1.0, 0.20 v5.0.0, 0.14 v4.1.0, 0.00 v2.7.0, 0.09 v2.6.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.38 v2.0.0
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 1 RR)
% Number of literals : 6 ( 6 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 13 ( 3 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments : This version contains an extra lemma
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%----Don't include ternary Boolean algebra axioms, as one is omitted
%include('axioms/BOO001-0.ax').
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cnf(associativity,axiom,
multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)) ).
cnf(ternary_multiply_1,axiom,
multiply(Y,X,X) = X ).
cnf(ternary_multiply_2,axiom,
multiply(X,X,Y) = X ).
cnf(left_inverse,axiom,
multiply(inverse(Y),Y,X) = X ).
%----This axiom is omitted
% input_clause(right_inverse,axiom,
% [++equal(multiply(X,Y,inverse(Y)),X)]).
cnf(extra_lemma,axiom,
multiply(X,Y,X) = X ).
cnf(prove_equation,negated_conjecture,
multiply(a,inverse(a),b) != b ).
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