TPTP Problem File: BOO021-1.p
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%--------------------------------------------------------------------------
% File : BOO021-1 : TPTP v9.0.0. Released v2.2.0.
% Domain : Boolean Algebra
% Problem : A Basis for Boolean Algebra
% Version : [MP96] (equality) axioms.
% English : This theorem starts with a (self-dual independent) basis_
% for Boolean algebra and derives commutativity of product.
% Refs : [McC98] McCune (1998), Email to G. Sutcliffe
% : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq
% Source : [McC98]
% Names : DUAL-BA-1 [MP96]
% Status : Unsatisfiable
% Rating : 0.00 v7.5.0, 0.04 v7.3.0, 0.05 v7.1.0, 0.06 v7.0.0, 0.05 v6.4.0, 0.11 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.06 v6.0.0, 0.10 v5.5.0, 0.16 v5.4.0, 0.13 v5.3.0, 0.08 v5.2.0, 0.07 v5.1.0, 0.20 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.14 v4.0.0, 0.15 v3.7.0, 0.00 v3.3.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 1 RR)
% Number of literals : 7 ( 7 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 2 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments : The other part of this problem is to prove associativity.
%--------------------------------------------------------------------------
%----Boolean Algebra:
cnf(multiply_add,axiom,
multiply(add(X,Y),Y) = Y ).
cnf(multiply_add_property,axiom,
multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ).
cnf(additive_inverse,axiom,
add(X,inverse(X)) = n1 ).
cnf(add_multiply,axiom,
add(multiply(X,Y),Y) = Y ).
cnf(add_multiply_property,axiom,
add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ).
cnf(multiplicative_inverse,axiom,
multiply(X,inverse(X)) = n0 ).
%----Denial of conclusion:
cnf(prove_commutativity_of_multiply,negated_conjecture,
multiply(b,a) != multiply(a,b) ).
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