TPTP Problem File: BOO029-1.p
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% File : BOO029-1 : TPTP v8.2.0. Released v2.2.0.
% Domain : Boolean Algebra
% Problem : Self-dual 2-basis from majority reduction, part 3.
% Version : [MP96] (equality) axioms : Especial.
% English : This is part of a proof that there exists an independent
% self-dual-2-basis for Boolean algebra by majority reduction.
% Refs : [McC98] McCune (1998), Email to G. Sutcliffe
% : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq
% Source : [McC98]
% Names : DUAL-BA-5-c [MP96]
% Status : Unsatisfiable
% Rating : 0.14 v8.2.0, 0.08 v8.1.0, 0.10 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, 0.12 v6.0.0, 0.29 v5.5.0, 0.26 v5.4.0, 0.07 v5.3.0, 0.00 v5.2.0, 0.07 v5.1.0, 0.13 v5.0.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v2.2.1
% 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 : 4 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 8 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments :
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%----Properties L1, L3, and B1 of Boolean Algebra:
cnf(l1,axiom,
add(X,multiply(Y,multiply(X,Z))) = X ).
cnf(l3,axiom,
add(add(multiply(X,Y),multiply(Y,Z)),Y) = Y ).
cnf(b1,axiom,
multiply(add(X,Y),add(X,inverse(Y))) = X ).
%----The corresponding dual properties L2, L4, and B2.
cnf(l2,axiom,
multiply(X,add(Y,add(X,Z))) = X ).
cnf(l4,axiom,
multiply(multiply(add(X,Y),add(Y,Z)),Y) = Y ).
cnf(b2,axiom,
add(multiply(X,Y),multiply(X,inverse(Y))) = X ).
%----Associativity and Commutativity of both operations:
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
cnf(commutativity_of_multiply,axiom,
multiply(X,Y) = multiply(Y,X) ).
cnf(associativity_of_add,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ).
%----Denial of conclusion:
cnf(prove_equal_inverse,negated_conjecture,
add(b,inverse(b)) != add(a,inverse(a)) ).
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