1%-------------------------------------------------------------------------- 2% File : BOO020-1 : TPTP v6.0.0. Released v2.2.0. 3% Domain : Boolean Algebra 4% Problem : Frink's Theorem 5% Version : [MP96] (equality) axioms. 6% English : Prove that Frink's implicational basis for Boolean algebra 7% implies Huntington's equational basis for Boolean algebra. 8 9% Refs : [McC98] McCune (1998), Email to G. Sutcliffe 10% : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq 11% Source : [McC98] 12% Names : BA-1 [MP96] 13 14% Status : Unsatisfiable 15% Rating : 0.82 v6.0.0, 0.71 v5.5.0, 0.75 v5.4.0, 0.67 v5.3.0, 0.80 v5.2.0, 0.62 v5.1.0, 0.78 v5.0.0, 0.80 v4.1.0, 0.78 v4.0.1, 0.88 v4.0.0, 0.71 v3.7.0, 0.43 v3.4.0, 0.33 v3.3.0, 0.44 v3.1.0, 0.20 v2.7.0, 0.50 v2.6.0, 0.33 v2.5.0, 0.50 v2.4.0, 0.50 v2.3.0, 0.67 v2.2.1 16% Syntax : Number of clauses : 4 ( 0 non-Horn; 1 unit; 3 RR) 17% Number of atoms : 8 ( 8 equality) 18% Maximal clause size : 3 ( 2 average) 19% Number of predicates : 1 ( 0 propositional; 2-2 arity) 20% Number of functors : 6 ( 4 constant; 0-2 arity) 21% Number of variables : 9 ( 0 singleton) 22% Maximal term depth : 5 ( 3 average) 23% SPC : CNF_UNS_RFO_PEQ_NUE 24 25% Comments : 26%-------------------------------------------------------------------------- 27%----Frink's implicational basis for Boolean Algebra: 28cnf(frink1,axiom, 29 ( add(X,X) = X )). 30 31cnf(frink2,axiom, 32 ( add(add(add(X,Y),Z),U) != add(add(Y,Z),X) 33 | add(add(add(X,Y),Z),inverse(U)) = n0 )). 34 35cnf(frink3,axiom, 36 ( add(add(add(X,Y),Z),inverse(U)) != n0 37 | add(add(add(X,Y),Z),U) = add(add(Y,Z),X) )). 38 39%----Denial of Huntington's equational basis for Boolean Algebra: 40cnf(prove_huntington,negated_conjecture, 41 ( add(inverse(add(a,inverse(b))),inverse(add(inverse(a),inverse(b)))) != b 42 | add(add(a,b),c) != add(a,add(b,c)) 43 | add(b,a) != add(a,b) )). 44 45%-------------------------------------------------------------------------- 46