%------------------------------------------------------------------------------ % File : BOO003-4 : TPTP v3.3.0. Released v1.1.0. % Domain : Boolean Algebra % Problem : Multiplication is idempotent (X * X = X) % Version : [Ver94] (equality) axioms. % English : % Refs : [Ver94] Veroff (1994), Problem Set % Source : [Ver94] % Names : TA [Ver94] % Status : Unsatisfiable % Rating : 0.00 v2.1.0, 0.13 v2.0.0 % Syntax : Number of clauses : 9 ( 0 non-Horn; 9 unit; 1 RR) % Number of atoms : 9 ( 9 equality) % Maximal clause size : 1 ( 1 average) % Number of predicates : 1 ( 0 propositional; 2-2 arity) % Number of functors : 6 ( 3 constant; 0-2 arity) % Number of variables : 14 ( 0 singleton) % Maximal term depth : 3 ( 2 average) % Comments : % : tptp2X -f tptp:short BOO003-4.p %------------------------------------------------------------------------------ cnf(commutativity_of_add,axiom,( add(X,Y) = add(Y,X) )). cnf(commutativity_of_multiply,axiom,( multiply(X,Y) = multiply(Y,X) )). cnf(distributivity1,axiom,( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )). cnf(distributivity2,axiom,( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )). cnf(additive_id1,axiom,( add(X,additive_identity) = X )). cnf(multiplicative_id1,axiom,( multiply(X,multiplicative_identity) = X )). cnf(additive_inverse1,axiom,( add(X,inverse(X)) = multiplicative_identity )). cnf(multiplicative_inverse1,axiom,( multiply(X,inverse(X)) = additive_identity )). cnf(prove_a_times_a_is_a,negated_conjecture,( multiply(a,a) != a )). %------------------------------------------------------------------------------