TPTP Problem File: NUM022-1.p
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%--------------------------------------------------------------------------
% File : NUM022-1 : TPTP v9.0.0. Released v1.0.0.
% Domain : Number Theory
% Problem : Numerator divisble by smaller denominators
% Version : [LS74] axioms : Incomplete.
% English : If a numerator is divisible by a denominator, then the numerator
% is divisible by numbers smaller than the denominator.
% Refs : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol
% : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% Source : [SPRFN]
% Names : ls651 [LS74]
% Status : Unsatisfiable
% Rating : 0.00 v7.1.0, 0.17 v7.0.0, 0.12 v6.3.0, 0.14 v6.2.0, 0.00 v2.0.0
% Syntax : Number of clauses : 10 ( 3 unt; 1 nHn; 10 RR)
% Number of literals : 20 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 3 usr; 0 prp; 2-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 1 sgn)
% SPC : CNF_UNS_RFO_NEQ_NHN
% Comments :
%--------------------------------------------------------------------------
%----Include the recursive function less axioms
include('Axioms/NUM001-1.ax').
%----Include the recursive function divides axioms
include('Axioms/NUM001-2.ax').
%--------------------------------------------------------------------------
cnf(transitivity,axiom,
( ~ equalish(A,B)
| ~ equalish(C,A)
| equalish(C,B) ) ).
cnf(a_less_than_b,hypothesis,
less(a,b) ).
cnf(b_divides_d,hypothesis,
divides(b,d) ).
cnf(prove_a_less_than_d,negated_conjecture,
~ less(a,d) ).
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