TPTP Problem File: NUM016-1.p
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% File : NUM016-1 : TPTP v9.0.0. Released v1.0.0.
% Domain : Number Theory
% Problem : There exist infinitely many primes
% Version : [LS74] axioms.
% English :
% Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore
% : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th
% : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol
% : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% Source : [SPRFN]
% Names : Example 8b [Luc68]
% : ls17 [LS74]
% : Problem 17 [LS74]
% : ls17 [WM76]
% 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 v5.4.0, 0.10 v5.3.0, 0.00 v2.0.0
% Syntax : Number of clauses : 12 ( 4 unt; 3 nHn; 7 RR)
% Number of literals : 22 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn)
% SPC : CNF_UNS_RFO_NEQ_NHN
% Comments : These axioms are the same as in [Luc68]
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cnf(nothing_is_less_than_itself,axiom,
~ less(X,X) ).
cnf(numbers_are_different,axiom,
( ~ less(X,Y)
| ~ less(Y,X) ) ).
cnf(everything_divides_itself,axiom,
divides(X,X) ).
cnf(transitivity_of_divides,axiom,
( ~ divides(X,Y)
| ~ divides(Y,Z)
| divides(X,Z) ) ).
cnf(small_divides_large,axiom,
( ~ divides(X,Y)
| ~ less(Y,X) ) ).
cnf(a_prime_is_less_than_the_next_one,axiom,
less(X,factorial_plus_one(X)) ).
cnf(divisor_is_smaller,axiom,
( ~ divides(X,factorial_plus_one(Y))
| less(Y,X) ) ).
cnf(division_by_prime_divisor,axiom,
( prime(X)
| divides(prime_divisor(X),X) ) ).
cnf(prime_divsiors,axiom,
( prime(X)
| prime(prime_divisor(X)) ) ).
cnf(smaller_prime_divisors,axiom,
( prime(X)
| less(prime_divisor(X),X) ) ).
cnf(a_is_prime,hypothesis,
prime(a) ).
cnf(prove_there_is_another_prime,negated_conjecture,
( ~ prime(X)
| ~ less(a,X)
| less(factorial_plus_one(a),X) ) ).
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