TSTP Solution File: NUM016-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:07:26 EDT 2022
% Result : Unsatisfiable 1.59s 1.80s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 8 unt; 3 nHn; 10 RR)
% Number of literals : 21 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ less(A,A),
file('NUM016-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ less(A,B)
| ~ less(B,A) ),
file('NUM016-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ divides(A,factorial_plus_one(B))
| less(B,A) ),
file('NUM016-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ prime(A)
| ~ less(a,A)
| less(factorial_plus_one(a),A) ),
file('NUM016-2.p',unknown),
[] ).
cnf(5,axiom,
less(A,factorial_plus_one(A)),
file('NUM016-2.p',unknown),
[] ).
cnf(6,axiom,
( prime(A)
| divides(prime_divisor(A),A) ),
file('NUM016-2.p',unknown),
[] ).
cnf(7,axiom,
( prime(A)
| prime(prime_divisor(A)) ),
file('NUM016-2.p',unknown),
[] ).
cnf(8,axiom,
( prime(A)
| less(prime_divisor(A),A) ),
file('NUM016-2.p',unknown),
[] ).
cnf(9,plain,
prime(prime_divisor(factorial_plus_one(a))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[7,4,5]),1]),
[iquote('hyper,7,4,5,unit_del,1')] ).
cnf(10,plain,
divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[6,4,5]),1]),
[iquote('hyper,6,4,5,unit_del,1')] ).
cnf(11,plain,
less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[8,4,5]),1]),
[iquote('hyper,8,4,5,unit_del,1')] ).
cnf(12,plain,
less(a,prime_divisor(factorial_plus_one(a))),
inference(hyper,[status(thm)],[10,3]),
[iquote('hyper,10,3')] ).
cnf(13,plain,
less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))),
inference(hyper,[status(thm)],[12,4,9]),
[iquote('hyper,12,4,9')] ).
cnf(14,plain,
$false,
inference(hyper,[status(thm)],[13,2,11]),
[iquote('hyper,13,2,11')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:47:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.59/1.80 ----- Otter 3.3f, August 2004 -----
% 1.59/1.80 The process was started by sandbox2 on n014.cluster.edu,
% 1.59/1.80 Wed Jul 27 09:47:54 2022
% 1.59/1.80 The command was "./otter". The process ID is 22681.
% 1.59/1.80
% 1.59/1.80 set(prolog_style_variables).
% 1.59/1.80 set(auto).
% 1.59/1.80 dependent: set(auto1).
% 1.59/1.80 dependent: set(process_input).
% 1.59/1.80 dependent: clear(print_kept).
% 1.59/1.80 dependent: clear(print_new_demod).
% 1.59/1.80 dependent: clear(print_back_demod).
% 1.59/1.80 dependent: clear(print_back_sub).
% 1.59/1.80 dependent: set(control_memory).
% 1.59/1.80 dependent: assign(max_mem, 12000).
% 1.59/1.80 dependent: assign(pick_given_ratio, 4).
% 1.59/1.80 dependent: assign(stats_level, 1).
% 1.59/1.80 dependent: assign(max_seconds, 10800).
% 1.59/1.80 clear(print_given).
% 1.59/1.80
% 1.59/1.80 list(usable).
% 1.59/1.80 0 [] -less(X,X).
% 1.59/1.80 0 [] -less(X,Y)| -less(Y,X).
% 1.59/1.80 0 [] less(X,factorial_plus_one(X)).
% 1.59/1.80 0 [] -divides(X,factorial_plus_one(Y))|less(Y,X).
% 1.59/1.80 0 [] prime(X)|divides(prime_divisor(X),X).
% 1.59/1.80 0 [] prime(X)|prime(prime_divisor(X)).
% 1.59/1.80 0 [] prime(X)|less(prime_divisor(X),X).
% 1.59/1.80 0 [] -prime(X)| -less(a,X)|less(factorial_plus_one(a),X).
% 1.59/1.80 end_of_list.
% 1.59/1.80
% 1.59/1.80 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.59/1.80
% 1.59/1.80 This is a non-Horn set without equality. The strategy will
% 1.59/1.80 be ordered hyper_res, unit deletion, and factoring, with
% 1.59/1.80 satellites in sos and with nuclei in usable.
% 1.59/1.80
% 1.59/1.80 dependent: set(hyper_res).
% 1.59/1.80 dependent: set(factor).
% 1.59/1.80 dependent: set(unit_deletion).
% 1.59/1.80
% 1.59/1.80 ------------> process usable:
% 1.59/1.80 ** KEPT (pick-wt=3): 1 [] -less(A,A).
% 1.59/1.80 ** KEPT (pick-wt=6): 2 [] -less(A,B)| -less(B,A).
% 1.59/1.80 ** KEPT (pick-wt=7): 3 [] -divides(A,factorial_plus_one(B))|less(B,A).
% 1.59/1.80 ** KEPT (pick-wt=9): 4 [] -prime(A)| -less(a,A)|less(factorial_plus_one(a),A).
% 1.59/1.80
% 1.59/1.80 ------------> process sos:
% 1.59/1.80 ** KEPT (pick-wt=4): 5 [] less(A,factorial_plus_one(A)).
% 1.59/1.80 ** KEPT (pick-wt=6): 6 [] prime(A)|divides(prime_divisor(A),A).
% 1.59/1.80 ** KEPT (pick-wt=5): 7 [] prime(A)|prime(prime_divisor(A)).
% 1.59/1.80 ** KEPT (pick-wt=6): 8 [] prime(A)|less(prime_divisor(A),A).
% 1.59/1.80
% 1.59/1.80 ======= end of input processing =======
% 1.59/1.80
% 1.59/1.80 =========== start of search ===========
% 1.59/1.80
% 1.59/1.80 -------- PROOF --------
% 1.59/1.80
% 1.59/1.80 -----> EMPTY CLAUSE at 0.00 sec ----> 14 [hyper,13,2,11] $F.
% 1.59/1.80
% 1.59/1.80 Length of proof is 5. Level of proof is 3.
% 1.59/1.80
% 1.59/1.80 ---------------- PROOF ----------------
% 1.59/1.80 % SZS status Unsatisfiable
% 1.59/1.80 % SZS output start Refutation
% See solution above
% 1.59/1.80 ------------ end of proof -------------
% 1.59/1.80
% 1.59/1.80
% 1.59/1.80 Search stopped by max_proofs option.
% 1.59/1.80
% 1.59/1.80
% 1.59/1.80 Search stopped by max_proofs option.
% 1.59/1.80
% 1.59/1.80 ============ end of search ============
% 1.59/1.80
% 1.59/1.80 -------------- statistics -------------
% 1.59/1.80 clauses given 9
% 1.59/1.80 clauses generated 11
% 1.59/1.80 clauses kept 13
% 1.59/1.80 clauses forward subsumed 5
% 1.59/1.80 clauses back subsumed 0
% 1.59/1.80 Kbytes malloced 976
% 1.59/1.80
% 1.59/1.80 ----------- times (seconds) -----------
% 1.59/1.80 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.59/1.80 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.59/1.80 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.59/1.80
% 1.59/1.80 That finishes the proof of the theorem.
% 1.59/1.80
% 1.59/1.80 Process 22681 finished Wed Jul 27 09:47:55 2022
% 1.59/1.80 Otter interrupted
% 1.59/1.80 PROOF FOUND
%------------------------------------------------------------------------------