%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM015-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 1.76s 1.94s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 8 unt; 3 nHn; 11 RR)
% Number of literals : 25 ( 0 equ; 8 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 : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ divides(A,B)
| ~ divides(B,C)
| divides(A,C) ),
file('NUM015-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ less(n1,A)
| ~ less(A,a)
| prime(factor_of(A)) ),
file('NUM015-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ less(n1,A)
| ~ less(A,a)
| divides(factor_of(A),A) ),
file('NUM015-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ prime(A)
| ~ divides(A,a) ),
file('NUM015-1.p',unknown),
[] ).
cnf(5,axiom,
divides(A,A),
file('NUM015-1.p',unknown),
[] ).
cnf(6,axiom,
( prime(A)
| divides(divisor(A),A) ),
file('NUM015-1.p',unknown),
[] ).
cnf(7,axiom,
( prime(A)
| less(n1,divisor(A)) ),
file('NUM015-1.p',unknown),
[] ).
cnf(8,axiom,
( prime(A)
| less(divisor(A),A) ),
file('NUM015-1.p',unknown),
[] ).
cnf(10,plain,
divides(divisor(a),a),
inference(hyper,[status(thm)],[6,4,5]),
[iquote('hyper,6,4,5')] ).
cnf(13,plain,
less(n1,divisor(a)),
inference(hyper,[status(thm)],[7,4,5]),
[iquote('hyper,7,4,5')] ).
cnf(15,plain,
less(divisor(a),a),
inference(hyper,[status(thm)],[8,4,5]),
[iquote('hyper,8,4,5')] ).
cnf(16,plain,
divides(factor_of(divisor(a)),divisor(a)),
inference(hyper,[status(thm)],[15,3,13]),
[iquote('hyper,15,3,13')] ).
cnf(17,plain,
prime(factor_of(divisor(a))),
inference(hyper,[status(thm)],[15,2,13]),
[iquote('hyper,15,2,13')] ).
cnf(22,plain,
divides(factor_of(divisor(a)),a),
inference(hyper,[status(thm)],[16,1,10]),
[iquote('hyper,16,1,10')] ).
cnf(23,plain,
$false,
inference(hyper,[status(thm)],[22,4,17]),
[iquote('hyper,22,4,17')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM015-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 09:49:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.76/1.94 ----- Otter 3.3f, August 2004 -----
% 1.76/1.94 The process was started by sandbox on n008.cluster.edu,
% 1.76/1.94 Wed Jul 27 09:49:23 2022
% 1.76/1.94 The command was "./otter". The process ID is 6522.
% 1.76/1.94
% 1.76/1.94 set(prolog_style_variables).
% 1.76/1.94 set(auto).
% 1.76/1.94 dependent: set(auto1).
% 1.76/1.94 dependent: set(process_input).
% 1.76/1.94 dependent: clear(print_kept).
% 1.76/1.94 dependent: clear(print_new_demod).
% 1.76/1.94 dependent: clear(print_back_demod).
% 1.76/1.94 dependent: clear(print_back_sub).
% 1.76/1.94 dependent: set(control_memory).
% 1.76/1.94 dependent: assign(max_mem, 12000).
% 1.76/1.94 dependent: assign(pick_given_ratio, 4).
% 1.76/1.94 dependent: assign(stats_level, 1).
% 1.76/1.94 dependent: assign(max_seconds, 10800).
% 1.76/1.94 clear(print_given).
% 1.76/1.94
% 1.76/1.94 list(usable).
% 1.76/1.94 0 [] divides(X,X).
% 1.76/1.94 0 [] -divides(X,Y)| -divides(Y,Z)|divides(X,Z).
% 1.76/1.94 0 [] prime(X)|divides(divisor(X),X).
% 1.76/1.94 0 [] prime(X)|less(n1,divisor(X)).
% 1.76/1.94 0 [] prime(X)|less(divisor(X),X).
% 1.76/1.94 0 [] -less(n1,X)| -less(X,a)|prime(factor_of(X)).
% 1.76/1.94 0 [] -less(n1,X)| -less(X,a)|divides(factor_of(X),X).
% 1.76/1.94 0 [] less(n1,a).
% 1.76/1.94 0 [] -prime(X)| -divides(X,a).
% 1.76/1.94 end_of_list.
% 1.76/1.94
% 1.76/1.94 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.76/1.94
% 1.76/1.94 This is a non-Horn set without equality. The strategy will
% 1.76/1.94 be ordered hyper_res, unit deletion, and factoring, with
% 1.76/1.94 satellites in sos and with nuclei in usable.
% 1.76/1.94
% 1.76/1.94 dependent: set(hyper_res).
% 1.76/1.94 dependent: set(factor).
% 1.76/1.94 dependent: set(unit_deletion).
% 1.76/1.94
% 1.76/1.94 ------------> process usable:
% 1.76/1.94 ** KEPT (pick-wt=9): 1 [] -divides(A,B)| -divides(B,C)|divides(A,C).
% 1.76/1.94 ** KEPT (pick-wt=9): 2 [] -less(n1,A)| -less(A,a)|prime(factor_of(A)).
% 1.76/1.94 ** KEPT (pick-wt=10): 3 [] -less(n1,A)| -less(A,a)|divides(factor_of(A),A).
% 1.76/1.94 ** KEPT (pick-wt=5): 4 [] -prime(A)| -divides(A,a).
% 1.76/1.94
% 1.76/1.94 ------------> process sos:
% 1.76/1.94 ** KEPT (pick-wt=3): 5 [] divides(A,A).
% 1.76/1.94 ** KEPT (pick-wt=6): 6 [] prime(A)|divides(divisor(A),A).
% 1.76/1.94 ** KEPT (pick-wt=6): 7 [] prime(A)|less(n1,divisor(A)).
% 1.76/1.94 ** KEPT (pick-wt=6): 8 [] prime(A)|less(divisor(A),A).
% 1.76/1.94 ** KEPT (pick-wt=3): 9 [] less(n1,a).
% 1.76/1.94
% 1.76/1.94 ======= end of input processing =======
% 1.76/1.94
% 1.76/1.94 =========== start of search ===========
% 1.76/1.94
% 1.76/1.94 -------- PROOF --------
% 1.76/1.94
% 1.76/1.94 -----> EMPTY CLAUSE at 0.00 sec ----> 23 [hyper,22,4,17] $F.
% 1.76/1.94
% 1.76/1.94 Length of proof is 6. Level of proof is 3.
% 1.76/1.94
% 1.76/1.94 ---------------- PROOF ----------------
% 1.76/1.94 % SZS status Unsatisfiable
% 1.76/1.94 % SZS output start Refutation
% See solution above
% 1.76/1.94 ------------ end of proof -------------
% 1.76/1.94
% 1.76/1.94
% 1.76/1.94 Search stopped by max_proofs option.
% 1.76/1.94
% 1.76/1.94
% 1.76/1.94 Search stopped by max_proofs option.
% 1.76/1.94
% 1.76/1.94 ============ end of search ============
% 1.76/1.94
% 1.76/1.94 -------------- statistics -------------
% 1.76/1.94 clauses given 15
% 1.76/1.94 clauses generated 25
% 1.76/1.94 clauses kept 22
% 1.76/1.94 clauses forward subsumed 10
% 1.76/1.94 clauses back subsumed 0
% 1.76/1.94 Kbytes malloced 976
% 1.76/1.94
% 1.76/1.94 ----------- times (seconds) -----------
% 1.76/1.94 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.76/1.94
% 1.76/1.94 That finishes the proof of the theorem.
% 1.76/1.94
% 1.76/1.94 Process 6522 finished Wed Jul 27 09:49:25 2022
% 1.76/1.94 Otter interrupted
% 1.76/1.94 PROOF FOUND
%------------------------------------------------------------------------------