%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 1.68s 1.89s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 7 unt; 1 nHn; 9 RR)
% Number of literals : 18 ( 0 equ; 8 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 11 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ product(A,B,C)
| divides(A,C) ),
file('NUM014-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ prime(A)
| ~ product(B,C,D)
| ~ divides(A,D)
| divides(A,B)
| divides(A,C) ),
file('NUM014-1.p',unknown),
[] ).
cnf(4,axiom,
~ divides(a,b),
file('NUM014-1.p',unknown),
[] ).
cnf(5,plain,
( ~ prime(A)
| ~ product(B,B,C)
| ~ divides(A,C)
| divides(A,B) ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.4.5')] ).
cnf(6,axiom,
product(A,A,square(A)),
file('NUM014-1.p',unknown),
[] ).
cnf(7,axiom,
prime(a),
file('NUM014-1.p',unknown),
[] ).
cnf(8,axiom,
product(a,square(c),square(b)),
file('NUM014-1.p',unknown),
[] ).
cnf(11,plain,
divides(a,square(b)),
inference(hyper,[status(thm)],[8,2]),
[iquote('hyper,8,2')] ).
cnf(13,plain,
divides(a,b),
inference(hyper,[status(thm)],[11,5,7,6]),
[iquote('hyper,11,5,7,6')] ).
cnf(14,plain,
$false,
inference(binary,[status(thm)],[13,4]),
[iquote('binary,13.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 09:38:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.89 ----- Otter 3.3f, August 2004 -----
% 1.68/1.89 The process was started by sandbox2 on n019.cluster.edu,
% 1.68/1.89 Wed Jul 27 09:38:07 2022
% 1.68/1.89 The command was "./otter". The process ID is 25142.
% 1.68/1.89
% 1.68/1.89 set(prolog_style_variables).
% 1.68/1.89 set(auto).
% 1.68/1.89 dependent: set(auto1).
% 1.68/1.89 dependent: set(process_input).
% 1.68/1.89 dependent: clear(print_kept).
% 1.68/1.89 dependent: clear(print_new_demod).
% 1.68/1.89 dependent: clear(print_back_demod).
% 1.68/1.89 dependent: clear(print_back_sub).
% 1.68/1.89 dependent: set(control_memory).
% 1.68/1.89 dependent: assign(max_mem, 12000).
% 1.68/1.89 dependent: assign(pick_given_ratio, 4).
% 1.68/1.89 dependent: assign(stats_level, 1).
% 1.68/1.89 dependent: assign(max_seconds, 10800).
% 1.68/1.89 clear(print_given).
% 1.68/1.89
% 1.68/1.89 list(usable).
% 1.68/1.89 0 [] product(X,X,square(X)).
% 1.68/1.89 0 [] -product(X,Y,Z)|product(Y,X,Z).
% 1.68/1.89 0 [] -product(X,Y,Z)|divides(X,Z).
% 1.68/1.89 0 [] -prime(X)| -product(Y,Z,U)| -divides(X,U)|divides(X,Y)|divides(X,Z).
% 1.68/1.89 0 [] prime(a).
% 1.68/1.89 0 [] product(a,square(c),square(b)).
% 1.68/1.89 0 [] -divides(a,b).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.68/1.89
% 1.68/1.89 This is a non-Horn set without equality. The strategy will
% 1.68/1.89 be ordered hyper_res, unit deletion, and factoring, with
% 1.68/1.89 satellites in sos and with nuclei in usable.
% 1.68/1.89
% 1.68/1.89 dependent: set(hyper_res).
% 1.68/1.89 dependent: set(factor).
% 1.68/1.89 dependent: set(unit_deletion).
% 1.68/1.89
% 1.68/1.89 ------------> process usable:
% 1.68/1.89 ** KEPT (pick-wt=8): 1 [] -product(A,B,C)|product(B,A,C).
% 1.68/1.89 ** KEPT (pick-wt=7): 2 [] -product(A,B,C)|divides(A,C).
% 1.68/1.89 ** KEPT (pick-wt=15): 3 [] -prime(A)| -product(B,C,D)| -divides(A,D)|divides(A,B)|divides(A,C).
% 1.68/1.89 ** KEPT (pick-wt=3): 4 [] -divides(a,b).
% 1.68/1.89
% 1.68/1.89 ------------> process sos:
% 1.68/1.89 ** KEPT (pick-wt=5): 6 [] product(A,A,square(A)).
% 1.68/1.89 ** KEPT (pick-wt=2): 7 [] prime(a).
% 1.68/1.89 ** KEPT (pick-wt=6): 8 [] product(a,square(c),square(b)).
% 1.68/1.89
% 1.68/1.89 ======= end of input processing =======
% 1.68/1.89
% 1.68/1.89 =========== start of search ===========
% 1.68/1.89
% 1.68/1.89 -------- PROOF --------
% 1.68/1.89
% 1.68/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 14 [binary,13.1,4.1] $F.
% 1.68/1.89
% 1.68/1.89 Length of proof is 3. Level of proof is 2.
% 1.68/1.89
% 1.68/1.89 ---------------- PROOF ----------------
% 1.68/1.89 % SZS status Unsatisfiable
% 1.68/1.89 % SZS output start Refutation
% See solution above
% 1.68/1.89 ------------ end of proof -------------
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89 ============ end of search ============
% 1.68/1.89
% 1.68/1.89 -------------- statistics -------------
% 1.68/1.89 clauses given 6
% 1.68/1.89 clauses generated 8
% 1.68/1.89 clauses kept 13
% 1.68/1.89 clauses forward subsumed 2
% 1.68/1.89 clauses back subsumed 0
% 1.68/1.89 Kbytes malloced 976
% 1.68/1.89
% 1.68/1.89 ----------- times (seconds) -----------
% 1.68/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.89
% 1.68/1.89 That finishes the proof of the theorem.
% 1.68/1.89
% 1.68/1.89 Process 25142 finished Wed Jul 27 09:38:08 2022
% 1.68/1.89 Otter interrupted
% 1.68/1.89 PROOF FOUND
%------------------------------------------------------------------------------