TSTP Solution File: NUM017-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM017-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:07:27 EDT 2022
% Result : Unsatisfiable 2.25s 2.44s
% Output : Refutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 30 ( 2 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(D,B,E)
| ~ product(F,D,A)
| product(F,E,C) ),
file('NUM017-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| product(B,A,C) ),
file('NUM017-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| B = D ),
file('NUM017-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ divides(A,B)
| product(A,second_divided_by_1st(A,B),B) ),
file('NUM017-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(A,B,C)
| divides(A,C) ),
file('NUM017-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ divides(A,B)
| ~ product(C,C,B)
| ~ prime(A)
| divides(A,C) ),
file('NUM017-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ divides(A,c)
| ~ divides(A,b) ),
file('NUM017-2.p',unknown),
[] ).
cnf(13,axiom,
product(A,B,multiply(A,B)),
file('NUM017-2.p',unknown),
[] ).
cnf(14,axiom,
prime(a),
file('NUM017-2.p',unknown),
[] ).
cnf(38,plain,
divides(A,multiply(A,B)),
inference(hyper,[status(thm)],[13,8]),
[iquote('hyper,13,8')] ).
cnf(43,plain,
product(A,B,multiply(B,A)),
inference(hyper,[status(thm)],[13,3]),
[iquote('hyper,13,3')] ).
cnf(61,plain,
divides(a,a),
inference(hyper,[status(thm)],[38,9,13,14]),
[iquote('hyper,38,9,13,14')] ).
cnf(68,plain,
product(a,second_divided_by_1st(a,a),a),
inference(hyper,[status(thm)],[61,7]),
[iquote('hyper,61,7')] ).
cnf(109,plain,
divides(A,multiply(B,A)),
inference(hyper,[status(thm)],[43,8]),
[iquote('hyper,43,8')] ).
cnf(201,plain,
product(a,multiply(A,second_divided_by_1st(a,a)),multiply(A,a)),
inference(hyper,[status(thm)],[68,2,43,43]),
[iquote('hyper,68,2,43,43')] ).
cnf(3202,plain,
multiply(A,second_divided_by_1st(a,a)) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[201,4,43])]),
[iquote('hyper,201,4,43,flip.1')] ).
cnf(3231,plain,
divides(second_divided_by_1st(a,a),A),
inference(para_from,[status(thm),theory(equality)],[3202,109]),
[iquote('para_from,3202.1.1,109.1.2')] ).
cnf(3238,plain,
$false,
inference(hyper,[status(thm)],[3231,11,3231]),
[iquote('hyper,3231,11,3231')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM017-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:36:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.25/2.44 ----- Otter 3.3f, August 2004 -----
% 2.25/2.44 The process was started by sandbox2 on n024.cluster.edu,
% 2.25/2.44 Wed Jul 27 09:36:40 2022
% 2.25/2.44 The command was "./otter". The process ID is 31947.
% 2.25/2.44
% 2.25/2.44 set(prolog_style_variables).
% 2.25/2.44 set(auto).
% 2.25/2.44 dependent: set(auto1).
% 2.25/2.44 dependent: set(process_input).
% 2.25/2.44 dependent: clear(print_kept).
% 2.25/2.44 dependent: clear(print_new_demod).
% 2.25/2.44 dependent: clear(print_back_demod).
% 2.25/2.44 dependent: clear(print_back_sub).
% 2.25/2.44 dependent: set(control_memory).
% 2.25/2.44 dependent: assign(max_mem, 12000).
% 2.25/2.44 dependent: assign(pick_given_ratio, 4).
% 2.25/2.44 dependent: assign(stats_level, 1).
% 2.25/2.44 dependent: assign(max_seconds, 10800).
% 2.25/2.44 clear(print_given).
% 2.25/2.44
% 2.25/2.44 list(usable).
% 2.25/2.44 0 [] A=A.
% 2.25/2.44 0 [] product(A,B,multiply(A,B)).
% 2.25/2.44 0 [] -product(A,B,C)| -product(D,E,B)| -product(A,D,F)|product(F,E,C).
% 2.25/2.44 0 [] -product(A,B,C)| -product(D,B,E)| -product(F,D,A)|product(F,E,C).
% 2.25/2.44 0 [] -product(A,B,C)|product(B,A,C).
% 2.25/2.44 0 [] -product(A,B,C)| -product(A,D,C)|B=D.
% 2.25/2.44 0 [] -divides(A,B)| -divides(C,A)|divides(C,B).
% 2.25/2.44 0 [] -product(A,B,C)| -product(A,B,D)|D=C.
% 2.25/2.44 0 [] -divides(A,B)|product(A,second_divided_by_1st(A,B),B).
% 2.25/2.44 0 [] -product(A,B,C)|divides(A,C).
% 2.25/2.44 0 [] -divides(A,B)| -product(C,C,B)| -prime(A)|divides(A,C).
% 2.25/2.44 0 [] prime(a).
% 2.25/2.44 0 [] product(b,b,d).
% 2.25/2.44 0 [] product(c,c,e).
% 2.25/2.44 0 [] -product(a,e,d).
% 2.25/2.44 0 [] -divides(A,c)| -divides(A,b).
% 2.25/2.44 end_of_list.
% 2.25/2.44
% 2.25/2.44 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.25/2.44
% 2.25/2.44 This is a Horn set with equality. The strategy will be
% 2.25/2.44 Knuth-Bendix and hyper_res, with positive clauses in
% 2.25/2.44 sos and nonpositive clauses in usable.
% 2.25/2.44
% 2.25/2.44 dependent: set(knuth_bendix).
% 2.25/2.44 dependent: set(anl_eq).
% 2.25/2.44 dependent: set(para_from).
% 2.25/2.44 dependent: set(para_into).
% 2.25/2.44 dependent: clear(para_from_right).
% 2.25/2.44 dependent: clear(para_into_right).
% 2.25/2.44 dependent: set(para_from_vars).
% 2.25/2.44 dependent: set(eq_units_both_ways).
% 2.25/2.44 dependent: set(dynamic_demod_all).
% 2.25/2.44 dependent: set(dynamic_demod).
% 2.25/2.44 dependent: set(order_eq).
% 2.25/2.44 dependent: set(back_demod).
% 2.25/2.44 dependent: set(lrpo).
% 2.25/2.44 dependent: set(hyper_res).
% 2.25/2.44 dependent: clear(order_hyper).
% 2.25/2.44
% 2.25/2.44 ------------> process usable:
% 2.25/2.44 ** KEPT (pick-wt=16): 1 [] -product(A,B,C)| -product(D,E,B)| -product(A,D,F)|product(F,E,C).
% 2.25/2.44 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(D,B,E)| -product(F,D,A)|product(F,E,C).
% 2.25/2.44 ** KEPT (pick-wt=8): 3 [] -product(A,B,C)|product(B,A,C).
% 2.25/2.44 ** KEPT (pick-wt=11): 4 [] -product(A,B,C)| -product(A,D,C)|B=D.
% 2.25/2.44 ** KEPT (pick-wt=9): 5 [] -divides(A,B)| -divides(C,A)|divides(C,B).
% 2.25/2.44 ** KEPT (pick-wt=11): 6 [] -product(A,B,C)| -product(A,B,D)|D=C.
% 2.25/2.44 ** KEPT (pick-wt=9): 7 [] -divides(A,B)|product(A,second_divided_by_1st(A,B),B).
% 2.25/2.44 ** KEPT (pick-wt=7): 8 [] -product(A,B,C)|divides(A,C).
% 2.25/2.44 ** KEPT (pick-wt=12): 9 [] -divides(A,B)| -product(C,C,B)| -prime(A)|divides(A,C).
% 2.25/2.44 ** KEPT (pick-wt=4): 10 [] -product(a,e,d).
% 2.25/2.44 ** KEPT (pick-wt=6): 11 [] -divides(A,c)| -divides(A,b).
% 2.25/2.44
% 2.25/2.44 ------------> process sos:
% 2.25/2.44 ** KEPT (pick-wt=3): 12 [] A=A.
% 2.25/2.44 ** KEPT (pick-wt=6): 13 [] product(A,B,multiply(A,B)).
% 2.25/2.44 ** KEPT (pick-wt=2): 14 [] prime(a).
% 2.25/2.44 ** KEPT (pick-wt=4): 15 [] product(b,b,d).
% 2.25/2.44 ** KEPT (pick-wt=4): 16 [] product(c,c,e).
% 2.25/2.44 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 2.25/2.44
% 2.25/2.44 ======= end of input processing =======
% 2.25/2.44
% 2.25/2.44 =========== start of search ===========
% 2.25/2.44
% 2.25/2.44
% 2.25/2.44 Resetting weight limit to 11.
% 2.25/2.44
% 2.25/2.44
% 2.25/2.44 Resetting weight limit to 11.
% 2.25/2.44
% 2.25/2.44 sos_size=1992
% 2.25/2.44
% 2.25/2.44 -------- PROOF --------
% 2.25/2.44
% 2.25/2.44 -----> EMPTY CLAUSE at 0.50 sec ----> 3238 [hyper,3231,11,3231] $F.
% 2.25/2.44
% 2.25/2.44 Length of proof is 8. Level of proof is 6.
% 2.25/2.44
% 2.25/2.44 ---------------- PROOF ----------------
% 2.25/2.44 % SZS status Unsatisfiable
% 2.25/2.44 % SZS output start Refutation
% See solution above
% 2.25/2.44 ------------ end of proof -------------
% 2.25/2.44
% 2.25/2.44
% 2.25/2.44 Search stopped by max_proofs option.
% 2.25/2.44
% 2.25/2.44
% 2.25/2.44 Search stopped by max_proofs option.
% 2.25/2.44
% 2.25/2.44 ============ end of search ============
% 2.25/2.44
% 2.25/2.44 -------------- statistics -------------
% 2.25/2.44 clauses given 199
% 2.25/2.44 clauses generated 23743
% 2.25/2.44 clauses kept 3152
% 2.25/2.44 clauses forward subsumed 9859
% 2.25/2.44 clauses back subsumed 372
% 2.25/2.44 Kbytes malloced 4882
% 2.25/2.44
% 2.25/2.44 ----------- times (seconds) -----------
% 2.25/2.44 user CPU time 0.50 (0 hr, 0 min, 0 sec)
% 2.25/2.44 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.25/2.44 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.25/2.44
% 2.25/2.44 That finishes the proof of the theorem.
% 2.25/2.44
% 2.25/2.44 Process 31947 finished Wed Jul 27 09:36:42 2022
% 2.25/2.44 Otter interrupted
% 2.25/2.44 PROOF FOUND
%------------------------------------------------------------------------------