TSTP Solution File: NUM017-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM017-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 6.96s 7.20s
% Output : Refutation 6.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 19 ( 11 unt; 0 nHn; 12 RR)
% Number of literals : 33 ( 0 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( ~ e_qualish(A,B)
| ~ divides(C,A)
| divides(C,B) ),
file('NUM017-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(A,B,C)
| ~ product(D,B,E)
| ~ product(F,D,A)
| product(F,E,C) ),
file('NUM017-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| product(B,A,C) ),
file('NUM017-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('NUM017-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ divides(A,B)
| product(A,second_divided_by_1st(A,B),B) ),
file('NUM017-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(A,B,C)
| divides(A,C) ),
file('NUM017-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ divides(A,B)
| ~ product(C,C,B)
| ~ prime(A)
| divides(A,C) ),
file('NUM017-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ divides(A,c)
| ~ divides(A,b) ),
file('NUM017-1.p',unknown),
[] ).
cnf(21,axiom,
product(A,B,multiply(A,B)),
file('NUM017-1.p',unknown),
[] ).
cnf(22,axiom,
prime(a),
file('NUM017-1.p',unknown),
[] ).
cnf(28,plain,
divides(A,multiply(A,B)),
inference(hyper,[status(thm)],[21,16]),
[iquote('hyper,21,16')] ).
cnf(33,plain,
product(A,B,multiply(B,A)),
inference(hyper,[status(thm)],[21,11]),
[iquote('hyper,21,11')] ).
cnf(45,plain,
divides(a,a),
inference(hyper,[status(thm)],[28,17,21,22]),
[iquote('hyper,28,17,21,22')] ).
cnf(50,plain,
product(a,second_divided_by_1st(a,a),a),
inference(hyper,[status(thm)],[45,15]),
[iquote('hyper,45,15')] ).
cnf(77,plain,
divides(A,multiply(B,A)),
inference(hyper,[status(thm)],[33,16]),
[iquote('hyper,33,16')] ).
cnf(380,plain,
product(a,multiply(A,second_divided_by_1st(a,a)),multiply(A,a)),
inference(hyper,[status(thm)],[50,10,33,33]),
[iquote('hyper,50,10,33,33')] ).
cnf(4397,plain,
e_qualish(multiply(A,second_divided_by_1st(a,a)),A),
inference(hyper,[status(thm)],[380,12,33]),
[iquote('hyper,380,12,33')] ).
cnf(4498,plain,
divides(second_divided_by_1st(a,a),A),
inference(hyper,[status(thm)],[4397,6,77]),
[iquote('hyper,4397,6,77')] ).
cnf(4657,plain,
$false,
inference(hyper,[status(thm)],[4498,19,4498]),
[iquote('hyper,4498,19,4498')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM017-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 10:10:51 EDT 2022
% 0.11/0.33 % CPUTime :
% 6.96/7.20 ----- Otter 3.3f, August 2004 -----
% 6.96/7.20 The process was started by sandbox2 on n027.cluster.edu,
% 6.96/7.20 Wed Jul 27 10:10:52 2022
% 6.96/7.20 The command was "./otter". The process ID is 18634.
% 6.96/7.20
% 6.96/7.20 set(prolog_style_variables).
% 6.96/7.20 set(auto).
% 6.96/7.20 dependent: set(auto1).
% 6.96/7.20 dependent: set(process_input).
% 6.96/7.20 dependent: clear(print_kept).
% 6.96/7.20 dependent: clear(print_new_demod).
% 6.96/7.20 dependent: clear(print_back_demod).
% 6.96/7.20 dependent: clear(print_back_sub).
% 6.96/7.20 dependent: set(control_memory).
% 6.96/7.20 dependent: assign(max_mem, 12000).
% 6.96/7.20 dependent: assign(pick_given_ratio, 4).
% 6.96/7.20 dependent: assign(stats_level, 1).
% 6.96/7.20 dependent: assign(max_seconds, 10800).
% 6.96/7.20 clear(print_given).
% 6.96/7.20
% 6.96/7.20 list(usable).
% 6.96/7.20 0 [] e_qualish(X,X).
% 6.96/7.20 0 [] -e_qualish(X,Y)|e_qualish(Y,X).
% 6.96/7.20 0 [] -e_qualish(X,Y)| -e_qualish(Y,Z)|e_qualish(X,Z).
% 6.96/7.20 0 [] -e_qualish(D,B)| -product(C,A,D)|product(C,A,B).
% 6.96/7.20 0 [] -e_qualish(D,B)| -product(C,D,A)|product(C,B,A).
% 6.96/7.20 0 [] -e_qualish(C,B)| -product(C,D,A)|product(B,D,A).
% 6.96/7.20 0 [] -e_qualish(B,A)| -divides(C,B)|divides(C,A).
% 6.96/7.20 0 [] -e_qualish(A,B)| -divides(A,C)|divides(B,C).
% 6.96/7.20 0 [] -e_qualish(A,B)| -prime(A)|prime(B).
% 6.96/7.20 0 [] product(A,B,multiply(A,B)).
% 6.96/7.20 0 [] -product(A,B,C)| -product(D,E,B)| -product(A,D,F)|product(F,E,C).
% 6.96/7.20 0 [] -product(A,B,C)| -product(D,B,E)| -product(F,D,A)|product(F,E,C).
% 6.96/7.20 0 [] -product(A,B,C)|product(B,A,C).
% 6.96/7.20 0 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 6.96/7.20 0 [] -divides(A,B)| -divides(C,A)|divides(C,B).
% 6.96/7.20 0 [] -product(A,B,C)| -product(A,B,D)|e_qualish(D,C).
% 6.96/7.20 0 [] -divides(A,B)|product(A,second_divided_by_1st(A,B),B).
% 6.96/7.20 0 [] -product(A,B,C)|divides(A,C).
% 6.96/7.20 0 [] -divides(A,B)| -product(C,C,B)| -prime(A)|divides(A,C).
% 6.96/7.20 0 [] prime(a).
% 6.96/7.20 0 [] product(b,b,d).
% 6.96/7.20 0 [] product(c,c,e).
% 6.96/7.20 0 [] -product(a,e,d).
% 6.96/7.20 0 [] -divides(A,c)| -divides(A,b).
% 6.96/7.20 end_of_list.
% 6.96/7.20
% 6.96/7.20 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 6.96/7.20
% 6.96/7.20 This is a Horn set without equality. The strategy will
% 6.96/7.20 be hyperresolution, with satellites in sos and nuclei
% 6.96/7.20 in usable.
% 6.96/7.20
% 6.96/7.20 dependent: set(hyper_res).
% 6.96/7.20 dependent: clear(order_hyper).
% 6.96/7.20
% 6.96/7.20 ------------> process usable:
% 6.96/7.20 ** KEPT (pick-wt=6): 1 [] -e_qualish(A,B)|e_qualish(B,A).
% 6.96/7.20 ** KEPT (pick-wt=9): 2 [] -e_qualish(A,B)| -e_qualish(B,C)|e_qualish(A,C).
% 6.96/7.20 ** KEPT (pick-wt=11): 3 [] -e_qualish(A,B)| -product(C,D,A)|product(C,D,B).
% 6.96/7.20 ** KEPT (pick-wt=11): 4 [] -e_qualish(A,B)| -product(C,A,D)|product(C,B,D).
% 6.96/7.20 ** KEPT (pick-wt=11): 5 [] -e_qualish(A,B)| -product(A,C,D)|product(B,C,D).
% 6.96/7.20 ** KEPT (pick-wt=9): 6 [] -e_qualish(A,B)| -divides(C,A)|divides(C,B).
% 6.96/7.20 ** KEPT (pick-wt=9): 7 [] -e_qualish(A,B)| -divides(A,C)|divides(B,C).
% 6.96/7.20 ** KEPT (pick-wt=7): 8 [] -e_qualish(A,B)| -prime(A)|prime(B).
% 6.96/7.20 ** KEPT (pick-wt=16): 9 [] -product(A,B,C)| -product(D,E,B)| -product(A,D,F)|product(F,E,C).
% 6.96/7.20 ** KEPT (pick-wt=16): 10 [] -product(A,B,C)| -product(D,B,E)| -product(F,D,A)|product(F,E,C).
% 6.96/7.20 ** KEPT (pick-wt=8): 11 [] -product(A,B,C)|product(B,A,C).
% 6.96/7.20 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 6.96/7.20 ** KEPT (pick-wt=9): 13 [] -divides(A,B)| -divides(C,A)|divides(C,B).
% 6.96/7.20 ** KEPT (pick-wt=11): 14 [] -product(A,B,C)| -product(A,B,D)|e_qualish(D,C).
% 6.96/7.20 ** KEPT (pick-wt=9): 15 [] -divides(A,B)|product(A,second_divided_by_1st(A,B),B).
% 6.96/7.20 ** KEPT (pick-wt=7): 16 [] -product(A,B,C)|divides(A,C).
% 6.96/7.20 ** KEPT (pick-wt=12): 17 [] -divides(A,B)| -product(C,C,B)| -prime(A)|divides(A,C).
% 6.96/7.20 ** KEPT (pick-wt=4): 18 [] -product(a,e,d).
% 6.96/7.20 ** KEPT (pick-wt=6): 19 [] -divides(A,c)| -divides(A,b).
% 6.96/7.20
% 6.96/7.20 ------------> process sos:
% 6.96/7.20 ** KEPT (pick-wt=3): 20 [] e_qualish(A,A).
% 6.96/7.20 ** KEPT (pick-wt=6): 21 [] product(A,B,multiply(A,B)).
% 6.96/7.20 ** KEPT (pick-wt=2): 22 [] prime(a).
% 6.96/7.20 ** KEPT (pick-wt=4): 23 [] product(b,b,d).
% 6.96/7.20 ** KEPT (pick-wt=4): 24 [] product(c,c,e).
% 6.96/7.20
% 6.96/7.20 ======= end of input processing =======
% 6.96/7.20
% 6.96/7.20 =========== start of search ===========
% 6.96/7.20
% 6.96/7.20
% 6.96/7.20 Resetting weight limit to 9.
% 6.96/7.20
% 6.96/7.20
% 6.96/7.20 Resetting weight limit to 9.
% 6.96/7.20
% 6.96/7.20 sos_size=3353
% 6.96/7.20
% 6.96/7.20 -------- PROOF --------
% 6.96/7.20
% 6.96/7.20 -----> EMPTY CLAUSE at 5.31 sec ----> 4657 [hyper,4498,19,4498] $F.
% 6.96/7.20
% 6.96/7.20 Length of proof is 8. Level of proof is 6.
% 6.96/7.20
% 6.96/7.20 ---------------- PROOF ----------------
% 6.96/7.20 % SZS status Unsatisfiable
% 6.96/7.20 % SZS output start Refutation
% See solution above
% 6.96/7.20 ------------ end of proof -------------
% 6.96/7.20
% 6.96/7.20
% 6.96/7.20 Search stopped by max_proofs option.
% 6.96/7.20
% 6.96/7.20
% 6.96/7.20 Search stopped by max_proofs option.
% 6.96/7.20
% 6.96/7.20 ============ end of search ============
% 6.96/7.20
% 6.96/7.20 -------------- statistics -------------
% 6.96/7.20 clauses given 1027
% 6.96/7.20 clauses generated 3217898
% 6.96/7.20 clauses kept 4656
% 6.96/7.20 clauses forward subsumed 28463
% 6.96/7.20 clauses back subsumed 260
% 6.96/7.20 Kbytes malloced 5859
% 6.96/7.20
% 6.96/7.20 ----------- times (seconds) -----------
% 6.96/7.20 user CPU time 5.31 (0 hr, 0 min, 5 sec)
% 6.96/7.20 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 6.96/7.20 wall-clock time 6 (0 hr, 0 min, 6 sec)
% 6.96/7.20
% 6.96/7.20 That finishes the proof of the theorem.
% 6.96/7.20
% 6.96/7.20 Process 18634 finished Wed Jul 27 10:10:58 2022
% 6.96/7.20 Otter interrupted
% 6.96/7.20 PROOF FOUND
%------------------------------------------------------------------------------