TSTP Solution File: GRP123-2.003 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% 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 12:56:07 EDT 2022
% Result : Unsatisfiable 1.62s 1.80s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 10 unt; 5 nHn; 17 RR)
% Number of literals : 37 ( 0 equ; 13 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
~ e_qualish(e_3,e_1),
file('GRP123-2.003.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_3,e_2),
file('GRP123-2.003.p',unknown),
[] ).
cnf(8,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
file('GRP123-2.003.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP123-2.003.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| e_qualish(B,E) ),
file('GRP123-2.003.p',unknown),
[] ).
cnf(21,plain,
( ~ product(A,B,C)
| ~ product(C,D,C)
| ~ product(C,B,A)
| e_qualish(B,D) ),
inference(factor,[status(thm)],[13]),
[iquote('factor,13.2.4')] ).
cnf(27,axiom,
group_element(e_1),
file('GRP123-2.003.p',unknown),
[] ).
cnf(28,axiom,
group_element(e_2),
file('GRP123-2.003.p',unknown),
[] ).
cnf(29,axiom,
group_element(e_3),
file('GRP123-2.003.p',unknown),
[] ).
cnf(30,axiom,
product(A,A,A),
file('GRP123-2.003.p',unknown),
[] ).
cnf(33,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(hyper,[status(thm)],[29,8,28]),
[iquote('hyper,29,8,28')] ).
cnf(34,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(hyper,[status(thm)],[29,8,27]),
[iquote('hyper,29,8,27')] ).
cnf(44,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[33,21,33,30]),7])])]),
[iquote('hyper,33,21,33,30,unit_del,7,factor_simp,factor_simp')] ).
cnf(46,plain,
product(e_2,e_3,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[44,11,30]),7]),
[iquote('hyper,44,11,30,unit_del,7')] ).
cnf(47,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[34,21,34,30]),6])])]),
[iquote('hyper,34,21,34,30,unit_del,6,factor_simp,factor_simp')] ).
cnf(53,plain,
product(e_1,e_3,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[47,21,46,30]),6]),
[iquote('hyper,47,21,46,30,unit_del,6')] ).
cnf(55,plain,
e_qualish(e_3,e_1),
inference(hyper,[status(thm)],[53,11,30]),
[iquote('hyper,53,11,30')] ).
cnf(56,plain,
$false,
inference(binary,[status(thm)],[55,6]),
[iquote('binary,55.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.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 05:00:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.62/1.80 ----- Otter 3.3f, August 2004 -----
% 1.62/1.80 The process was started by sandbox2 on n024.cluster.edu,
% 1.62/1.80 Wed Jul 27 05:00:40 2022
% 1.62/1.80 The command was "./otter". The process ID is 7895.
% 1.62/1.80
% 1.62/1.80 set(prolog_style_variables).
% 1.62/1.80 set(auto).
% 1.62/1.80 dependent: set(auto1).
% 1.62/1.80 dependent: set(process_input).
% 1.62/1.80 dependent: clear(print_kept).
% 1.62/1.80 dependent: clear(print_new_demod).
% 1.62/1.80 dependent: clear(print_back_demod).
% 1.62/1.80 dependent: clear(print_back_sub).
% 1.62/1.80 dependent: set(control_memory).
% 1.62/1.80 dependent: assign(max_mem, 12000).
% 1.62/1.80 dependent: assign(pick_given_ratio, 4).
% 1.62/1.80 dependent: assign(stats_level, 1).
% 1.62/1.80 dependent: assign(max_seconds, 10800).
% 1.62/1.80 clear(print_given).
% 1.62/1.80
% 1.62/1.80 list(usable).
% 1.62/1.80 0 [] next(e_1,e_2).
% 1.62/1.80 0 [] next(e_2,e_3).
% 1.62/1.80 0 [] greater(e_2,e_1).
% 1.62/1.80 0 [] greater(e_3,e_1).
% 1.62/1.80 0 [] greater(e_3,e_2).
% 1.62/1.80 0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.62/1.80 0 [] group_element(e_1).
% 1.62/1.80 0 [] group_element(e_2).
% 1.62/1.80 0 [] group_element(e_3).
% 1.62/1.80 0 [] -e_qualish(e_1,e_2).
% 1.62/1.80 0 [] -e_qualish(e_1,e_3).
% 1.62/1.80 0 [] -e_qualish(e_2,e_1).
% 1.62/1.80 0 [] -e_qualish(e_2,e_3).
% 1.62/1.80 0 [] -e_qualish(e_3,e_1).
% 1.62/1.80 0 [] -e_qualish(e_3,e_2).
% 1.62/1.80 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3).
% 1.62/1.80 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.62/1.80 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.62/1.80 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.62/1.80 0 [] product(X,X,X).
% 1.62/1.80 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,Y1,X1)| -product(Z2,Y2,X2)|e_qualish(X1,X2).
% 1.62/1.80 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,Y1,X1)| -product(Z2,Y2,X2)|e_qualish(Y1,Y2).
% 1.62/1.80 end_of_list.
% 1.62/1.80
% 1.62/1.80 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.62/1.80
% 1.62/1.80 This is a non-Horn set without equality. The strategy will
% 1.62/1.80 be ordered hyper_res, unit deletion, and factoring, with
% 1.62/1.80 satellites in sos and with nuclei in usable.
% 1.62/1.80
% 1.62/1.80 dependent: set(hyper_res).
% 1.62/1.80 dependent: set(factor).
% 1.62/1.80 dependent: set(unit_deletion).
% 1.62/1.80
% 1.62/1.80 ------------> process usable:
% 1.62/1.80 ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.62/1.80 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.62/1.80 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_3).
% 1.62/1.80 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_1).
% 1.62/1.80 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_3).
% 1.62/1.80 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_3,e_1).
% 1.62/1.80 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_2).
% 1.62/1.80 ** KEPT (pick-wt=16): 8 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3).
% 1.62/1.80 ** KEPT (pick-wt=11): 9 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.62/1.80 ** KEPT (pick-wt=11): 10 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.62/1.80 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.62/1.80 ** KEPT (pick-wt=19): 12 [] -product(A,B,C)| -product(D,E,C)| -product(F,B,A)| -product(F,E,D)|e_qualish(A,D).
% 1.62/1.80 ** KEPT (pick-wt=19): 13 [] -product(A,B,C)| -product(D,E,C)| -product(F,B,A)| -product(F,E,D)|e_qualish(B,E).
% 1.62/1.80
% 1.62/1.80 ------------> process sos:
% 1.62/1.80 ** KEPT (pick-wt=3): 22 [] next(e_1,e_2).
% 1.62/1.80 ** KEPT (pick-wt=3): 23 [] next(e_2,e_3).
% 1.62/1.80 ** KEPT (pick-wt=3): 24 [] greater(e_2,e_1).
% 1.62/1.80 ** KEPT (pick-wt=3): 25 [] greater(e_3,e_1).
% 1.62/1.80 ** KEPT (pick-wt=3): 26 [] greater(e_3,e_2).
% 1.62/1.80 ** KEPT (pick-wt=2): 27 [] group_element(e_1).
% 1.62/1.80 ** KEPT (pick-wt=2): 28 [] group_element(e_2).
% 1.62/1.80 ** KEPT (pick-wt=2): 29 [] group_element(e_3).
% 1.62/1.80 ** KEPT (pick-wt=4): 30 [] product(A,A,A).
% 1.62/1.80
% 1.62/1.80 ======= end of input processing =======
% 1.62/1.80
% 1.62/1.80 =========== start of search ===========
% 1.62/1.80
% 1.62/1.80 -------- PROOF --------
% 1.62/1.80
% 1.62/1.80 ----> UNIT CONFLICT at 0.02 sec ----> 56 [binary,55.1,6.1] $F.
% 1.62/1.80
% 1.62/1.80 Length of proof is 8. Level of proof is 5.
% 1.62/1.80
% 1.62/1.80 ---------------- PROOF ----------------
% 1.62/1.80 % SZS status Unsatisfiable
% 1.62/1.80 % SZS output start Refutation
% See solution above
% 1.62/1.80 ------------ end of proof -------------
% 1.62/1.80
% 1.62/1.80
% 1.62/1.80 Search stopped by max_proofs option.
% 1.62/1.80
% 1.62/1.80
% 1.62/1.80 Search stopped by max_proofs option.
% 1.62/1.80
% 1.62/1.80 ============ end of search ============
% 1.62/1.80
% 1.62/1.80 -------------- statistics -------------
% 1.62/1.80 clauses given 23
% 1.62/1.80 clauses generated 904
% 1.62/1.80 clauses kept 55
% 1.62/1.80 clauses forward subsumed 871
% 1.62/1.80 clauses back subsumed 17
% 1.62/1.80 Kbytes malloced 976
% 1.62/1.80
% 1.62/1.80 ----------- times (seconds) -----------
% 1.62/1.80 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.62/1.80 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.62/1.80 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.62/1.80
% 1.62/1.80 That finishes the proof of the theorem.
% 1.62/1.80
% 1.62/1.80 Process 7895 finished Wed Jul 27 05:00:41 2022
% 1.62/1.80 Otter interrupted
% 1.62/1.80 PROOF FOUND
%------------------------------------------------------------------------------