TSTP Solution File: GRP126-1.004 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP126-1.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 12:56:11 EDT 2022
% Result : Unsatisfiable 1.89s 2.08s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of clauses : 40 ( 18 unt; 18 nHn; 39 RR)
% Number of literals : 83 ( 0 equ; 18 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ e_qualish(e_1,e_2),
file('GRP126-1.004.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_3),
file('GRP126-1.004.p',unknown),
[] ).
cnf(4,axiom,
~ e_qualish(e_2,e_1),
file('GRP126-1.004.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_2,e_3),
file('GRP126-1.004.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_3,e_1),
file('GRP126-1.004.p',unknown),
[] ).
cnf(8,axiom,
~ e_qualish(e_3,e_2),
file('GRP126-1.004.p',unknown),
[] ).
cnf(10,axiom,
~ e_qualish(e_4,e_1),
file('GRP126-1.004.p',unknown),
[] ).
cnf(11,axiom,
~ e_qualish(e_4,e_2),
file('GRP126-1.004.p',unknown),
[] ).
cnf(13,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3)
| product(A,B,e_4) ),
file('GRP126-1.004.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP126-1.004.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP126-1.004.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP126-1.004.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,B) ),
file('GRP126-1.004.p',unknown),
[] ).
cnf(23,axiom,
group_element(e_1),
file('GRP126-1.004.p',unknown),
[] ).
cnf(24,axiom,
group_element(e_2),
file('GRP126-1.004.p',unknown),
[] ).
cnf(25,axiom,
group_element(e_3),
file('GRP126-1.004.p',unknown),
[] ).
cnf(27,axiom,
product(A,A,A),
file('GRP126-1.004.p',unknown),
[] ).
cnf(28,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(hyper,[status(thm)],[24,13,23]),
[iquote('hyper,24,13,23')] ).
cnf(29,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(hyper,[status(thm)],[24,13,23]),
[iquote('hyper,24,13,23')] ).
cnf(30,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(hyper,[status(thm)],[25,13,24]),
[iquote('hyper,25,13,24')] ).
cnf(31,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(hyper,[status(thm)],[25,13,23]),
[iquote('hyper,25,13,23')] ).
cnf(41,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[28,15,27]),1]),
[iquote('hyper,28,15,27,unit_del,1')] ).
cnf(43,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[41,16,27]),4]),
[iquote('hyper,41,16,27,unit_del,4')] ).
cnf(48,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[29,16,27]),1]),
[iquote('hyper,29,16,27,unit_del,1')] ).
cnf(62,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[30,15,27]),5]),
[iquote('hyper,30,15,27,unit_del,5')] ).
cnf(68,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[48,15,27]),4]),
[iquote('hyper,48,15,27,unit_del,4')] ).
cnf(78,plain,
( product(e_2,e_1,e_4)
| product(e_3,e_3,e_2)
| product(e_1,e_2,e_4) ),
inference(hyper,[status(thm)],[68,17,43]),
[iquote('hyper,68,17,43')] ).
cnf(85,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[62,16,27]),8]),
[iquote('hyper,62,16,27,unit_del,8')] ).
cnf(89,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[31,15,27]),2]),
[iquote('hyper,31,15,27,unit_del,2')] ).
cnf(108,plain,
( product(e_2,e_1,e_4)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[78,14,27]),8]),
[iquote('hyper,78,14,27,unit_del,8')] ).
cnf(112,plain,
( product(e_1,e_2,e_4)
| product(e_4,e_3,e_1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[108,17,43])]),
[iquote('hyper,108,17,43,factor_simp')] ).
cnf(113,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_3,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[108,15,85]),7]),
[iquote('hyper,108,15,85,unit_del,7')] ).
cnf(159,plain,
product(e_1,e_2,e_4),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[113,16,112]),11])]),
[iquote('hyper,113,16,112,unit_del,11,factor_simp')] ).
cnf(160,plain,
( product(e_4,e_4,e_1)
| product(e_2,e_1,e_3) ),
inference(hyper,[status(thm)],[159,17,68]),
[iquote('hyper,159,17,68')] ).
cnf(176,plain,
product(e_2,e_1,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[160,14,27]),10]),
[iquote('hyper,160,14,27,unit_del,10')] ).
cnf(177,plain,
product(e_4,e_3,e_2),
inference(hyper,[status(thm)],[176,17,159]),
[iquote('hyper,176,17,159')] ).
cnf(183,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[89,16,177]),10]),
[iquote('hyper,89,16,177,unit_del,10')] ).
cnf(187,plain,
product(e_1,e_3,e_4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[183,16,27]),7]),
[iquote('hyper,183,16,27,unit_del,7')] ).
cnf(191,plain,
e_qualish(e_2,e_3),
inference(hyper,[status(thm)],[187,15,159]),
[iquote('hyper,187,15,159')] ).
cnf(192,plain,
$false,
inference(binary,[status(thm)],[191,5]),
[iquote('binary,191.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP126-1.004 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 05:22:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.89/2.08 ----- Otter 3.3f, August 2004 -----
% 1.89/2.08 The process was started by sandbox2 on n023.cluster.edu,
% 1.89/2.08 Wed Jul 27 05:22:03 2022
% 1.89/2.08 The command was "./otter". The process ID is 4508.
% 1.89/2.08
% 1.89/2.08 set(prolog_style_variables).
% 1.89/2.08 set(auto).
% 1.89/2.08 dependent: set(auto1).
% 1.89/2.08 dependent: set(process_input).
% 1.89/2.08 dependent: clear(print_kept).
% 1.89/2.08 dependent: clear(print_new_demod).
% 1.89/2.08 dependent: clear(print_back_demod).
% 1.89/2.08 dependent: clear(print_back_sub).
% 1.89/2.08 dependent: set(control_memory).
% 1.89/2.08 dependent: assign(max_mem, 12000).
% 1.89/2.08 dependent: assign(pick_given_ratio, 4).
% 1.89/2.08 dependent: assign(stats_level, 1).
% 1.89/2.08 dependent: assign(max_seconds, 10800).
% 1.89/2.08 clear(print_given).
% 1.89/2.08
% 1.89/2.08 list(usable).
% 1.89/2.08 0 [] group_element(e_1).
% 1.89/2.08 0 [] group_element(e_2).
% 1.89/2.08 0 [] group_element(e_3).
% 1.89/2.08 0 [] group_element(e_4).
% 1.89/2.08 0 [] -e_qualish(e_1,e_2).
% 1.89/2.08 0 [] -e_qualish(e_1,e_3).
% 1.89/2.08 0 [] -e_qualish(e_1,e_4).
% 1.89/2.08 0 [] -e_qualish(e_2,e_1).
% 1.89/2.08 0 [] -e_qualish(e_2,e_3).
% 1.89/2.08 0 [] -e_qualish(e_2,e_4).
% 1.89/2.08 0 [] -e_qualish(e_3,e_1).
% 1.89/2.08 0 [] -e_qualish(e_3,e_2).
% 1.89/2.08 0 [] -e_qualish(e_3,e_4).
% 1.89/2.08 0 [] -e_qualish(e_4,e_1).
% 1.89/2.08 0 [] -e_qualish(e_4,e_2).
% 1.89/2.08 0 [] -e_qualish(e_4,e_3).
% 1.89/2.08 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3)|product(X,Y,e_4).
% 1.89/2.08 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.89/2.08 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.89/2.08 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.89/2.08 0 [] product(X,X,X).
% 1.89/2.08 0 [] -product(X,Y,Z1)| -product(Y,X,Z2)|product(Z1,Z2,Y).
% 1.89/2.08 end_of_list.
% 1.89/2.08
% 1.89/2.08 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.89/2.08
% 1.89/2.08 This is a non-Horn set without equality. The strategy will
% 1.89/2.08 be ordered hyper_res, unit deletion, and factoring, with
% 1.89/2.08 satellites in sos and with nuclei in usable.
% 1.89/2.08
% 1.89/2.08 dependent: set(hyper_res).
% 1.89/2.08 dependent: set(factor).
% 1.89/2.08 dependent: set(unit_deletion).
% 1.89/2.08
% 1.89/2.08 ------------> process usable:
% 1.89/2.08 ** KEPT (pick-wt=3): 1 [] -e_qualish(e_1,e_2).
% 1.89/2.08 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_3).
% 1.89/2.08 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_4).
% 1.89/2.08 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_1).
% 1.89/2.08 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_3).
% 1.89/2.08 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_4).
% 1.89/2.08 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_1).
% 1.89/2.08 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_3,e_2).
% 1.89/2.08 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_3,e_4).
% 1.89/2.08 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_4,e_1).
% 1.89/2.08 ** KEPT (pick-wt=3): 11 [] -e_qualish(e_4,e_2).
% 1.89/2.08 ** KEPT (pick-wt=3): 12 [] -e_qualish(e_4,e_3).
% 1.89/2.08 ** KEPT (pick-wt=20): 13 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)|product(A,B,e_4).
% 1.89/2.08 ** KEPT (pick-wt=11): 14 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.89/2.08 ** KEPT (pick-wt=11): 15 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.89/2.08 ** KEPT (pick-wt=11): 16 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.89/2.08 ** KEPT (pick-wt=12): 17 [] -product(A,B,C)| -product(B,A,D)|product(C,D,B).
% 1.89/2.08
% 1.89/2.08 ------------> process sos:
% 1.89/2.08 ** KEPT (pick-wt=2): 23 [] group_element(e_1).
% 1.89/2.08 ** KEPT (pick-wt=2): 24 [] group_element(e_2).
% 1.89/2.08 ** KEPT (pick-wt=2): 25 [] group_element(e_3).
% 1.89/2.08 ** KEPT (pick-wt=2): 26 [] group_element(e_4).
% 1.89/2.08 ** KEPT (pick-wt=4): 27 [] product(A,A,A).
% 1.89/2.08
% 1.89/2.08 ======= end of input processing =======
% 1.89/2.08
% 1.89/2.08 =========== start of search ===========
% 1.89/2.08
% 1.89/2.08 -------- PROOF --------
% 1.89/2.08
% 1.89/2.08 ----> UNIT CONFLICT at 0.02 sec ----> 192 [binary,191.1,5.1] $F.
% 1.89/2.08
% 1.89/2.08 Length of proof is 22. Level of proof is 13.
% 1.89/2.08
% 1.89/2.08 ---------------- PROOF ----------------
% 1.89/2.08 % SZS status Unsatisfiable
% 1.89/2.08 % SZS output start Refutation
% See solution above
% 1.89/2.08 ------------ end of proof -------------
% 1.89/2.08
% 1.89/2.08
% 1.89/2.08 Search stopped by max_proofs option.
% 1.89/2.08
% 1.89/2.08
% 1.89/2.08 Search stopped by max_proofs option.
% 1.89/2.08
% 1.89/2.08 ============ end of search ============
% 1.89/2.08
% 1.89/2.08 -------------- statistics -------------
% 1.89/2.08 clauses given 39
% 1.89/2.08 clauses generated 1375
% 1.89/2.08 clauses kept 191
% 1.89/2.08 clauses forward subsumed 1206
% 1.89/2.08 clauses back subsumed 136
% 1.89/2.08 Kbytes malloced 976
% 1.89/2.08
% 1.89/2.08 ----------- times (seconds) -----------
% 1.89/2.08 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.89/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.08 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.89/2.08
% 1.89/2.08 That finishes the proof of the theorem.
% 1.89/2.08
% 1.89/2.08 Process 4508 finished Wed Jul 27 05:22:05 2022
% 1.89/2.08 Otter interrupted
% 1.89/2.08 PROOF FOUND
%------------------------------------------------------------------------------