TSTP Solution File: GRP124-4.004 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP124-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 12:56:09 EDT 2022
% Result : Unsatisfiable 2.01s 2.22s
% Output : Refutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 33 ( 14 unt; 14 nHn; 32 RR)
% Number of literals : 81 ( 0 equ; 25 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 : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(e_1,A,B)
| product(e_2,A,B)
| product(e_3,A,B)
| product(e_4,A,B) ),
file('GRP124-4.004.p',unknown),
[] ).
cnf(2,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,e_1,B)
| product(A,e_2,B)
| product(A,e_3,B)
| product(A,e_4,B) ),
file('GRP124-4.004.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_1,e_2),
file('GRP124-4.004.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_2,e_1),
file('GRP124-4.004.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_2,e_3),
file('GRP124-4.004.p',unknown),
[] ).
cnf(8,axiom,
~ e_qualish(e_2,e_4),
file('GRP124-4.004.p',unknown),
[] ).
cnf(9,axiom,
~ e_qualish(e_3,e_1),
file('GRP124-4.004.p',unknown),
[] ).
cnf(12,axiom,
~ e_qualish(e_4,e_1),
file('GRP124-4.004.p',unknown),
[] ).
cnf(15,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('GRP124-4.004.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP124-4.004.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP124-4.004.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP124-4.004.p',unknown),
[] ).
cnf(20,axiom,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| e_qualish(B,E) ),
file('GRP124-4.004.p',unknown),
[] ).
cnf(34,plain,
( ~ product(A,B,C)
| ~ product(C,C,C)
| ~ product(C,A,B)
| e_qualish(B,C) ),
inference(factor,[status(thm)],[20]),
[iquote('factor,20.2.4')] ).
cnf(35,axiom,
group_element(e_1),
file('GRP124-4.004.p',unknown),
[] ).
cnf(36,axiom,
group_element(e_2),
file('GRP124-4.004.p',unknown),
[] ).
cnf(39,axiom,
product(A,A,A),
file('GRP124-4.004.p',unknown),
[] ).
cnf(40,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)],[36,15,35]),
[iquote('hyper,36,15,35')] ).
cnf(43,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(hyper,[status(thm)],[36,2,35]),
[iquote('hyper,36,2,35')] ).
cnf(44,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(hyper,[status(thm)],[36,1,35]),
[iquote('hyper,36,1,35')] ).
cnf(77,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)],[40,17,39]),3]),
[iquote('hyper,40,17,39,unit_del,3')] ).
cnf(79,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[77,18,39]),6]),
[iquote('hyper,77,18,39,unit_del,6')] ).
cnf(90,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[43,18,39]),3]),
[iquote('hyper,43,18,39,unit_del,3')] ).
cnf(94,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[90,16,39]),6]),
[iquote('hyper,90,16,39,unit_del,6')] ).
cnf(98,plain,
( product(e_2,e_3,e_1)
| product(e_1,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[94,34,39,79]),12]),
[iquote('hyper,94,34,39,79,unit_del,12')] ).
cnf(103,plain,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[44,16,39]),3]),
[iquote('hyper,44,16,39,unit_del,3')] ).
cnf(109,plain,
( product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[103,17,39]),6]),
[iquote('hyper,103,17,39,unit_del,6')] ).
cnf(118,plain,
( product(e_4,e_1,e_2)
| product(e_2,e_3,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[109,34,98,39]),7]),
[iquote('hyper,109,34,98,39,unit_del,7')] ).
cnf(141,plain,
product(e_2,e_3,e_1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[118,34,39,94]),3])]),
[iquote('hyper,118,34,39,94,unit_del,3,factor_simp')] ).
cnf(142,plain,
product(e_4,e_1,e_2),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[118,34,109,39]),3])]),
[iquote('hyper,118,34,109,39,unit_del,3,factor_simp')] ).
cnf(143,plain,
product(e_1,e_2,e_4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[141,34,39,79]),9]),
[iquote('hyper,141,34,39,79,unit_del,9')] ).
cnf(144,plain,
e_qualish(e_2,e_4),
inference(hyper,[status(thm)],[143,34,39,142]),
[iquote('hyper,143,34,39,142')] ).
cnf(145,plain,
$false,
inference(binary,[status(thm)],[144,8]),
[iquote('binary,144.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP124-4.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 05:22:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.01/2.22 ----- Otter 3.3f, August 2004 -----
% 2.01/2.22 The process was started by sandbox on n011.cluster.edu,
% 2.01/2.22 Wed Jul 27 05:22:55 2022
% 2.01/2.22 The command was "./otter". The process ID is 25493.
% 2.01/2.22
% 2.01/2.22 set(prolog_style_variables).
% 2.01/2.22 set(auto).
% 2.01/2.22 dependent: set(auto1).
% 2.01/2.22 dependent: set(process_input).
% 2.01/2.22 dependent: clear(print_kept).
% 2.01/2.22 dependent: clear(print_new_demod).
% 2.01/2.22 dependent: clear(print_back_demod).
% 2.01/2.22 dependent: clear(print_back_sub).
% 2.01/2.22 dependent: set(control_memory).
% 2.01/2.22 dependent: assign(max_mem, 12000).
% 2.01/2.22 dependent: assign(pick_given_ratio, 4).
% 2.01/2.22 dependent: assign(stats_level, 1).
% 2.01/2.22 dependent: assign(max_seconds, 10800).
% 2.01/2.22 clear(print_given).
% 2.01/2.22
% 2.01/2.22 list(usable).
% 2.01/2.22 0 [] -group_element(X)| -group_element(Y)|product(e_1,X,Y)|product(e_2,X,Y)|product(e_3,X,Y)|product(e_4,X,Y).
% 2.01/2.22 0 [] -group_element(X)| -group_element(Y)|product(X,e_1,Y)|product(X,e_2,Y)|product(X,e_3,Y)|product(X,e_4,Y).
% 2.01/2.22 0 [] group_element(e_1).
% 2.01/2.22 0 [] group_element(e_2).
% 2.01/2.22 0 [] group_element(e_3).
% 2.01/2.22 0 [] group_element(e_4).
% 2.01/2.22 0 [] -e_qualish(e_1,e_2).
% 2.01/2.22 0 [] -e_qualish(e_1,e_3).
% 2.01/2.22 0 [] -e_qualish(e_1,e_4).
% 2.01/2.22 0 [] -e_qualish(e_2,e_1).
% 2.01/2.22 0 [] -e_qualish(e_2,e_3).
% 2.01/2.22 0 [] -e_qualish(e_2,e_4).
% 2.01/2.22 0 [] -e_qualish(e_3,e_1).
% 2.01/2.22 0 [] -e_qualish(e_3,e_2).
% 2.01/2.22 0 [] -e_qualish(e_3,e_4).
% 2.01/2.22 0 [] -e_qualish(e_4,e_1).
% 2.01/2.22 0 [] -e_qualish(e_4,e_2).
% 2.01/2.22 0 [] -e_qualish(e_4,e_3).
% 2.01/2.22 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).
% 2.01/2.22 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 2.01/2.22 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 2.01/2.22 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 2.01/2.22 0 [] product(X,X,X).
% 2.01/2.22 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(X1,X2).
% 2.01/2.22 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(Y1,Y2).
% 2.01/2.22 end_of_list.
% 2.01/2.22
% 2.01/2.22 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 2.01/2.22
% 2.01/2.22 This is a non-Horn set without equality. The strategy will
% 2.01/2.22 be ordered hyper_res, unit deletion, and factoring, with
% 2.01/2.22 satellites in sos and with nuclei in usable.
% 2.01/2.22
% 2.01/2.22 dependent: set(hyper_res).
% 2.01/2.22 dependent: set(factor).
% 2.01/2.22 dependent: set(unit_deletion).
% 2.01/2.22
% 2.01/2.22 ------------> process usable:
% 2.01/2.22 ** KEPT (pick-wt=20): 1 [] -group_element(A)| -group_element(B)|product(e_1,A,B)|product(e_2,A,B)|product(e_3,A,B)|product(e_4,A,B).
% 2.01/2.22 ** KEPT (pick-wt=20): 2 [] -group_element(A)| -group_element(B)|product(A,e_1,B)|product(A,e_2,B)|product(A,e_3,B)|product(A,e_4,B).
% 2.01/2.22 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_2).
% 2.01/2.22 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_1,e_3).
% 2.01/2.22 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_1,e_4).
% 2.01/2.22 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_1).
% 2.01/2.22 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_2,e_3).
% 2.01/2.22 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_2,e_4).
% 2.01/2.22 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_3,e_1).
% 2.01/2.22 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_3,e_2).
% 2.01/2.22 ** KEPT (pick-wt=3): 11 [] -e_qualish(e_3,e_4).
% 2.01/2.22 ** KEPT (pick-wt=3): 12 [] -e_qualish(e_4,e_1).
% 2.01/2.22 ** KEPT (pick-wt=3): 13 [] -e_qualish(e_4,e_2).
% 2.01/2.22 ** KEPT (pick-wt=3): 14 [] -e_qualish(e_4,e_3).
% 2.01/2.22 ** KEPT (pick-wt=20): 15 [] -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).
% 2.01/2.22 ** KEPT (pick-wt=11): 16 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 2.01/2.22 ** KEPT (pick-wt=11): 17 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 2.01/2.22 ** KEPT (pick-wt=11): 18 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 2.01/2.22 ** KEPT (pick-wt=19): 19 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(A,D).
% 2.01/2.22 ** KEPT (pick-wt=19): 20 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(B,E).
% 2.01/2.22
% 2.01/2.22 ------------> process sos:
% 2.01/2.22 ** KEPT (pick-wt=2): 35 [] group_element(e_1).
% 2.01/2.22 ** KEPT (pick-wt=2): 36 [] group_element(e_2).
% 2.01/2.22 ** KEPT (pick-wt=2): 37 [] group_element(e_3).
% 2.01/2.22 ** KEPT (pick-wt=2): 38 [] group_element(e_4).
% 2.01/2.22 ** KEPT (pick-wt=4): 39 [] product(A,A,A).
% 2.01/2.22
% 2.01/2.22 ======= end of input processing =======
% 2.01/2.22
% 2.01/2.22 =========== start of search ===========
% 2.01/2.22
% 2.01/2.22 -------- PROOF --------
% 2.01/2.22
% 2.01/2.22 ----> UNIT CONFLICT at 0.11 sec ----> 145 [binary,144.1,8.1] $F.
% 2.01/2.22
% 2.01/2.22 Length of proof is 16. Level of proof is 8.
% 2.01/2.22
% 2.01/2.22 ---------------- PROOF ----------------
% 2.01/2.22 % SZS status Unsatisfiable
% 2.01/2.22 % SZS output start Refutation
% See solution above
% 2.01/2.22 ------------ end of proof -------------
% 2.01/2.22
% 2.01/2.22
% 2.01/2.22 Search stopped by max_proofs option.
% 2.01/2.22
% 2.01/2.22
% 2.01/2.22 Search stopped by max_proofs option.
% 2.01/2.22
% 2.01/2.22 ============ end of search ============
% 2.01/2.22
% 2.01/2.22 -------------- statistics -------------
% 2.01/2.22 clauses given 30
% 2.01/2.22 clauses generated 3526
% 2.01/2.22 clauses kept 144
% 2.01/2.22 clauses forward subsumed 3407
% 2.01/2.22 clauses back subsumed 63
% 2.01/2.22 Kbytes malloced 976
% 2.01/2.22
% 2.01/2.22 ----------- times (seconds) -----------
% 2.01/2.22 user CPU time 0.11 (0 hr, 0 min, 0 sec)
% 2.01/2.22 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.01/2.22 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.01/2.22
% 2.01/2.22 That finishes the proof of the theorem.
% 2.01/2.22
% 2.01/2.22 Process 25493 finished Wed Jul 27 05:22:57 2022
% 2.01/2.22 Otter interrupted
% 2.01/2.22 PROOF FOUND
%------------------------------------------------------------------------------