TSTP Solution File: GRP124-1.004 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP124-1.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 12:56:08 EDT 2022
% Result : Unsatisfiable 1.79s 1.97s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 38 ( 15 unt; 19 nHn; 37 RR)
% Number of literals : 87 ( 0 equ; 19 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 : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ e_qualish(e_1,e_2),
file('GRP124-1.004.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_3),
file('GRP124-1.004.p',unknown),
[] ).
cnf(4,axiom,
~ e_qualish(e_2,e_1),
file('GRP124-1.004.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_2,e_3),
file('GRP124-1.004.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_3,e_1),
file('GRP124-1.004.p',unknown),
[] ).
cnf(8,axiom,
~ e_qualish(e_3,e_2),
file('GRP124-1.004.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('GRP124-1.004.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP124-1.004.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP124-1.004.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| e_qualish(B,E) ),
file('GRP124-1.004.p',unknown),
[] ).
cnf(30,plain,
( ~ product(A,B,C)
| ~ product(C,C,C)
| ~ product(C,A,B)
| e_qualish(B,C) ),
inference(factor,[status(thm)],[18]),
[iquote('factor,18.2.4')] ).
cnf(31,axiom,
group_element(e_1),
file('GRP124-1.004.p',unknown),
[] ).
cnf(32,axiom,
group_element(e_2),
file('GRP124-1.004.p',unknown),
[] ).
cnf(33,axiom,
group_element(e_3),
file('GRP124-1.004.p',unknown),
[] ).
cnf(35,axiom,
product(A,A,A),
file('GRP124-1.004.p',unknown),
[] ).
cnf(36,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)],[32,13,31]),
[iquote('hyper,32,13,31')] ).
cnf(37,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)],[32,13,31]),
[iquote('hyper,32,13,31')] ).
cnf(38,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)],[33,13,32]),
[iquote('hyper,33,13,32')] ).
cnf(39,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)],[33,13,31]),
[iquote('hyper,33,13,31')] ).
cnf(40,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(hyper,[status(thm)],[33,13,32]),
[iquote('hyper,33,13,32')] ).
cnf(49,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)],[36,15,35]),1]),
[iquote('hyper,36,15,35,unit_del,1')] ).
cnf(51,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[49,16,35]),4]),
[iquote('hyper,49,16,35,unit_del,4')] ).
cnf(52,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)],[37,16,35]),1]),
[iquote('hyper,37,16,35,unit_del,1')] ).
cnf(55,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)],[38,15,35]),5]),
[iquote('hyper,38,15,35,unit_del,5')] ).
cnf(57,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[52,15,35]),4]),
[iquote('hyper,52,15,35,unit_del,4')] ).
cnf(59,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[55,16,35]),8]),
[iquote('hyper,55,16,35,unit_del,8')] ).
cnf(61,plain,
( product(e_2,e_3,e_4)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[59,30,35,51]),7]),
[iquote('hyper,59,30,35,51,unit_del,7')] ).
cnf(64,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)],[39,15,35]),2]),
[iquote('hyper,39,15,35,unit_del,2')] ).
cnf(69,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[61,15,57]),2]),
[iquote('hyper,61,15,57,unit_del,2')] ).
cnf(73,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[64,16,35]),7]),
[iquote('hyper,64,16,35,unit_del,7')] ).
cnf(82,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[40,16,35]),5]),
[iquote('hyper,40,16,35,unit_del,5')] ).
cnf(88,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[73,30,35,69]),8]),
[iquote('hyper,73,30,35,69,unit_del,8')] ).
cnf(96,plain,
product(e_1,e_2,e_4),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[88,16,61]),4])]),
[iquote('hyper,88,16,61,unit_del,4,factor_simp')] ).
cnf(97,plain,
product(e_1,e_3,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[96,15,73]),8]),
[iquote('hyper,96,15,73,unit_del,8')] ).
cnf(102,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[82,30,35,97]),4]),
[iquote('hyper,82,30,35,97,unit_del,4')] ).
cnf(105,plain,
product(e_3,e_2,e_4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[102,15,35]),8]),
[iquote('hyper,102,15,35,unit_del,8')] ).
cnf(109,plain,
e_qualish(e_1,e_3),
inference(hyper,[status(thm)],[105,16,96]),
[iquote('hyper,105,16,96')] ).
cnf(110,plain,
$false,
inference(binary,[status(thm)],[109,2]),
[iquote('binary,109.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP124-1.004 : TPTP v8.1.0. Released v1.2.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 05:16:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.79/1.97 ----- Otter 3.3f, August 2004 -----
% 1.79/1.97 The process was started by sandbox on n014.cluster.edu,
% 1.79/1.97 Wed Jul 27 05:16:54 2022
% 1.79/1.97 The command was "./otter". The process ID is 23043.
% 1.79/1.97
% 1.79/1.97 set(prolog_style_variables).
% 1.79/1.97 set(auto).
% 1.79/1.97 dependent: set(auto1).
% 1.79/1.97 dependent: set(process_input).
% 1.79/1.97 dependent: clear(print_kept).
% 1.79/1.97 dependent: clear(print_new_demod).
% 1.79/1.97 dependent: clear(print_back_demod).
% 1.79/1.97 dependent: clear(print_back_sub).
% 1.79/1.97 dependent: set(control_memory).
% 1.79/1.97 dependent: assign(max_mem, 12000).
% 1.79/1.97 dependent: assign(pick_given_ratio, 4).
% 1.79/1.97 dependent: assign(stats_level, 1).
% 1.79/1.97 dependent: assign(max_seconds, 10800).
% 1.79/1.97 clear(print_given).
% 1.79/1.97
% 1.79/1.97 list(usable).
% 1.79/1.97 0 [] group_element(e_1).
% 1.79/1.97 0 [] group_element(e_2).
% 1.79/1.97 0 [] group_element(e_3).
% 1.79/1.97 0 [] group_element(e_4).
% 1.79/1.97 0 [] -e_qualish(e_1,e_2).
% 1.79/1.97 0 [] -e_qualish(e_1,e_3).
% 1.79/1.97 0 [] -e_qualish(e_1,e_4).
% 1.79/1.97 0 [] -e_qualish(e_2,e_1).
% 1.79/1.97 0 [] -e_qualish(e_2,e_3).
% 1.79/1.97 0 [] -e_qualish(e_2,e_4).
% 1.79/1.97 0 [] -e_qualish(e_3,e_1).
% 1.79/1.97 0 [] -e_qualish(e_3,e_2).
% 1.79/1.97 0 [] -e_qualish(e_3,e_4).
% 1.79/1.97 0 [] -e_qualish(e_4,e_1).
% 1.79/1.97 0 [] -e_qualish(e_4,e_2).
% 1.79/1.97 0 [] -e_qualish(e_4,e_3).
% 1.79/1.97 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).
% 1.79/1.97 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.79/1.97 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.79/1.97 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.79/1.97 0 [] product(X,X,X).
% 1.79/1.97 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(X1,X2).
% 1.79/1.97 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(Y1,Y2).
% 1.79/1.97 end_of_list.
% 1.79/1.97
% 1.79/1.97 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.79/1.97
% 1.79/1.97 This is a non-Horn set without equality. The strategy will
% 1.79/1.97 be ordered hyper_res, unit deletion, and factoring, with
% 1.79/1.97 satellites in sos and with nuclei in usable.
% 1.79/1.97
% 1.79/1.97 dependent: set(hyper_res).
% 1.79/1.97 dependent: set(factor).
% 1.79/1.97 dependent: set(unit_deletion).
% 1.79/1.97
% 1.79/1.97 ------------> process usable:
% 1.79/1.97 ** KEPT (pick-wt=3): 1 [] -e_qualish(e_1,e_2).
% 1.79/1.97 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_3).
% 1.79/1.97 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_4).
% 1.79/1.97 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_1).
% 1.79/1.97 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_3).
% 1.79/1.97 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_4).
% 1.79/1.97 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_1).
% 1.79/1.97 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_3,e_2).
% 1.79/1.97 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_3,e_4).
% 1.79/1.97 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_4,e_1).
% 1.79/1.97 ** KEPT (pick-wt=3): 11 [] -e_qualish(e_4,e_2).
% 1.79/1.97 ** KEPT (pick-wt=3): 12 [] -e_qualish(e_4,e_3).
% 1.79/1.97 ** 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).
% 1.79/1.97 ** KEPT (pick-wt=11): 14 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.79/1.97 ** KEPT (pick-wt=11): 15 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.79/1.97 ** KEPT (pick-wt=11): 16 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.79/1.97 ** KEPT (pick-wt=19): 17 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(A,D).
% 1.79/1.97 ** KEPT (pick-wt=19): 18 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(B,E).
% 1.79/1.97
% 1.79/1.97 ------------> process sos:
% 1.79/1.97 ** KEPT (pick-wt=2): 31 [] group_element(e_1).
% 1.79/1.97 ** KEPT (pick-wt=2): 32 [] group_element(e_2).
% 1.79/1.97 ** KEPT (pick-wt=2): 33 [] group_element(e_3).
% 1.79/1.97 ** KEPT (pick-wt=2): 34 [] group_element(e_4).
% 1.79/1.97 ** KEPT (pick-wt=4): 35 [] product(A,A,A).
% 1.79/1.97
% 1.79/1.97 ======= end of input processing =======
% 1.79/1.97
% 1.79/1.97 =========== start of search ===========
% 1.79/1.97
% 1.79/1.97 -------- PROOF --------
% 1.79/1.97
% 1.79/1.97 ----> UNIT CONFLICT at 0.05 sec ----> 110 [binary,109.1,2.1] $F.
% 1.79/1.97
% 1.79/1.97 Length of proof is 23. Level of proof is 11.
% 1.79/1.97
% 1.79/1.97 ---------------- PROOF ----------------
% 1.79/1.97 % SZS status Unsatisfiable
% 1.79/1.97 % SZS output start Refutation
% See solution above
% 1.79/1.97 ------------ end of proof -------------
% 1.79/1.97
% 1.79/1.97
% 1.79/1.97 Search stopped by max_proofs option.
% 1.79/1.97
% 1.79/1.97
% 1.79/1.97 Search stopped by max_proofs option.
% 1.79/1.97
% 1.79/1.97 ============ end of search ============
% 1.79/1.97
% 1.79/1.97 -------------- statistics -------------
% 1.79/1.97 clauses given 32
% 1.79/1.97 clauses generated 1603
% 1.79/1.97 clauses kept 109
% 1.79/1.97 clauses forward subsumed 1517
% 1.79/1.97 clauses back subsumed 60
% 1.79/1.97 Kbytes malloced 976
% 1.79/1.97
% 1.79/1.97 ----------- times (seconds) -----------
% 1.79/1.97 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 1.79/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/1.97 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.79/1.97
% 1.79/1.97 That finishes the proof of the theorem.
% 1.79/1.97
% 1.79/1.97 Process 23043 finished Wed Jul 27 05:16:56 2022
% 1.79/1.97 Otter interrupted
% 1.79/1.97 PROOF FOUND
%------------------------------------------------------------------------------