TSTP Solution File: GRP125-4.003 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP125-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:56:10 EDT 2022
% Result : Unsatisfiable 1.65s 1.87s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 11 unt; 5 nHn; 19 RR)
% Number of literals : 38 ( 0 equ; 13 neg)
% Maximal clause size : 5 ( 1 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 : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
~ e_qualish(e_1,e_2),
file('GRP125-4.003.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_2,e_1),
file('GRP125-4.003.p',unknown),
[] ).
cnf(9,axiom,
~ e_qualish(e_3,e_1),
file('GRP125-4.003.p',unknown),
[] ).
cnf(11,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
file('GRP125-4.003.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP125-4.003.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP125-4.003.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP125-4.003.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,A) ),
file('GRP125-4.003.p',unknown),
[] ).
cnf(25,axiom,
group_element(e_1),
file('GRP125-4.003.p',unknown),
[] ).
cnf(26,axiom,
group_element(e_2),
file('GRP125-4.003.p',unknown),
[] ).
cnf(28,axiom,
product(A,A,A),
file('GRP125-4.003.p',unknown),
[] ).
cnf(29,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(hyper,[status(thm)],[26,11,25]),
[iquote('hyper,26,11,25')] ).
cnf(30,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(hyper,[status(thm)],[26,11,25]),
[iquote('hyper,26,11,25')] ).
cnf(49,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[29,13,28]),5]),
[iquote('hyper,29,13,28,unit_del,5')] ).
cnf(53,plain,
product(e_1,e_2,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[49,14,28]),7]),
[iquote('hyper,49,14,28,unit_del,7')] ).
cnf(57,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[30,14,28]),5]),
[iquote('hyper,30,14,28,unit_del,5')] ).
cnf(67,plain,
product(e_2,e_1,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[57,13,28]),7]),
[iquote('hyper,57,13,28,unit_del,7')] ).
cnf(78,plain,
product(e_3,e_3,e_1),
inference(hyper,[status(thm)],[67,15,53]),
[iquote('hyper,67,15,53')] ).
cnf(83,plain,
e_qualish(e_3,e_1),
inference(hyper,[status(thm)],[78,12,28]),
[iquote('hyper,78,12,28')] ).
cnf(84,plain,
$false,
inference(binary,[status(thm)],[83,9]),
[iquote('binary,83.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP125-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Jul 27 05:03:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.87 ----- Otter 3.3f, August 2004 -----
% 1.65/1.87 The process was started by sandbox on n012.cluster.edu,
% 1.65/1.87 Wed Jul 27 05:03:05 2022
% 1.65/1.87 The command was "./otter". The process ID is 30044.
% 1.65/1.87
% 1.65/1.87 set(prolog_style_variables).
% 1.65/1.87 set(auto).
% 1.65/1.87 dependent: set(auto1).
% 1.65/1.87 dependent: set(process_input).
% 1.65/1.87 dependent: clear(print_kept).
% 1.65/1.87 dependent: clear(print_new_demod).
% 1.65/1.87 dependent: clear(print_back_demod).
% 1.65/1.87 dependent: clear(print_back_sub).
% 1.65/1.87 dependent: set(control_memory).
% 1.65/1.87 dependent: assign(max_mem, 12000).
% 1.65/1.87 dependent: assign(pick_given_ratio, 4).
% 1.65/1.87 dependent: assign(stats_level, 1).
% 1.65/1.87 dependent: assign(max_seconds, 10800).
% 1.65/1.87 clear(print_given).
% 1.65/1.87
% 1.65/1.87 list(usable).
% 1.65/1.87 0 [] -group_element(X)| -group_element(Y)|product(e_1,X,Y)|product(e_2,X,Y)|product(e_3,X,Y).
% 1.65/1.87 0 [] -group_element(X)| -group_element(Y)|product(X,e_1,Y)|product(X,e_2,Y)|product(X,e_3,Y).
% 1.65/1.87 0 [] product(X,Y,Z1)| -product(Z1,Z2,X)| -product(Y,X,Z2).
% 1.65/1.87 0 [] product(Y,X,Z2)| -product(Z1,Z2,X)| -product(X,Y,Z1).
% 1.65/1.87 0 [] group_element(e_1).
% 1.65/1.87 0 [] group_element(e_2).
% 1.65/1.87 0 [] group_element(e_3).
% 1.65/1.87 0 [] -e_qualish(e_1,e_2).
% 1.65/1.87 0 [] -e_qualish(e_1,e_3).
% 1.65/1.87 0 [] -e_qualish(e_2,e_1).
% 1.65/1.87 0 [] -e_qualish(e_2,e_3).
% 1.65/1.87 0 [] -e_qualish(e_3,e_1).
% 1.65/1.87 0 [] -e_qualish(e_3,e_2).
% 1.65/1.87 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3).
% 1.65/1.87 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.65/1.87 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.65/1.87 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.65/1.87 0 [] product(X,X,X).
% 1.65/1.87 0 [] -product(X,Y,Z1)| -product(Y,X,Z2)|product(Z1,Z2,X).
% 1.65/1.87 end_of_list.
% 1.65/1.87
% 1.65/1.87 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.65/1.87
% 1.65/1.87 This is a non-Horn set without equality. The strategy will
% 1.65/1.87 be ordered hyper_res, unit deletion, and factoring, with
% 1.65/1.87 satellites in sos and with nuclei in usable.
% 1.65/1.87
% 1.65/1.87 dependent: set(hyper_res).
% 1.65/1.87 dependent: set(factor).
% 1.65/1.87 dependent: set(unit_deletion).
% 1.65/1.87
% 1.65/1.87 ------------> process usable:
% 1.65/1.87 ** KEPT (pick-wt=16): 1 [] -group_element(A)| -group_element(B)|product(e_1,A,B)|product(e_2,A,B)|product(e_3,A,B).
% 1.65/1.87 ** KEPT (pick-wt=16): 2 [] -group_element(A)| -group_element(B)|product(A,e_1,B)|product(A,e_2,B)|product(A,e_3,B).
% 1.65/1.87 ** KEPT (pick-wt=12): 3 [] product(A,B,C)| -product(C,D,A)| -product(B,A,D).
% 1.65/1.87 ** KEPT (pick-wt=12): 4 [] product(A,B,C)| -product(D,C,B)| -product(B,A,D).
% 1.65/1.87 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_1,e_2).
% 1.65/1.87 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_1,e_3).
% 1.65/1.87 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_2,e_1).
% 1.65/1.87 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_2,e_3).
% 1.65/1.87 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_3,e_1).
% 1.65/1.87 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_3,e_2).
% 1.65/1.87 ** KEPT (pick-wt=16): 11 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3).
% 1.65/1.87 ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.65/1.87 ** KEPT (pick-wt=11): 13 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.65/1.87 ** KEPT (pick-wt=11): 14 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.65/1.87 ** KEPT (pick-wt=12): 15 [] -product(A,B,C)| -product(B,A,D)|product(C,D,A).
% 1.65/1.87
% 1.65/1.87 ------------> process sos:
% 1.65/1.87 ** KEPT (pick-wt=2): 25 [] group_element(e_1).
% 1.65/1.87 ** KEPT (pick-wt=2): 26 [] group_element(e_2).
% 1.65/1.87 ** KEPT (pick-wt=2): 27 [] group_element(e_3).
% 1.65/1.87 ** KEPT (pick-wt=4): 28 [] product(A,A,A).
% 1.65/1.87
% 1.65/1.87 ======= end of input processing =======
% 1.65/1.87
% 1.65/1.87 =========== start of search ===========
% 1.65/1.87
% 1.65/1.87 -------- PROOF --------
% 1.65/1.87
% 1.65/1.87 ----> UNIT CONFLICT at 0.00 sec ----> 84 [binary,83.1,9.1] $F.
% 1.65/1.87
% 1.65/1.87 Length of proof is 8. Level of proof is 5.
% 1.65/1.87
% 1.65/1.87 ---------------- PROOF ----------------
% 1.65/1.87 % SZS status Unsatisfiable
% 1.65/1.87 % SZS output start Refutation
% See solution above
% 1.65/1.87 ------------ end of proof -------------
% 1.65/1.87
% 1.65/1.87
% 1.65/1.87 Search stopped by max_proofs option.
% 1.65/1.87
% 1.65/1.87
% 1.65/1.87 Search stopped by max_proofs option.
% 1.65/1.87
% 1.65/1.87 ============ end of search ============
% 1.65/1.87
% 1.65/1.87 -------------- statistics -------------
% 1.65/1.87 clauses given 13
% 1.65/1.87 clauses generated 289
% 1.65/1.87 clauses kept 83
% 1.65/1.87 clauses forward subsumed 225
% 1.65/1.87 clauses back subsumed 38
% 1.65/1.87 Kbytes malloced 976
% 1.65/1.87
% 1.65/1.87 ----------- times (seconds) -----------
% 1.65/1.87 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.87 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.87 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.87
% 1.65/1.87 That finishes the proof of the theorem.
% 1.65/1.87
% 1.65/1.87 Process 30044 finished Wed Jul 27 05:03:07 2022
% 1.65/1.87 Otter interrupted
% 1.65/1.87 PROOF FOUND
%------------------------------------------------------------------------------