TSTP Solution File: GRP131-2.002 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP131-2.002 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 12:56:30 EDT 2022
% Result : Unsatisfiable 1.73s 1.97s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 10 unt; 10 nHn; 26 RR)
% Number of literals : 57 ( 0 equ; 23 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 31 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ e_qualish(e_1,e_2),
file('GRP131-2.002.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_2,e_1),
file('GRP131-2.002.p',unknown),
[] ).
cnf(4,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
file('GRP131-2.002.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP131-2.002.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP131-2.002.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| e_qualish(A,D) ),
file('GRP131-2.002.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| e_qualish(B,E) ),
file('GRP131-2.002.p',unknown),
[] ).
cnf(10,plain,
( ~ group_element(A)
| product(A,A,e_1)
| product(A,A,e_2) ),
inference(factor,[status(thm)],[4]),
[iquote('factor,4.1.2')] ).
cnf(15,plain,
( ~ product(A,B,C)
| ~ product(C,D,C)
| ~ product(C,B,A)
| e_qualish(A,C) ),
inference(factor,[status(thm)],[8]),
[iquote('factor,8.2.4')] ).
cnf(17,plain,
( ~ product(A,B,C)
| ~ product(C,D,C)
| ~ product(C,B,A)
| e_qualish(B,D) ),
inference(factor,[status(thm)],[9]),
[iquote('factor,9.2.4')] ).
cnf(20,axiom,
group_element(e_1),
file('GRP131-2.002.p',unknown),
[] ).
cnf(21,axiom,
group_element(e_2),
file('GRP131-2.002.p',unknown),
[] ).
cnf(22,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(hyper,[status(thm)],[20,10]),
[iquote('hyper,20,10')] ).
cnf(23,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(hyper,[status(thm)],[21,10]),
[iquote('hyper,21,10')] ).
cnf(24,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(hyper,[status(thm)],[21,4,20]),
[iquote('hyper,21,4,20')] ).
cnf(25,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(hyper,[status(thm)],[21,4,20]),
[iquote('hyper,21,4,20')] ).
cnf(35,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[24,7,23]),3]),
[iquote('hyper,24,7,23,unit_del,3')] ).
cnf(39,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[24,7,23]),3]),
[iquote('hyper,24,7,23,unit_del,3')] ).
cnf(40,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[24,6,22]),2]),
[iquote('hyper,24,6,22,unit_del,2')] ).
cnf(48,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[25,17,25,23]),2])]),
[iquote('hyper,25,17,25,23,unit_del,2,factor_simp')] ).
cnf(66,plain,
product(e_1,e_2,e_1),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[40,17,39,24]),3])])]),
[iquote('hyper,40,17,39,24,unit_del,3,factor_simp,factor_simp')] ).
cnf(68,plain,
product(e_1,e_1,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[66,17,66,22]),3]),
[iquote('hyper,66,17,66,22,unit_del,3')] ).
cnf(70,plain,
product(e_2,e_2,e_2),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[66,15,23,35]),3])]),
[iquote('hyper,66,15,23,35,unit_del,3,factor_simp')] ).
cnf(71,plain,
product(e_2,e_1,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[48,7,66]),2]),
[iquote('hyper,48,7,66,unit_del,2')] ).
cnf(72,plain,
e_qualish(e_1,e_2),
inference(hyper,[status(thm)],[71,17,68,70]),
[iquote('hyper,71,17,68,70')] ).
cnf(73,plain,
$false,
inference(binary,[status(thm)],[72,2]),
[iquote('binary,72.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP131-2.002 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n021.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 04:58:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.73/1.97 ----- Otter 3.3f, August 2004 -----
% 1.73/1.97 The process was started by sandbox on n021.cluster.edu,
% 1.73/1.97 Wed Jul 27 04:58:53 2022
% 1.73/1.97 The command was "./otter". The process ID is 22021.
% 1.73/1.97
% 1.73/1.97 set(prolog_style_variables).
% 1.73/1.97 set(auto).
% 1.73/1.97 dependent: set(auto1).
% 1.73/1.97 dependent: set(process_input).
% 1.73/1.97 dependent: clear(print_kept).
% 1.73/1.97 dependent: clear(print_new_demod).
% 1.73/1.97 dependent: clear(print_back_demod).
% 1.73/1.97 dependent: clear(print_back_sub).
% 1.73/1.97 dependent: set(control_memory).
% 1.73/1.97 dependent: assign(max_mem, 12000).
% 1.73/1.97 dependent: assign(pick_given_ratio, 4).
% 1.73/1.97 dependent: assign(stats_level, 1).
% 1.73/1.97 dependent: assign(max_seconds, 10800).
% 1.73/1.97 clear(print_given).
% 1.73/1.97
% 1.73/1.97 list(usable).
% 1.73/1.97 0 [] next(e_1,e_2).
% 1.73/1.97 0 [] greater(e_2,e_1).
% 1.73/1.97 0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.73/1.97 0 [] group_element(e_1).
% 1.73/1.97 0 [] group_element(e_2).
% 1.73/1.97 0 [] -e_qualish(e_1,e_2).
% 1.73/1.97 0 [] -e_qualish(e_2,e_1).
% 1.73/1.97 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2).
% 1.73/1.97 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.73/1.97 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.73/1.97 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.73/1.97 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,Y1,X1)| -product(Z2,Y2,X2)|e_qualish(X1,X2).
% 1.73/1.97 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,Y1,X1)| -product(Z2,Y2,X2)|e_qualish(Y1,Y2).
% 1.73/1.97 end_of_list.
% 1.73/1.97
% 1.73/1.97 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.73/1.97
% 1.73/1.97 This is a non-Horn set without equality. The strategy will
% 1.73/1.97 be ordered hyper_res, unit deletion, and factoring, with
% 1.73/1.97 satellites in sos and with nuclei in usable.
% 1.73/1.97
% 1.73/1.97 dependent: set(hyper_res).
% 1.73/1.97 dependent: set(factor).
% 1.73/1.97 dependent: set(unit_deletion).
% 1.73/1.97
% 1.73/1.97 ------------> process usable:
% 1.73/1.97 ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.73/1.97 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.73/1.97 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_2,e_1).
% 1.73/1.97 ** KEPT (pick-wt=12): 4 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2).
% 1.73/1.97 ** KEPT (pick-wt=11): 5 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.73/1.97 ** KEPT (pick-wt=11): 6 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.73/1.97 ** KEPT (pick-wt=11): 7 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.73/1.97 ** KEPT (pick-wt=19): 8 [] -product(A,B,C)| -product(D,E,C)| -product(F,B,A)| -product(F,E,D)|e_qualish(A,D).
% 1.73/1.97 ** KEPT (pick-wt=19): 9 [] -product(A,B,C)| -product(D,E,C)| -product(F,B,A)| -product(F,E,D)|e_qualish(B,E).
% 1.73/1.97
% 1.73/1.97 ------------> process sos:
% 1.73/1.97 ** KEPT (pick-wt=3): 18 [] next(e_1,e_2).
% 1.73/1.97 ** KEPT (pick-wt=3): 19 [] greater(e_2,e_1).
% 1.73/1.97 ** KEPT (pick-wt=2): 20 [] group_element(e_1).
% 1.73/1.97 ** KEPT (pick-wt=2): 21 [] group_element(e_2).
% 1.73/1.97
% 1.73/1.97 ======= end of input processing =======
% 1.73/1.97
% 1.73/1.97 =========== start of search ===========
% 1.73/1.97
% 1.73/1.97 -------- PROOF --------
% 1.73/1.97
% 1.73/1.97 ----> UNIT CONFLICT at 0.08 sec ----> 73 [binary,72.1,2.1] $F.
% 1.73/1.97
% 1.73/1.97 Length of proof is 16. Level of proof is 6.
% 1.73/1.97
% 1.73/1.97 ---------------- PROOF ----------------
% 1.73/1.97 % SZS status Unsatisfiable
% 1.73/1.97 % SZS output start Refutation
% See solution above
% 1.73/1.97 ------------ end of proof -------------
% 1.73/1.97
% 1.73/1.97
% 1.73/1.97 Search stopped by max_proofs option.
% 1.73/1.97
% 1.73/1.97
% 1.73/1.97 Search stopped by max_proofs option.
% 1.73/1.97
% 1.73/1.97 ============ end of search ============
% 1.73/1.97
% 1.73/1.97 -------------- statistics -------------
% 1.73/1.97 clauses given 35
% 1.73/1.97 clauses generated 4850
% 1.73/1.97 clauses kept 72
% 1.73/1.97 clauses forward subsumed 4791
% 1.73/1.97 clauses back subsumed 42
% 1.73/1.97 Kbytes malloced 976
% 1.73/1.97
% 1.73/1.97 ----------- times (seconds) -----------
% 1.73/1.97 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.73/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.97 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.73/1.97
% 1.73/1.97 That finishes the proof of the theorem.
% 1.73/1.97
% 1.73/1.97 Process 22021 finished Wed Jul 27 04:58:54 2022
% 1.73/1.97 Otter interrupted
% 1.73/1.97 PROOF FOUND
%------------------------------------------------------------------------------