%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP130-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 12:56:29 EDT 2022
% Result : Unsatisfiable 1.73s 1.97s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of clauses : 43 ( 17 unt; 21 nHn; 43 RR)
% Number of literals : 85 ( 0 equ; 18 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,e_1,B)
| ~ next(A,C)
| ~ greater(B,C) ),
file('GRP130-2.003.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_2),
file('GRP130-2.003.p',unknown),
[] ).
cnf(4,axiom,
~ e_qualish(e_2,e_1),
file('GRP130-2.003.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_2,e_3),
file('GRP130-2.003.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_3,e_1),
file('GRP130-2.003.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_3,e_2),
file('GRP130-2.003.p',unknown),
[] ).
cnf(8,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
file('GRP130-2.003.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP130-2.003.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP130-2.003.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(A,B,C)
| ~ product(A,C,D)
| product(D,B,A) ),
file('GRP130-2.003.p',unknown),
[] ).
cnf(13,plain,
( ~ group_element(A)
| product(A,A,e_1)
| product(A,A,e_2)
| product(A,A,e_3) ),
inference(factor,[status(thm)],[8]),
[iquote('factor,8.1.2')] ).
cnf(17,plain,
( ~ product(A,B,B)
| product(B,B,A) ),
inference(factor,[status(thm)],[12]),
[iquote('factor,12.1.2')] ).
cnf(18,axiom,
next(e_1,e_2),
file('GRP130-2.003.p',unknown),
[] ).
cnf(22,axiom,
greater(e_3,e_2),
file('GRP130-2.003.p',unknown),
[] ).
cnf(23,axiom,
group_element(e_1),
file('GRP130-2.003.p',unknown),
[] ).
cnf(24,axiom,
group_element(e_2),
file('GRP130-2.003.p',unknown),
[] ).
cnf(25,axiom,
group_element(e_3),
file('GRP130-2.003.p',unknown),
[] ).
cnf(26,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(hyper,[status(thm)],[23,13]),
[iquote('hyper,23,13')] ).
cnf(27,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(hyper,[status(thm)],[24,13]),
[iquote('hyper,24,13')] ).
cnf(28,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)],[24,8,23]),
[iquote('hyper,24,8,23')] ).
cnf(29,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(hyper,[status(thm)],[24,8,23]),
[iquote('hyper,24,8,23')] ).
cnf(32,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(hyper,[status(thm)],[25,8,23]),
[iquote('hyper,25,8,23')] ).
cnf(34,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(hyper,[status(thm)],[25,8,23]),
[iquote('hyper,25,8,23')] ).
cnf(40,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(hyper,[status(thm)],[26,1,18,22]),
[iquote('hyper,26,1,18,22')] ).
cnf(51,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[28,12,40])]),
[iquote('hyper,28,12,40,factor_simp')] ).
cnf(188,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[51,10,40]),2])]),
[iquote('hyper,51,10,40,unit_del,2,factor_simp')] ).
cnf(197,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[51,10,28]),4])])]),
[iquote('hyper,51,10,28,unit_del,4,factor_simp,factor_simp')] ).
cnf(199,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[188,12,40])]),
[iquote('hyper,188,12,40,factor_simp')] ).
cnf(209,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_1) ),
inference(hyper,[status(thm)],[197,17]),
[iquote('hyper,197,17')] ).
cnf(263,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(hyper,[status(thm)],[199,17]),
[iquote('hyper,199,17')] ).
cnf(276,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[209,11,27]),4])]),
[iquote('hyper,209,11,27,unit_del,4,factor_simp')] ).
cnf(300,plain,
product(e_1,e_1,e_1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[263,10,188]),4])]),
[iquote('hyper,263,10,188,unit_del,4,factor_simp')] ).
cnf(302,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[300,11,34]),6]),
[iquote('hyper,300,11,34,unit_del,6')] ).
cnf(303,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[300,11,29]),4]),
[iquote('hyper,300,11,29,unit_del,4')] ).
cnf(304,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[300,10,32]),6]),
[iquote('hyper,300,10,32,unit_del,6')] ).
cnf(348,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_2,e_2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[303,12,276])]),
[iquote('hyper,303,12,276,factor_simp')] ).
cnf(377,plain,
( product(e_1,e_3,e_3)
| product(e_2,e_2,e_1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[304,12,209])]),
[iquote('hyper,304,12,209,factor_simp')] ).
cnf(410,plain,
product(e_2,e_1,e_3),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[348,10,303]),2])]),
[iquote('hyper,348,10,303,unit_del,2,factor_simp')] ).
cnf(436,plain,
product(e_3,e_1,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[410,11,302]),7]),
[iquote('hyper,410,11,302,unit_del,7')] ).
cnf(456,plain,
product(e_2,e_2,e_1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[377,10,209]),5])]),
[iquote('hyper,377,10,209,unit_del,5,factor_simp')] ).
cnf(458,plain,
product(e_3,e_2,e_2),
inference(hyper,[status(thm)],[456,12,410]),
[iquote('hyper,456,12,410')] ).
cnf(461,plain,
e_qualish(e_1,e_2),
inference(hyper,[status(thm)],[458,10,436]),
[iquote('hyper,458,10,436')] ).
cnf(462,plain,
$false,
inference(binary,[status(thm)],[461,2]),
[iquote('binary,461.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP130-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 05:12:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.96 ----- Otter 3.3f, August 2004 -----
% 1.73/1.96 The process was started by sandbox on n027.cluster.edu,
% 1.73/1.96 Wed Jul 27 05:12:51 2022
% 1.73/1.96 The command was "./otter". The process ID is 9278.
% 1.73/1.96
% 1.73/1.96 set(prolog_style_variables).
% 1.73/1.96 set(auto).
% 1.73/1.96 dependent: set(auto1).
% 1.73/1.96 dependent: set(process_input).
% 1.73/1.96 dependent: clear(print_kept).
% 1.73/1.96 dependent: clear(print_new_demod).
% 1.73/1.96 dependent: clear(print_back_demod).
% 1.73/1.96 dependent: clear(print_back_sub).
% 1.73/1.96 dependent: set(control_memory).
% 1.73/1.96 dependent: assign(max_mem, 12000).
% 1.73/1.96 dependent: assign(pick_given_ratio, 4).
% 1.73/1.96 dependent: assign(stats_level, 1).
% 1.73/1.96 dependent: assign(max_seconds, 10800).
% 1.73/1.96 clear(print_given).
% 1.73/1.96
% 1.73/1.96 list(usable).
% 1.73/1.96 0 [] next(e_1,e_2).
% 1.73/1.96 0 [] next(e_2,e_3).
% 1.73/1.96 0 [] greater(e_2,e_1).
% 1.73/1.96 0 [] greater(e_3,e_1).
% 1.73/1.96 0 [] greater(e_3,e_2).
% 1.73/1.96 0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.73/1.96 0 [] group_element(e_1).
% 1.73/1.96 0 [] group_element(e_2).
% 1.73/1.96 0 [] group_element(e_3).
% 1.73/1.96 0 [] -e_qualish(e_1,e_2).
% 1.73/1.96 0 [] -e_qualish(e_1,e_3).
% 1.73/1.96 0 [] -e_qualish(e_2,e_1).
% 1.73/1.96 0 [] -e_qualish(e_2,e_3).
% 1.73/1.96 0 [] -e_qualish(e_3,e_1).
% 1.73/1.96 0 [] -e_qualish(e_3,e_2).
% 1.73/1.96 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3).
% 1.73/1.96 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.73/1.96 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.73/1.96 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.73/1.96 0 [] -product(X,Y,Z1)| -product(X,Z1,Z2)|product(Z2,Y,X).
% 1.73/1.96 end_of_list.
% 1.73/1.96
% 1.73/1.96 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.73/1.96
% 1.73/1.96 This is a non-Horn set without equality. The strategy will
% 1.73/1.96 be ordered hyper_res, unit deletion, and factoring, with
% 1.73/1.96 satellites in sos and with nuclei in usable.
% 1.73/1.96
% 1.73/1.96 dependent: set(hyper_res).
% 1.73/1.96 dependent: set(factor).
% 1.73/1.96 dependent: set(unit_deletion).
% 1.73/1.96
% 1.73/1.96 ------------> process usable:
% 1.73/1.96 ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.73/1.96 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.73/1.96 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_3).
% 1.73/1.96 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_1).
% 1.73/1.96 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_3).
% 1.73/1.96 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_3,e_1).
% 1.73/1.96 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_2).
% 1.73/1.96 ** KEPT (pick-wt=16): 8 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3).
% 1.73/1.96 ** KEPT (pick-wt=11): 9 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.73/1.96 ** KEPT (pick-wt=11): 10 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.73/1.96 ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.73/1.96 ** KEPT (pick-wt=12): 12 [] -product(A,B,C)| -product(A,C,D)|product(D,B,A).
% 1.73/1.96
% 1.73/1.96 ------------> process sos:
% 1.73/1.96 ** KEPT (pick-wt=3): 18 [] next(e_1,e_2).
% 1.73/1.96 ** KEPT (pick-wt=3): 19 [] next(e_2,e_3).
% 1.73/1.96 ** KEPT (pick-wt=3): 20 [] greater(e_2,e_1).
% 1.73/1.96 ** KEPT (pick-wt=3): 21 [] greater(e_3,e_1).
% 1.73/1.96 ** KEPT (pick-wt=3): 22 [] greater(e_3,e_2).
% 1.73/1.96 ** KEPT (pick-wt=2): 23 [] group_element(e_1).
% 1.73/1.96 ** KEPT (pick-wt=2): 24 [] group_element(e_2).
% 1.73/1.96 ** KEPT (pick-wt=2): 25 [] group_element(e_3).
% 1.73/1.96
% 1.73/1.96 ======= end of input processing =======
% 1.73/1.96
% 1.73/1.96 =========== start of search ===========
% 1.73/1.96
% 1.73/1.96 -------- PROOF --------
% 1.73/1.96
% 1.73/1.96 ----> UNIT CONFLICT at 0.06 sec ----> 462 [binary,461.1,2.1] $F.
% 1.73/1.96
% 1.73/1.96 Length of proof is 27. Level of proof is 13.
% 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 99
% 1.73/1.97 clauses generated 2647
% 1.73/1.97 clauses kept 461
% 1.73/1.97 clauses forward subsumed 2206
% 1.73/1.97 clauses back subsumed 397
% 1.73/1.97 Kbytes malloced 976
% 1.73/1.97
% 1.73/1.97 ----------- times (seconds) -----------
% 1.73/1.97 user CPU time 0.06 (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 2 (0 hr, 0 min, 2 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 9278 finished Wed Jul 27 05:12:53 2022
% 1.73/1.97 Otter interrupted
% 1.73/1.97 PROOF FOUND
%------------------------------------------------------------------------------