%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP123-8.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 1.67s 1.91s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 29 ( 16 unt; 8 nHn; 27 RR)
% Number of literals : 56 ( 0 equ; 19 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
~ e_qualish(e_1,e_2),
file('GRP123-8.003.p',unknown),
[] ).
cnf(9,axiom,
~ e_qualish(e_2,e_1),
file('GRP123-8.003.p',unknown),
[] ).
cnf(10,axiom,
~ e_qualish(e_2,e_3),
file('GRP123-8.003.p',unknown),
[] ).
cnf(11,axiom,
~ e_qualish(e_3,e_1),
file('GRP123-8.003.p',unknown),
[] ).
cnf(12,axiom,
~ e_qualish(e_3,e_2),
file('GRP123-8.003.p',unknown),
[] ).
cnf(13,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(15,axiom,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| e_qualish(B,D) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(16,axiom,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| e_qualish(A,D) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(17,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product2(A,B,e_1)
| product2(A,B,e_2)
| product2(A,B,e_3) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(19,axiom,
( ~ product2(A,B,C)
| ~ product2(A,D,C)
| e_qualish(B,D) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(20,axiom,
( ~ product2(A,B,C)
| ~ product2(D,B,C)
| e_qualish(A,D) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(21,axiom,
( ~ product1(A,B,C)
| ~ product1(C,B,D)
| product2(D,A,B) ),
file('GRP123-8.003.p',unknown),
[] ).
cnf(53,axiom,
group_element(e_1),
file('GRP123-8.003.p',unknown),
[] ).
cnf(54,axiom,
group_element(e_2),
file('GRP123-8.003.p',unknown),
[] ).
cnf(55,axiom,
group_element(e_3),
file('GRP123-8.003.p',unknown),
[] ).
cnf(56,axiom,
product1(A,A,A),
file('GRP123-8.003.p',unknown),
[] ).
cnf(57,axiom,
product2(A,A,A),
file('GRP123-8.003.p',unknown),
[] ).
cnf(59,plain,
( product2(e_1,e_2,e_1)
| product2(e_1,e_2,e_2)
| product2(e_1,e_2,e_3) ),
inference(hyper,[status(thm)],[54,17,53]),
[iquote('hyper,54,17,53')] ).
cnf(68,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(hyper,[status(thm)],[55,13,54]),
[iquote('hyper,55,13,54')] ).
cnf(69,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3) ),
inference(hyper,[status(thm)],[55,13,53]),
[iquote('hyper,55,13,53')] ).
cnf(83,plain,
( product2(e_1,e_2,e_2)
| product2(e_1,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[59,19,57]),7]),
[iquote('hyper,59,19,57,unit_del,7')] ).
cnf(85,plain,
product2(e_1,e_2,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[83,20,57]),9]),
[iquote('hyper,83,20,57,unit_del,9')] ).
cnf(115,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[68,15,56]),10]),
[iquote('hyper,68,15,56,unit_del,10')] ).
cnf(120,plain,
product1(e_2,e_3,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[115,16,56]),12]),
[iquote('hyper,115,16,56,unit_del,12')] ).
cnf(122,plain,
( product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[69,16,120]),9]),
[iquote('hyper,69,16,120,unit_del,9')] ).
cnf(132,plain,
product1(e_1,e_3,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[122,16,56]),11]),
[iquote('hyper,122,16,56,unit_del,11')] ).
cnf(133,plain,
product2(e_2,e_2,e_3),
inference(hyper,[status(thm)],[132,21,120]),
[iquote('hyper,132,21,120')] ).
cnf(135,plain,
e_qualish(e_1,e_2),
inference(hyper,[status(thm)],[133,20,85]),
[iquote('hyper,133,20,85')] ).
cnf(136,plain,
$false,
inference(binary,[status(thm)],[135,7]),
[iquote('binary,135.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP123-8.003 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n016.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 05:19:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.89 ----- Otter 3.3f, August 2004 -----
% 1.67/1.89 The process was started by sandbox2 on n016.cluster.edu,
% 1.67/1.89 Wed Jul 27 05:19:07 2022
% 1.67/1.89 The command was "./otter". The process ID is 23308.
% 1.67/1.89
% 1.67/1.89 set(prolog_style_variables).
% 1.67/1.89 set(auto).
% 1.67/1.89 dependent: set(auto1).
% 1.67/1.89 dependent: set(process_input).
% 1.67/1.89 dependent: clear(print_kept).
% 1.67/1.89 dependent: clear(print_new_demod).
% 1.67/1.89 dependent: clear(print_back_demod).
% 1.67/1.89 dependent: clear(print_back_sub).
% 1.67/1.89 dependent: set(control_memory).
% 1.67/1.89 dependent: assign(max_mem, 12000).
% 1.67/1.89 dependent: assign(pick_given_ratio, 4).
% 1.67/1.89 dependent: assign(stats_level, 1).
% 1.67/1.89 dependent: assign(max_seconds, 10800).
% 1.67/1.89 clear(print_given).
% 1.67/1.89
% 1.67/1.89 list(usable).
% 1.67/1.89 0 [] next(e_0,e_1).
% 1.67/1.89 0 [] next(e_1,e_2).
% 1.67/1.89 0 [] next(e_2,e_3).
% 1.67/1.89 0 [] greater(e_1,e_0).
% 1.67/1.89 0 [] greater(e_2,e_0).
% 1.67/1.89 0 [] greater(e_3,e_0).
% 1.67/1.89 0 [] greater(e_2,e_1).
% 1.67/1.89 0 [] greater(e_3,e_1).
% 1.67/1.89 0 [] greater(e_3,e_2).
% 1.67/1.89 0 [] -cycle(X,Y)| -cycle(X,Z)|e_qualish(Y,Z).
% 1.67/1.89 0 [] -group_element(X)|cycle(X,e_0)|cycle(X,e_1)|cycle(X,e_2).
% 1.67/1.89 0 [] cycle(e_3,e_0).
% 1.67/1.89 0 [] -cycle(X,Y)| -cycle(W,Z)| -next(X,W)| -greater(Y,e_0)| -next(Z,Z1)|e_qualish(Y,Z1).
% 1.67/1.89 0 [] -cycle(X,Z1)| -cycle(Y,e_0)| -cycle(W,Z2)| -next(Y,W)| -greater(Y,X)| -greater(Z1,Z2).
% 1.67/1.89 0 [] -cycle(X,e_0)| -product(X,e_1,Y)| -greater(Y,X).
% 1.67/1.89 0 [] -cycle(X,Y)| -product(X,e_1,Z)| -greater(Y,e_0)| -next(X,X1)|e_qualish(Z,X1).
% 1.67/1.89 0 [] group_element(e_1).
% 1.67/1.89 0 [] group_element(e_2).
% 1.67/1.89 0 [] group_element(e_3).
% 1.67/1.89 0 [] -e_qualish(e_1,e_2).
% 1.67/1.89 0 [] -e_qualish(e_1,e_3).
% 1.67/1.89 0 [] -e_qualish(e_2,e_1).
% 1.67/1.89 0 [] -e_qualish(e_2,e_3).
% 1.67/1.89 0 [] -e_qualish(e_3,e_1).
% 1.67/1.89 0 [] -e_qualish(e_3,e_2).
% 1.67/1.89 0 [] -group_element(X)| -group_element(Y)|product1(X,Y,e_1)|product1(X,Y,e_2)|product1(X,Y,e_3).
% 1.67/1.89 0 [] -product1(X,Y,W)| -product1(X,Y,Z)|e_qualish(W,Z).
% 1.67/1.89 0 [] -product1(X,W,Y)| -product1(X,Z,Y)|e_qualish(W,Z).
% 1.67/1.89 0 [] -product1(W,Y,X)| -product1(Z,Y,X)|e_qualish(W,Z).
% 1.67/1.89 0 [] product1(X,X,X).
% 1.67/1.89 0 [] -group_element(X)| -group_element(Y)|product2(X,Y,e_1)|product2(X,Y,e_2)|product2(X,Y,e_3).
% 1.67/1.89 0 [] -product2(X,Y,W)| -product2(X,Y,Z)|e_qualish(W,Z).
% 1.67/1.89 0 [] -product2(X,W,Y)| -product2(X,Z,Y)|e_qualish(W,Z).
% 1.67/1.89 0 [] -product2(W,Y,X)| -product2(Z,Y,X)|e_qualish(W,Z).
% 1.67/1.89 0 [] product2(X,X,X).
% 1.67/1.89 0 [] -product1(X,Y,Z1)| -product1(Z1,Y,Z2)|product2(Z2,X,Y).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.67/1.89
% 1.67/1.89 This is a non-Horn set without equality. The strategy will
% 1.67/1.89 be ordered hyper_res, unit deletion, and factoring, with
% 1.67/1.89 satellites in sos and with nuclei in usable.
% 1.67/1.89
% 1.67/1.89 dependent: set(hyper_res).
% 1.67/1.89 dependent: set(factor).
% 1.67/1.89 dependent: set(unit_deletion).
% 1.67/1.89
% 1.67/1.89 ------------> process usable:
% 1.67/1.89 ** KEPT (pick-wt=9): 1 [] -cycle(A,B)| -cycle(A,C)|e_qualish(B,C).
% 1.67/1.89 ** KEPT (pick-wt=11): 2 [] -group_element(A)|cycle(A,e_0)|cycle(A,e_1)|cycle(A,e_2).
% 1.67/1.89 ** KEPT (pick-wt=18): 3 [] -cycle(A,B)| -cycle(C,D)| -next(A,C)| -greater(B,e_0)| -next(D,E)|e_qualish(B,E).
% 1.67/1.89 ** KEPT (pick-wt=18): 4 [] -cycle(A,B)| -cycle(C,e_0)| -cycle(D,E)| -next(C,D)| -greater(C,A)| -greater(B,E).
% 1.67/1.89 ** KEPT (pick-wt=10): 5 [] -cycle(A,e_0)| -product(A,e_1,B)| -greater(B,A).
% 1.67/1.89 ** KEPT (pick-wt=16): 6 [] -cycle(A,B)| -product(A,e_1,C)| -greater(B,e_0)| -next(A,D)|e_qualish(C,D).
% 1.67/1.89 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_1,e_2).
% 1.67/1.89 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_1,e_3).
% 1.67/1.89 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_2,e_1).
% 1.67/1.89 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_2,e_3).
% 1.67/1.89 ** KEPT (pick-wt=3): 11 [] -e_qualish(e_3,e_1).
% 1.67/1.89 ** KEPT (pick-wt=3): 12 [] -e_qualish(e_3,e_2).
% 1.67/1.89 ** KEPT (pick-wt=16): 13 [] -group_element(A)| -group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3).
% 1.67/1.89 ** KEPT (pick-wt=11): 14 [] -product1(A,B,C)| -product1(A,B,D)|e_qualish(C,D).
% 1.67/1.89 ** KEPT (pick-wt=11): 15 [] -product1(A,B,C)| -product1(A,D,C)|e_qualish(B,D).
% 1.67/1.89 ** KEPT (pick-wt=11): 16 [] -product1(A,B,C)| -product1(D,B,C)|e_qualish(A,D).
% 1.67/1.89 ** KEPT (pick-wt=16): 17 [] -group_element(A)| -group_element(B)|product2(A,B,e_1)|product2(A,B,e_2)|product2(A,B,e_3).
% 1.67/1.89 ** KEPT (pick-wt=11): 18 [] -product2(A,B,C)| -product2(A,B,D)|e_qualish(C,D).
% 1.67/1.89 ** KEPT (pick-wt=11): 19 [] -product2(A,B,C)| -product2(A,D,C)|e_qualish(B,D).
% 1.67/1.89 ** KEPT (pick-wt=11): 20 [] -product2(A,B,C)| -product2(D,B,C)|e_qualish(A,D).
% 1.67/1.89 ** KEPT (pick-wt=12): 21 [] -product1(A,B,C)| -product1(C,B,D)|product2(D,A,B).
% 1.67/1.91
% 1.67/1.91 ------------> process sos:
% 1.67/1.91 ** KEPT (pick-wt=3): 43 [] next(e_0,e_1).
% 1.67/1.91 ** KEPT (pick-wt=3): 44 [] next(e_1,e_2).
% 1.67/1.91 ** KEPT (pick-wt=3): 45 [] next(e_2,e_3).
% 1.67/1.91 ** KEPT (pick-wt=3): 46 [] greater(e_1,e_0).
% 1.67/1.91 ** KEPT (pick-wt=3): 47 [] greater(e_2,e_0).
% 1.67/1.91 ** KEPT (pick-wt=3): 48 [] greater(e_3,e_0).
% 1.67/1.91 ** KEPT (pick-wt=3): 49 [] greater(e_2,e_1).
% 1.67/1.91 ** KEPT (pick-wt=3): 50 [] greater(e_3,e_1).
% 1.67/1.91 ** KEPT (pick-wt=3): 51 [] greater(e_3,e_2).
% 1.67/1.91 ** KEPT (pick-wt=3): 52 [] cycle(e_3,e_0).
% 1.67/1.91 ** KEPT (pick-wt=2): 53 [] group_element(e_1).
% 1.67/1.91 ** KEPT (pick-wt=2): 54 [] group_element(e_2).
% 1.67/1.91 ** KEPT (pick-wt=2): 55 [] group_element(e_3).
% 1.67/1.91 ** KEPT (pick-wt=4): 56 [] product1(A,A,A).
% 1.67/1.91 ** KEPT (pick-wt=4): 57 [] product2(A,A,A).
% 1.67/1.91
% 1.67/1.91 ======= end of input processing =======
% 1.67/1.91
% 1.67/1.91 =========== start of search ===========
% 1.67/1.91
% 1.67/1.91 -------- PROOF --------
% 1.67/1.91
% 1.67/1.91 ----> UNIT CONFLICT at 0.02 sec ----> 136 [binary,135.1,7.1] $F.
% 1.67/1.91
% 1.67/1.91 Length of proof is 11. Level of proof is 7.
% 1.67/1.91
% 1.67/1.91 ---------------- PROOF ----------------
% 1.67/1.91 % SZS status Unsatisfiable
% 1.67/1.91 % SZS output start Refutation
% See solution above
% 1.67/1.91 ------------ end of proof -------------
% 1.67/1.91
% 1.67/1.91
% 1.67/1.91 Search stopped by max_proofs option.
% 1.67/1.91
% 1.67/1.91
% 1.67/1.91 Search stopped by max_proofs option.
% 1.67/1.91
% 1.67/1.91 ============ end of search ============
% 1.67/1.91
% 1.67/1.91 -------------- statistics -------------
% 1.67/1.91 clauses given 54
% 1.67/1.91 clauses generated 887
% 1.67/1.91 clauses kept 135
% 1.67/1.91 clauses forward subsumed 788
% 1.67/1.91 clauses back subsumed 66
% 1.67/1.91 Kbytes malloced 976
% 1.67/1.91
% 1.67/1.91 ----------- times (seconds) -----------
% 1.67/1.91 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.67/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.91
% 1.67/1.91 That finishes the proof of the theorem.
% 1.67/1.91
% 1.67/1.91 Process 23308 finished Wed Jul 27 05:19:08 2022
% 1.67/1.91 Otter interrupted
% 1.67/1.91 PROOF FOUND
%------------------------------------------------------------------------------