TSTP Solution File: GRP123-9.003 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP123-9.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 12:56:08 EDT 2022
% Result : Unsatisfiable 1.67s 1.88s
% 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(3,axiom,
~ e_qualish(e_1,e_2),
file('GRP123-9.003.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_2,e_1),
file('GRP123-9.003.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_2,e_3),
file('GRP123-9.003.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_3,e_1),
file('GRP123-9.003.p',unknown),
[] ).
cnf(8,axiom,
~ e_qualish(e_3,e_2),
file('GRP123-9.003.p',unknown),
[] ).
cnf(9,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(11,axiom,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| e_qualish(B,D) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(12,axiom,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| e_qualish(A,D) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(13,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product2(A,B,e_1)
| product2(A,B,e_2)
| product2(A,B,e_3) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(15,axiom,
( ~ product2(A,B,C)
| ~ product2(A,D,C)
| e_qualish(B,D) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(16,axiom,
( ~ product2(A,B,C)
| ~ product2(D,B,C)
| e_qualish(A,D) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(17,axiom,
( ~ product1(A,B,C)
| ~ product1(C,B,D)
| product2(D,A,B) ),
file('GRP123-9.003.p',unknown),
[] ).
cnf(29,axiom,
group_element(e_1),
file('GRP123-9.003.p',unknown),
[] ).
cnf(30,axiom,
group_element(e_2),
file('GRP123-9.003.p',unknown),
[] ).
cnf(31,axiom,
group_element(e_3),
file('GRP123-9.003.p',unknown),
[] ).
cnf(32,axiom,
product1(A,A,A),
file('GRP123-9.003.p',unknown),
[] ).
cnf(33,axiom,
product2(A,A,A),
file('GRP123-9.003.p',unknown),
[] ).
cnf(38,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)],[30,13,29]),
[iquote('hyper,30,13,29')] ).
cnf(52,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)],[31,9,30]),
[iquote('hyper,31,9,30')] ).
cnf(53,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)],[31,9,29]),
[iquote('hyper,31,9,29')] ).
cnf(65,plain,
( product2(e_1,e_2,e_2)
| product2(e_1,e_2,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[38,15,33]),3]),
[iquote('hyper,38,15,33,unit_del,3')] ).
cnf(67,plain,
product2(e_1,e_2,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[65,16,33]),5]),
[iquote('hyper,65,16,33,unit_del,5')] ).
cnf(96,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[52,11,32]),6]),
[iquote('hyper,52,11,32,unit_del,6')] ).
cnf(100,plain,
product1(e_2,e_3,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[96,12,32]),8]),
[iquote('hyper,96,12,32,unit_del,8')] ).
cnf(102,plain,
( product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[53,12,100]),5]),
[iquote('hyper,53,12,100,unit_del,5')] ).
cnf(112,plain,
product1(e_1,e_3,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[102,12,32]),7]),
[iquote('hyper,102,12,32,unit_del,7')] ).
cnf(120,plain,
product2(e_2,e_2,e_3),
inference(hyper,[status(thm)],[112,17,100]),
[iquote('hyper,112,17,100')] ).
cnf(122,plain,
e_qualish(e_1,e_2),
inference(hyper,[status(thm)],[120,16,67]),
[iquote('hyper,120,16,67')] ).
cnf(123,plain,
$false,
inference(binary,[status(thm)],[122,3]),
[iquote('binary,122.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP123-9.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 05:13:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.88 ----- Otter 3.3f, August 2004 -----
% 1.67/1.88 The process was started by sandbox on n027.cluster.edu,
% 1.67/1.88 Wed Jul 27 05:13:21 2022
% 1.67/1.88 The command was "./otter". The process ID is 11027.
% 1.67/1.88
% 1.67/1.88 set(prolog_style_variables).
% 1.67/1.88 set(auto).
% 1.67/1.88 dependent: set(auto1).
% 1.67/1.88 dependent: set(process_input).
% 1.67/1.88 dependent: clear(print_kept).
% 1.67/1.88 dependent: clear(print_new_demod).
% 1.67/1.88 dependent: clear(print_back_demod).
% 1.67/1.88 dependent: clear(print_back_sub).
% 1.67/1.88 dependent: set(control_memory).
% 1.67/1.88 dependent: assign(max_mem, 12000).
% 1.67/1.88 dependent: assign(pick_given_ratio, 4).
% 1.67/1.88 dependent: assign(stats_level, 1).
% 1.67/1.88 dependent: assign(max_seconds, 10800).
% 1.67/1.88 clear(print_given).
% 1.67/1.88
% 1.67/1.88 list(usable).
% 1.67/1.88 0 [] -group_element(X)| -group_element(Y)|product(e_1,X,Y)|product(e_2,X,Y)|product(e_3,X,Y).
% 1.67/1.88 0 [] -group_element(X)| -group_element(Y)|product(X,e_1,Y)|product(X,e_2,Y)|product(X,e_3,Y).
% 1.67/1.88 0 [] group_element(e_1).
% 1.67/1.88 0 [] group_element(e_2).
% 1.67/1.88 0 [] group_element(e_3).
% 1.67/1.88 0 [] -e_qualish(e_1,e_2).
% 1.67/1.88 0 [] -e_qualish(e_1,e_3).
% 1.67/1.88 0 [] -e_qualish(e_2,e_1).
% 1.67/1.88 0 [] -e_qualish(e_2,e_3).
% 1.67/1.88 0 [] -e_qualish(e_3,e_1).
% 1.67/1.88 0 [] -e_qualish(e_3,e_2).
% 1.67/1.88 0 [] -group_element(X)| -group_element(Y)|product1(X,Y,e_1)|product1(X,Y,e_2)|product1(X,Y,e_3).
% 1.67/1.88 0 [] -product1(X,Y,W)| -product1(X,Y,Z)|e_qualish(W,Z).
% 1.67/1.88 0 [] -product1(X,W,Y)| -product1(X,Z,Y)|e_qualish(W,Z).
% 1.67/1.88 0 [] -product1(W,Y,X)| -product1(Z,Y,X)|e_qualish(W,Z).
% 1.67/1.88 0 [] product1(X,X,X).
% 1.67/1.88 0 [] -group_element(X)| -group_element(Y)|product2(X,Y,e_1)|product2(X,Y,e_2)|product2(X,Y,e_3).
% 1.67/1.88 0 [] -product2(X,Y,W)| -product2(X,Y,Z)|e_qualish(W,Z).
% 1.67/1.88 0 [] -product2(X,W,Y)| -product2(X,Z,Y)|e_qualish(W,Z).
% 1.67/1.88 0 [] -product2(W,Y,X)| -product2(Z,Y,X)|e_qualish(W,Z).
% 1.67/1.88 0 [] product2(X,X,X).
% 1.67/1.88 0 [] -product1(X,Y,Z1)| -product1(Z1,Y,Z2)|product2(Z2,X,Y).
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.67/1.88
% 1.67/1.88 This is a non-Horn set without equality. The strategy will
% 1.67/1.88 be ordered hyper_res, unit deletion, and factoring, with
% 1.67/1.88 satellites in sos and with nuclei in usable.
% 1.67/1.88
% 1.67/1.88 dependent: set(hyper_res).
% 1.67/1.88 dependent: set(factor).
% 1.67/1.88 dependent: set(unit_deletion).
% 1.67/1.88
% 1.67/1.88 ------------> process usable:
% 1.67/1.88 ** 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).
% 1.67/1.88 ** 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).
% 1.67/1.88 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_2).
% 1.67/1.88 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_1,e_3).
% 1.67/1.88 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_1).
% 1.67/1.88 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_3).
% 1.67/1.88 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_1).
% 1.67/1.88 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_3,e_2).
% 1.67/1.88 ** KEPT (pick-wt=16): 9 [] -group_element(A)| -group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3).
% 1.67/1.88 ** KEPT (pick-wt=11): 10 [] -product1(A,B,C)| -product1(A,B,D)|e_qualish(C,D).
% 1.67/1.88 ** KEPT (pick-wt=11): 11 [] -product1(A,B,C)| -product1(A,D,C)|e_qualish(B,D).
% 1.67/1.88 ** KEPT (pick-wt=11): 12 [] -product1(A,B,C)| -product1(D,B,C)|e_qualish(A,D).
% 1.67/1.88 ** KEPT (pick-wt=16): 13 [] -group_element(A)| -group_element(B)|product2(A,B,e_1)|product2(A,B,e_2)|product2(A,B,e_3).
% 1.67/1.88 ** KEPT (pick-wt=11): 14 [] -product2(A,B,C)| -product2(A,B,D)|e_qualish(C,D).
% 1.67/1.88 ** KEPT (pick-wt=11): 15 [] -product2(A,B,C)| -product2(A,D,C)|e_qualish(B,D).
% 1.67/1.88 ** KEPT (pick-wt=11): 16 [] -product2(A,B,C)| -product2(D,B,C)|e_qualish(A,D).
% 1.67/1.88 ** KEPT (pick-wt=12): 17 [] -product1(A,B,C)| -product1(C,B,D)|product2(D,A,B).
% 1.67/1.88
% 1.67/1.88 ------------> process sos:
% 1.67/1.88 ** KEPT (pick-wt=2): 29 [] group_element(e_1).
% 1.67/1.88 ** KEPT (pick-wt=2): 30 [] group_element(e_2).
% 1.67/1.88 ** KEPT (pick-wt=2): 31 [] group_element(e_3).
% 1.67/1.88 ** KEPT (pick-wt=4): 32 [] product1(A,A,A).
% 1.67/1.88 ** KEPT (pick-wt=4): 33 [] product2(A,A,A).
% 1.67/1.88
% 1.67/1.88 ======= end of input processing =======
% 1.67/1.88
% 1.67/1.88 =========== start of search ===========
% 1.67/1.88
% 1.67/1.88 -------- PROOF --------
% 1.67/1.88
% 1.67/1.88 ----> UNIT CONFLICT at 0.01 sec ----> 123 [binary,122.1,3.1] $F.
% 1.67/1.88
% 1.67/1.88 Length of proof is 11. Level of proof is 7.
% 1.67/1.88
% 1.67/1.88 ---------------- PROOF ----------------
% 1.67/1.88 % SZS status Unsatisfiable
% 1.67/1.88 % SZS output start Refutation
% See solution above
% 1.67/1.88 ------------ end of proof -------------
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88 ============ end of search ============
% 1.67/1.88
% 1.67/1.88 -------------- statistics -------------
% 1.67/1.88 clauses given 48
% 1.67/1.88 clauses generated 794
% 1.67/1.88 clauses kept 122
% 1.67/1.88 clauses forward subsumed 694
% 1.67/1.88 clauses back subsumed 58
% 1.67/1.88 Kbytes malloced 976
% 1.67/1.88
% 1.67/1.88 ----------- times (seconds) -----------
% 1.67/1.88 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.67/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.67/1.88
% 1.67/1.88 That finishes the proof of the theorem.
% 1.67/1.88
% 1.67/1.88 Process 11027 finished Wed Jul 27 05:13:23 2022
% 1.67/1.88 Otter interrupted
% 1.67/1.88 PROOF FOUND
%------------------------------------------------------------------------------