TSTP Solution File: GRP126-2.004 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP126-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 12:56:11 EDT 2022
% Result : Unsatisfiable 1.69s 1.89s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of clauses : 35 ( 19 unt; 11 nHn; 34 RR)
% Number of literals : 69 ( 0 equ; 20 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,e_1,B)
| ~ next(A,C)
| ~ greater(B,C) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_2),
file('GRP126-2.004.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_1,e_3),
file('GRP126-2.004.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_2,e_1),
file('GRP126-2.004.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_2,e_3),
file('GRP126-2.004.p',unknown),
[] ).
cnf(8,axiom,
~ e_qualish(e_3,e_1),
file('GRP126-2.004.p',unknown),
[] ).
cnf(9,axiom,
~ e_qualish(e_3,e_2),
file('GRP126-2.004.p',unknown),
[] ).
cnf(11,axiom,
~ e_qualish(e_4,e_1),
file('GRP126-2.004.p',unknown),
[] ).
cnf(14,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3)
| product(A,B,e_4) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| e_qualish(C,D) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,B) ),
file('GRP126-2.004.p',unknown),
[] ).
cnf(25,axiom,
next(e_2,e_3),
file('GRP126-2.004.p',unknown),
[] ).
cnf(32,axiom,
greater(e_4,e_3),
file('GRP126-2.004.p',unknown),
[] ).
cnf(33,axiom,
group_element(e_1),
file('GRP126-2.004.p',unknown),
[] ).
cnf(34,axiom,
group_element(e_2),
file('GRP126-2.004.p',unknown),
[] ).
cnf(35,axiom,
group_element(e_3),
file('GRP126-2.004.p',unknown),
[] ).
cnf(37,axiom,
product(A,A,A),
file('GRP126-2.004.p',unknown),
[] ).
cnf(38,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(hyper,[status(thm)],[34,14,33]),
[iquote('hyper,34,14,33')] ).
cnf(39,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(hyper,[status(thm)],[34,14,33]),
[iquote('hyper,34,14,33')] ).
cnf(41,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(hyper,[status(thm)],[35,14,33]),
[iquote('hyper,35,14,33')] ).
cnf(51,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[38,16,37]),2]),
[iquote('hyper,38,16,37,unit_del,2')] ).
cnf(53,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[51,17,37]),5]),
[iquote('hyper,51,17,37,unit_del,5')] ).
cnf(58,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[39,17,37]),2]),
[iquote('hyper,39,17,37,unit_del,2')] ).
cnf(77,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[58,16,37]),5]),
[iquote('hyper,58,16,37,unit_del,5')] ).
cnf(97,plain,
product(e_2,e_1,e_3),
inference(hyper,[status(thm)],[77,1,25,32]),
[iquote('hyper,77,1,25,32')] ).
cnf(99,plain,
( product(e_3,e_3,e_2)
| product(e_1,e_2,e_4) ),
inference(hyper,[status(thm)],[97,18,53]),
[iquote('hyper,97,18,53')] ).
cnf(107,plain,
product(e_1,e_2,e_4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[99,15,37]),9]),
[iquote('hyper,99,15,37,unit_del,9')] ).
cnf(109,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[41,16,37]),3]),
[iquote('hyper,41,16,37,unit_del,3')] ).
cnf(113,plain,
product(e_4,e_3,e_2),
inference(hyper,[status(thm)],[107,18,97]),
[iquote('hyper,107,18,97')] ).
cnf(119,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[109,17,113]),11]),
[iquote('hyper,109,17,113,unit_del,11')] ).
cnf(123,plain,
product(e_1,e_3,e_4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[119,17,37]),8]),
[iquote('hyper,119,17,37,unit_del,8')] ).
cnf(127,plain,
e_qualish(e_2,e_3),
inference(hyper,[status(thm)],[123,16,107]),
[iquote('hyper,123,16,107')] ).
cnf(128,plain,
$false,
inference(binary,[status(thm)],[127,6]),
[iquote('binary,127.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP126-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 05:18:24 EDT 2022
% 0.19/0.33 % CPUTime :
% 1.69/1.89 ----- Otter 3.3f, August 2004 -----
% 1.69/1.89 The process was started by sandbox on n014.cluster.edu,
% 1.69/1.89 Wed Jul 27 05:18:24 2022
% 1.69/1.89 The command was "./otter". The process ID is 28307.
% 1.69/1.89
% 1.69/1.89 set(prolog_style_variables).
% 1.69/1.89 set(auto).
% 1.69/1.89 dependent: set(auto1).
% 1.69/1.89 dependent: set(process_input).
% 1.69/1.89 dependent: clear(print_kept).
% 1.69/1.89 dependent: clear(print_new_demod).
% 1.69/1.89 dependent: clear(print_back_demod).
% 1.69/1.89 dependent: clear(print_back_sub).
% 1.69/1.89 dependent: set(control_memory).
% 1.69/1.89 dependent: assign(max_mem, 12000).
% 1.69/1.89 dependent: assign(pick_given_ratio, 4).
% 1.69/1.89 dependent: assign(stats_level, 1).
% 1.69/1.89 dependent: assign(max_seconds, 10800).
% 1.69/1.89 clear(print_given).
% 1.69/1.89
% 1.69/1.89 list(usable).
% 1.69/1.89 0 [] next(e_1,e_2).
% 1.69/1.89 0 [] next(e_2,e_3).
% 1.69/1.89 0 [] next(e_3,e_4).
% 1.69/1.89 0 [] greater(e_2,e_1).
% 1.69/1.89 0 [] greater(e_3,e_1).
% 1.69/1.89 0 [] greater(e_4,e_1).
% 1.69/1.89 0 [] greater(e_3,e_2).
% 1.69/1.89 0 [] greater(e_4,e_2).
% 1.69/1.89 0 [] greater(e_4,e_3).
% 1.69/1.89 0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.69/1.89 0 [] group_element(e_1).
% 1.69/1.89 0 [] group_element(e_2).
% 1.69/1.89 0 [] group_element(e_3).
% 1.69/1.89 0 [] group_element(e_4).
% 1.69/1.89 0 [] -e_qualish(e_1,e_2).
% 1.69/1.89 0 [] -e_qualish(e_1,e_3).
% 1.69/1.89 0 [] -e_qualish(e_1,e_4).
% 1.69/1.89 0 [] -e_qualish(e_2,e_1).
% 1.69/1.89 0 [] -e_qualish(e_2,e_3).
% 1.69/1.89 0 [] -e_qualish(e_2,e_4).
% 1.69/1.89 0 [] -e_qualish(e_3,e_1).
% 1.69/1.89 0 [] -e_qualish(e_3,e_2).
% 1.69/1.89 0 [] -e_qualish(e_3,e_4).
% 1.69/1.89 0 [] -e_qualish(e_4,e_1).
% 1.69/1.89 0 [] -e_qualish(e_4,e_2).
% 1.69/1.89 0 [] -e_qualish(e_4,e_3).
% 1.69/1.89 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2)|product(X,Y,e_3)|product(X,Y,e_4).
% 1.69/1.89 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.69/1.89 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.69/1.89 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.69/1.89 0 [] product(X,X,X).
% 1.69/1.89 0 [] -product(X,Y,Z1)| -product(Y,X,Z2)|product(Z1,Z2,Y).
% 1.69/1.89 end_of_list.
% 1.69/1.89
% 1.69/1.89 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.69/1.89
% 1.69/1.89 This is a non-Horn set without equality. The strategy will
% 1.69/1.89 be ordered hyper_res, unit deletion, and factoring, with
% 1.69/1.89 satellites in sos and with nuclei in usable.
% 1.69/1.89
% 1.69/1.89 dependent: set(hyper_res).
% 1.69/1.89 dependent: set(factor).
% 1.69/1.89 dependent: set(unit_deletion).
% 1.69/1.89
% 1.69/1.89 ------------> process usable:
% 1.69/1.89 ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.69/1.89 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.69/1.89 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_3).
% 1.69/1.89 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_1,e_4).
% 1.69/1.89 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_1).
% 1.69/1.89 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_3).
% 1.69/1.89 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_2,e_4).
% 1.69/1.89 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_3,e_1).
% 1.69/1.89 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_3,e_2).
% 1.69/1.89 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_3,e_4).
% 1.69/1.89 ** KEPT (pick-wt=3): 11 [] -e_qualish(e_4,e_1).
% 1.69/1.89 ** KEPT (pick-wt=3): 12 [] -e_qualish(e_4,e_2).
% 1.69/1.89 ** KEPT (pick-wt=3): 13 [] -e_qualish(e_4,e_3).
% 1.69/1.89 ** KEPT (pick-wt=20): 14 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)|product(A,B,e_4).
% 1.69/1.89 ** KEPT (pick-wt=11): 15 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.69/1.89 ** KEPT (pick-wt=11): 16 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.69/1.89 ** KEPT (pick-wt=11): 17 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.69/1.89 ** KEPT (pick-wt=12): 18 [] -product(A,B,C)| -product(B,A,D)|product(C,D,B).
% 1.69/1.89
% 1.69/1.89 ------------> process sos:
% 1.69/1.89 ** KEPT (pick-wt=3): 24 [] next(e_1,e_2).
% 1.69/1.89 ** KEPT (pick-wt=3): 25 [] next(e_2,e_3).
% 1.69/1.89 ** KEPT (pick-wt=3): 26 [] next(e_3,e_4).
% 1.69/1.89 ** KEPT (pick-wt=3): 27 [] greater(e_2,e_1).
% 1.69/1.89 ** KEPT (pick-wt=3): 28 [] greater(e_3,e_1).
% 1.69/1.89 ** KEPT (pick-wt=3): 29 [] greater(e_4,e_1).
% 1.69/1.89 ** KEPT (pick-wt=3): 30 [] greater(e_3,e_2).
% 1.69/1.89 ** KEPT (pick-wt=3): 31 [] greater(e_4,e_2).
% 1.69/1.89 ** KEPT (pick-wt=3): 32 [] greater(e_4,e_3).
% 1.69/1.89 ** KEPT (pick-wt=2): 33 [] group_element(e_1).
% 1.69/1.89 ** KEPT (pick-wt=2): 34 [] group_element(e_2).
% 1.69/1.89 ** KEPT (pick-wt=2): 35 [] group_element(e_3).
% 1.69/1.89 ** KEPT (pick-wt=2): 36 [] group_element(e_4).
% 1.69/1.89 ** KEPT (pick-wt=4): 37 [] product(A,A,A).
% 1.69/1.89
% 1.69/1.89 ======= end of input processing =======
% 1.69/1.89
% 1.69/1.89 =========== start of search ===========
% 1.69/1.89
% 1.69/1.89 -------- PROOF --------
% 1.69/1.89
% 1.69/1.89 ----> UNIT CONFLICT at 0.01 sec ----> 128 [binary,127.1,6.1] $F.
% 1.69/1.89
% 1.69/1.89 Length of proof is 15. Level of proof is 10.
% 1.69/1.89
% 1.69/1.89 ---------------- PROOF ----------------
% 1.69/1.89 % SZS status Unsatisfiable
% 1.69/1.89 % SZS output start Refutation
% See solution above
% 1.69/1.89 ------------ end of proof -------------
% 1.69/1.89
% 1.69/1.89
% 1.69/1.89 Search stopped by max_proofs option.
% 1.69/1.89
% 1.69/1.89
% 1.69/1.89 Search stopped by max_proofs option.
% 1.69/1.89
% 1.69/1.89 ============ end of search ============
% 1.69/1.89
% 1.69/1.89 -------------- statistics -------------
% 1.69/1.89 clauses given 35
% 1.69/1.89 clauses generated 649
% 1.69/1.89 clauses kept 127
% 1.69/1.89 clauses forward subsumed 554
% 1.69/1.89 clauses back subsumed 74
% 1.69/1.89 Kbytes malloced 976
% 1.69/1.89
% 1.69/1.89 ----------- times (seconds) -----------
% 1.69/1.89 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.69/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.89
% 1.69/1.89 That finishes the proof of the theorem.
% 1.69/1.89
% 1.69/1.89 Process 28307 finished Wed Jul 27 05:18:25 2022
% 1.69/1.89 Otter interrupted
% 1.69/1.89 PROOF FOUND
%------------------------------------------------------------------------------