TSTP Solution File: GRP132-2.002 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP132-2.002 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 1.83s 2.03s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 10 unt; 9 nHn; 23 RR)
% Number of literals : 46 ( 0 equ; 16 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 : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ e_qualish(e_1,e_2),
file('GRP132-2.002.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_2,e_1),
file('GRP132-2.002.p',unknown),
[] ).
cnf(4,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
file('GRP132-2.002.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP132-2.002.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP132-2.002.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| e_qualish(B,E) ),
file('GRP132-2.002.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(21,plain,
( ~ product(A,B,C)
| ~ product(C,C,C)
| ~ product(C,A,B)
| e_qualish(B,C) ),
inference(factor,[status(thm)],[9]),
[iquote('factor,9.2.4')] ).
cnf(24,axiom,
group_element(e_1),
file('GRP132-2.002.p',unknown),
[] ).
cnf(25,axiom,
group_element(e_2),
file('GRP132-2.002.p',unknown),
[] ).
cnf(26,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(hyper,[status(thm)],[24,10]),
[iquote('hyper,24,10')] ).
cnf(27,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(hyper,[status(thm)],[25,10]),
[iquote('hyper,25,10')] ).
cnf(28,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(hyper,[status(thm)],[25,4,24]),
[iquote('hyper,25,4,24')] ).
cnf(29,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(hyper,[status(thm)],[25,4,24]),
[iquote('hyper,25,4,24')] ).
cnf(44,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[28,7,27]),3]),
[iquote('hyper,28,7,27,unit_del,3')] ).
cnf(45,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[28,6,26]),2]),
[iquote('hyper,28,6,26,unit_del,2')] ).
cnf(56,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[29,7,26]),2]),
[iquote('hyper,29,7,26,unit_del,2')] ).
cnf(71,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)],[45,21,44,28]),3])])]),
[iquote('hyper,45,21,44,28,unit_del,3,factor_simp,factor_simp')] ).
cnf(74,plain,
product(e_2,e_2,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[71,7,27]),3]),
[iquote('hyper,71,7,27,unit_del,3')] ).
cnf(75,plain,
product(e_1,e_1,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[71,6,26]),2]),
[iquote('hyper,71,6,26,unit_del,2')] ).
cnf(76,plain,
product(e_2,e_1,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[56,6,71]),3]),
[iquote('hyper,56,6,71,unit_del,3')] ).
cnf(77,plain,
e_qualish(e_1,e_2),
inference(hyper,[status(thm)],[76,21,75,74]),
[iquote('hyper,76,21,75,74')] ).
cnf(78,plain,
$false,
inference(binary,[status(thm)],[77,2]),
[iquote('binary,77.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP132-2.002 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:13:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.83/2.03 ----- Otter 3.3f, August 2004 -----
% 1.83/2.03 The process was started by sandbox2 on n003.cluster.edu,
% 1.83/2.03 Wed Jul 27 05:13:56 2022
% 1.83/2.03 The command was "./otter". The process ID is 1359.
% 1.83/2.03
% 1.83/2.03 set(prolog_style_variables).
% 1.83/2.03 set(auto).
% 1.83/2.03 dependent: set(auto1).
% 1.83/2.03 dependent: set(process_input).
% 1.83/2.03 dependent: clear(print_kept).
% 1.83/2.03 dependent: clear(print_new_demod).
% 1.83/2.03 dependent: clear(print_back_demod).
% 1.83/2.03 dependent: clear(print_back_sub).
% 1.83/2.03 dependent: set(control_memory).
% 1.83/2.03 dependent: assign(max_mem, 12000).
% 1.83/2.03 dependent: assign(pick_given_ratio, 4).
% 1.83/2.03 dependent: assign(stats_level, 1).
% 1.83/2.03 dependent: assign(max_seconds, 10800).
% 1.83/2.03 clear(print_given).
% 1.83/2.03
% 1.83/2.03 list(usable).
% 1.83/2.03 0 [] next(e_1,e_2).
% 1.83/2.03 0 [] greater(e_2,e_1).
% 1.83/2.03 0 [] -product(X,e_1,Y)| -next(X,X1)| -greater(Y,X1).
% 1.83/2.03 0 [] group_element(e_1).
% 1.83/2.03 0 [] group_element(e_2).
% 1.83/2.03 0 [] -e_qualish(e_1,e_2).
% 1.83/2.03 0 [] -e_qualish(e_2,e_1).
% 1.83/2.03 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2).
% 1.83/2.03 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.83/2.03 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.83/2.03 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.83/2.03 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(X1,X2).
% 1.83/2.03 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(Y1,Y2).
% 1.83/2.03 end_of_list.
% 1.83/2.03
% 1.83/2.03 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.83/2.03
% 1.83/2.03 This is a non-Horn set without equality. The strategy will
% 1.83/2.03 be ordered hyper_res, unit deletion, and factoring, with
% 1.83/2.03 satellites in sos and with nuclei in usable.
% 1.83/2.03
% 1.83/2.03 dependent: set(hyper_res).
% 1.83/2.03 dependent: set(factor).
% 1.83/2.03 dependent: set(unit_deletion).
% 1.83/2.03
% 1.83/2.03 ------------> process usable:
% 1.83/2.03 ** KEPT (pick-wt=10): 1 [] -product(A,e_1,B)| -next(A,C)| -greater(B,C).
% 1.83/2.03 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_2).
% 1.83/2.03 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_2,e_1).
% 1.83/2.03 ** KEPT (pick-wt=12): 4 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2).
% 1.83/2.03 ** KEPT (pick-wt=11): 5 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.83/2.03 ** KEPT (pick-wt=11): 6 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.83/2.03 ** KEPT (pick-wt=11): 7 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.83/2.03 ** KEPT (pick-wt=19): 8 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(A,D).
% 1.83/2.03 ** KEPT (pick-wt=19): 9 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(B,E).
% 1.83/2.03
% 1.83/2.03 ------------> process sos:
% 1.83/2.03 ** KEPT (pick-wt=3): 22 [] next(e_1,e_2).
% 1.83/2.03 ** KEPT (pick-wt=3): 23 [] greater(e_2,e_1).
% 1.83/2.03 ** KEPT (pick-wt=2): 24 [] group_element(e_1).
% 1.83/2.03 ** KEPT (pick-wt=2): 25 [] group_element(e_2).
% 1.83/2.03
% 1.83/2.03 ======= end of input processing =======
% 1.83/2.03
% 1.83/2.03 =========== start of search ===========
% 1.83/2.03
% 1.83/2.03 -------- PROOF --------
% 1.83/2.03
% 1.83/2.03 ----> UNIT CONFLICT at 0.08 sec ----> 78 [binary,77.1,2.1] $F.
% 1.83/2.03
% 1.83/2.03 Length of proof is 14. Level of proof is 6.
% 1.83/2.03
% 1.83/2.03 ---------------- PROOF ----------------
% 1.83/2.03 % SZS status Unsatisfiable
% 1.83/2.03 % SZS output start Refutation
% See solution above
% 1.83/2.03 ------------ end of proof -------------
% 1.83/2.03
% 1.83/2.03
% 1.83/2.03 Search stopped by max_proofs option.
% 1.83/2.03
% 1.83/2.03
% 1.83/2.03 Search stopped by max_proofs option.
% 1.83/2.03
% 1.83/2.03 ============ end of search ============
% 1.83/2.03
% 1.83/2.03 -------------- statistics -------------
% 1.83/2.03 clauses given 35
% 1.83/2.03 clauses generated 3958
% 1.83/2.03 clauses kept 77
% 1.83/2.03 clauses forward subsumed 3894
% 1.83/2.03 clauses back subsumed 43
% 1.83/2.03 Kbytes malloced 976
% 1.83/2.03
% 1.83/2.03 ----------- times (seconds) -----------
% 1.83/2.03 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.83/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/2.03 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.83/2.03
% 1.83/2.03 That finishes the proof of the theorem.
% 1.83/2.03
% 1.83/2.03 Process 1359 finished Wed Jul 27 05:13:58 2022
% 1.83/2.03 Otter interrupted
% 1.83/2.03 PROOF FOUND
%------------------------------------------------------------------------------