TSTP Solution File: GRP132-1.002 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP132-1.002 : 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 12:56:30 EDT 2022
% Result : Unsatisfiable 1.75s 1.99s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 22 ( 10 unt; 8 nHn; 22 RR)
% Number of literals : 44 ( 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(1,axiom,
~ e_qualish(e_1,e_2),
file('GRP132-1.002.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_2,e_1),
file('GRP132-1.002.p',unknown),
[] ).
cnf(3,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
file('GRP132-1.002.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP132-1.002.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP132-1.002.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| e_qualish(B,E) ),
file('GRP132-1.002.p',unknown),
[] ).
cnf(9,plain,
( ~ group_element(A)
| product(A,A,e_1)
| product(A,A,e_2) ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.1.2')] ).
cnf(20,plain,
( ~ product(A,B,C)
| ~ product(C,C,C)
| ~ product(C,A,B)
| e_qualish(B,C) ),
inference(factor,[status(thm)],[8]),
[iquote('factor,8.2.4')] ).
cnf(21,axiom,
group_element(e_1),
file('GRP132-1.002.p',unknown),
[] ).
cnf(22,axiom,
group_element(e_2),
file('GRP132-1.002.p',unknown),
[] ).
cnf(23,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(hyper,[status(thm)],[21,9]),
[iquote('hyper,21,9')] ).
cnf(24,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(hyper,[status(thm)],[22,9]),
[iquote('hyper,22,9')] ).
cnf(25,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(hyper,[status(thm)],[22,3,21]),
[iquote('hyper,22,3,21')] ).
cnf(26,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(hyper,[status(thm)],[22,3,21]),
[iquote('hyper,22,3,21')] ).
cnf(41,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[25,6,24]),2]),
[iquote('hyper,25,6,24,unit_del,2')] ).
cnf(42,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[25,5,23]),1]),
[iquote('hyper,25,5,23,unit_del,1')] ).
cnf(68,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)],[42,20,41,25]),2])])]),
[iquote('hyper,42,20,41,25,unit_del,2,factor_simp,factor_simp')] ).
cnf(71,plain,
product(e_2,e_2,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[68,6,24]),2]),
[iquote('hyper,68,6,24,unit_del,2')] ).
cnf(72,plain,
product(e_1,e_1,e_2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[68,5,23]),1]),
[iquote('hyper,68,5,23,unit_del,1')] ).
cnf(73,plain,
product(e_2,e_1,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[71,5,26]),1]),
[iquote('hyper,71,5,26,unit_del,1')] ).
cnf(76,plain,
e_qualish(e_1,e_2),
inference(hyper,[status(thm)],[73,20,72,71]),
[iquote('hyper,73,20,72,71')] ).
cnf(77,plain,
$false,
inference(binary,[status(thm)],[76,1]),
[iquote('binary,76.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP132-1.002 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13 % 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 05:27:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.75/1.99 ----- Otter 3.3f, August 2004 -----
% 1.75/1.99 The process was started by sandbox2 on n016.cluster.edu,
% 1.75/1.99 Wed Jul 27 05:27:37 2022
% 1.75/1.99 The command was "./otter". The process ID is 7712.
% 1.75/1.99
% 1.75/1.99 set(prolog_style_variables).
% 1.75/1.99 set(auto).
% 1.75/1.99 dependent: set(auto1).
% 1.75/1.99 dependent: set(process_input).
% 1.75/1.99 dependent: clear(print_kept).
% 1.75/1.99 dependent: clear(print_new_demod).
% 1.75/1.99 dependent: clear(print_back_demod).
% 1.75/1.99 dependent: clear(print_back_sub).
% 1.75/1.99 dependent: set(control_memory).
% 1.75/1.99 dependent: assign(max_mem, 12000).
% 1.75/1.99 dependent: assign(pick_given_ratio, 4).
% 1.75/1.99 dependent: assign(stats_level, 1).
% 1.75/1.99 dependent: assign(max_seconds, 10800).
% 1.75/1.99 clear(print_given).
% 1.75/1.99
% 1.75/1.99 list(usable).
% 1.75/1.99 0 [] group_element(e_1).
% 1.75/1.99 0 [] group_element(e_2).
% 1.75/1.99 0 [] -e_qualish(e_1,e_2).
% 1.75/1.99 0 [] -e_qualish(e_2,e_1).
% 1.75/1.99 0 [] -group_element(X)| -group_element(Y)|product(X,Y,e_1)|product(X,Y,e_2).
% 1.75/1.99 0 [] -product(X,Y,W)| -product(X,Y,Z)|e_qualish(W,Z).
% 1.75/1.99 0 [] -product(X,W,Y)| -product(X,Z,Y)|e_qualish(W,Z).
% 1.75/1.99 0 [] -product(W,Y,X)| -product(Z,Y,X)|e_qualish(W,Z).
% 1.75/1.99 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(X1,X2).
% 1.75/1.99 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(Y1,Y2).
% 1.75/1.99 end_of_list.
% 1.75/1.99
% 1.75/1.99 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.75/1.99
% 1.75/1.99 This is a non-Horn set without equality. The strategy will
% 1.75/1.99 be ordered hyper_res, unit deletion, and factoring, with
% 1.75/1.99 satellites in sos and with nuclei in usable.
% 1.75/1.99
% 1.75/1.99 dependent: set(hyper_res).
% 1.75/1.99 dependent: set(factor).
% 1.75/1.99 dependent: set(unit_deletion).
% 1.75/1.99
% 1.75/1.99 ------------> process usable:
% 1.75/1.99 ** KEPT (pick-wt=3): 1 [] -e_qualish(e_1,e_2).
% 1.75/1.99 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_2,e_1).
% 1.75/1.99 ** KEPT (pick-wt=12): 3 [] -group_element(A)| -group_element(B)|product(A,B,e_1)|product(A,B,e_2).
% 1.75/1.99 ** KEPT (pick-wt=11): 4 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.75/1.99 ** KEPT (pick-wt=11): 5 [] -product(A,B,C)| -product(A,D,C)|e_qualish(B,D).
% 1.75/1.99 ** KEPT (pick-wt=11): 6 [] -product(A,B,C)| -product(D,B,C)|e_qualish(A,D).
% 1.75/1.99 ** KEPT (pick-wt=19): 7 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(A,D).
% 1.75/1.99 ** KEPT (pick-wt=19): 8 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(B,E).
% 1.75/1.99
% 1.75/1.99 ------------> process sos:
% 1.75/1.99 ** KEPT (pick-wt=2): 21 [] group_element(e_1).
% 1.75/1.99 ** KEPT (pick-wt=2): 22 [] group_element(e_2).
% 1.75/1.99
% 1.75/1.99 ======= end of input processing =======
% 1.75/1.99
% 1.75/1.99 =========== start of search ===========
% 1.75/1.99
% 1.75/1.99 -------- PROOF --------
% 1.75/1.99
% 1.75/1.99 ----> UNIT CONFLICT at 0.08 sec ----> 77 [binary,76.1,1.1] $F.
% 1.75/1.99
% 1.75/1.99 Length of proof is 13. Level of proof is 7.
% 1.75/1.99
% 1.75/1.99 ---------------- PROOF ----------------
% 1.75/1.99 % SZS status Unsatisfiable
% 1.75/1.99 % SZS output start Refutation
% See solution above
% 1.75/1.99 ------------ end of proof -------------
% 1.75/1.99
% 1.75/1.99
% 1.75/1.99 Search stopped by max_proofs option.
% 1.75/1.99
% 1.75/1.99
% 1.75/1.99 Search stopped by max_proofs option.
% 1.75/1.99
% 1.75/1.99 ============ end of search ============
% 1.75/1.99
% 1.75/1.99 -------------- statistics -------------
% 1.75/1.99 clauses given 33
% 1.75/1.99 clauses generated 3886
% 1.75/1.99 clauses kept 76
% 1.75/1.99 clauses forward subsumed 3820
% 1.75/1.99 clauses back subsumed 45
% 1.75/1.99 Kbytes malloced 976
% 1.75/1.99
% 1.75/1.99 ----------- times (seconds) -----------
% 1.75/1.99 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.75/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.99 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.75/1.99
% 1.75/1.99 That finishes the proof of the theorem.
% 1.75/1.99
% 1.75/1.99 Process 7712 finished Wed Jul 27 05:27:39 2022
% 1.75/1.99 Otter interrupted
% 1.75/1.99 PROOF FOUND
%------------------------------------------------------------------------------