TSTP Solution File: GRP124-2.004 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP124-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 1.69s 1.92s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of clauses : 36 ( 17 unt; 14 nHn; 35 RR)
% Number of literals : 79 ( 0 equ; 22 neg)
% Maximal clause size : 6 ( 2 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 : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,e_1,B)
| ~ next(A,C)
| ~ greater(B,C) ),
file('GRP124-2.004.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_2),
file('GRP124-2.004.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_1,e_3),
file('GRP124-2.004.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_2,e_1),
file('GRP124-2.004.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_2,e_3),
file('GRP124-2.004.p',unknown),
[] ).
cnf(8,axiom,
~ e_qualish(e_3,e_1),
file('GRP124-2.004.p',unknown),
[] ).
cnf(9,axiom,
~ e_qualish(e_3,e_2),
file('GRP124-2.004.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('GRP124-2.004.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| e_qualish(B,D) ),
file('GRP124-2.004.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(A,B,C)
| ~ product(D,B,C)
| e_qualish(A,D) ),
file('GRP124-2.004.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| e_qualish(B,E) ),
file('GRP124-2.004.p',unknown),
[] ).
cnf(31,plain,
( ~ product(A,B,C)
| ~ product(C,C,C)
| ~ product(C,A,B)
| e_qualish(B,C) ),
inference(factor,[status(thm)],[19]),
[iquote('factor,19.2.4')] ).
cnf(33,axiom,
next(e_2,e_3),
file('GRP124-2.004.p',unknown),
[] ).
cnf(40,axiom,
greater(e_4,e_3),
file('GRP124-2.004.p',unknown),
[] ).
cnf(41,axiom,
group_element(e_1),
file('GRP124-2.004.p',unknown),
[] ).
cnf(42,axiom,
group_element(e_2),
file('GRP124-2.004.p',unknown),
[] ).
cnf(43,axiom,
group_element(e_3),
file('GRP124-2.004.p',unknown),
[] ).
cnf(45,axiom,
product(A,A,A),
file('GRP124-2.004.p',unknown),
[] ).
cnf(46,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)],[42,14,41]),
[iquote('hyper,42,14,41')] ).
cnf(47,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)],[42,14,41]),
[iquote('hyper,42,14,41')] ).
cnf(48,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(hyper,[status(thm)],[43,14,42]),
[iquote('hyper,43,14,42')] ).
cnf(49,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)],[43,14,41]),
[iquote('hyper,43,14,41')] ).
cnf(59,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)],[46,16,45]),2]),
[iquote('hyper,46,16,45,unit_del,2')] ).
cnf(61,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[59,17,45]),5]),
[iquote('hyper,59,17,45,unit_del,5')] ).
cnf(62,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)],[47,17,45]),2]),
[iquote('hyper,47,17,45,unit_del,2')] ).
cnf(65,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[62,16,45]),5]),
[iquote('hyper,62,16,45,unit_del,5')] ).
cnf(68,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[48,16,45]),6]),
[iquote('hyper,48,16,45,unit_del,6')] ).
cnf(70,plain,
product(e_2,e_1,e_3),
inference(hyper,[status(thm)],[65,1,33,40]),
[iquote('hyper,65,1,33,40')] ).
cnf(72,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[68,17,45]),9]),
[iquote('hyper,68,17,45,unit_del,9')] ).
cnf(73,plain,
( product(e_2,e_3,e_4)
| product(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[72,31,45,61]),8]),
[iquote('hyper,72,31,45,61,unit_del,8')] ).
cnf(75,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)],[49,16,45]),3]),
[iquote('hyper,49,16,45,unit_del,3')] ).
cnf(80,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[75,31,45,70]),9]),
[iquote('hyper,75,31,45,70,unit_del,9')] ).
cnf(86,plain,
product(e_1,e_3,e_4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[80,17,45]),8]),
[iquote('hyper,80,17,45,unit_del,8')] ).
cnf(91,plain,
product(e_1,e_2,e_4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[86,17,73]),5]),
[iquote('hyper,86,17,73,unit_del,5')] ).
cnf(98,plain,
e_qualish(e_3,e_2),
inference(hyper,[status(thm)],[91,16,86]),
[iquote('hyper,91,16,86')] ).
cnf(99,plain,
$false,
inference(binary,[status(thm)],[98,9]),
[iquote('binary,98.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP124-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n017.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 04:47:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.69/1.89 ----- Otter 3.3f, August 2004 -----
% 1.69/1.89 The process was started by sandbox on n017.cluster.edu,
% 1.69/1.89 Wed Jul 27 04:47:33 2022
% 1.69/1.89 The command was "./otter". The process ID is 6263.
% 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(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(X1,X2).
% 1.69/1.89 0 [] -product(X1,Y1,Z1)| -product(X2,Y2,Z1)| -product(Z2,X1,Y1)| -product(Z2,X2,Y2)|e_qualish(Y1,Y2).
% 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=19): 18 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(A,D).
% 1.69/1.89 ** KEPT (pick-wt=19): 19 [] -product(A,B,C)| -product(D,E,C)| -product(F,A,B)| -product(F,D,E)|e_qualish(B,E).
% 1.69/1.89
% 1.69/1.89 ------------> process sos:
% 1.69/1.89 ** KEPT (pick-wt=3): 32 [] next(e_1,e_2).
% 1.69/1.89 ** KEPT (pick-wt=3): 33 [] next(e_2,e_3).
% 1.69/1.89 ** KEPT (pick-wt=3): 34 [] next(e_3,e_4).
% 1.69/1.89 ** KEPT (pick-wt=3): 35 [] greater(e_2,e_1).
% 1.69/1.89 ** KEPT (pick-wt=3): 36 [] greater(e_3,e_1).
% 1.69/1.89 ** KEPT (pick-wt=3): 37 [] greater(e_4,e_1).
% 1.69/1.89 ** KEPT (pick-wt=3): 38 [] greater(e_3,e_2).
% 1.69/1.89 ** KEPT (pick-wt=3): 39 [] greater(e_4,e_2).
% 1.69/1.89 ** KEPT (pick-wt=3): 40 [] greater(e_4,e_3).
% 1.69/1.89 ** KEPT (pick-wt=2): 41 [] group_element(e_1).
% 1.69/1.89 ** KEPT (pick-wt=2): 42 [] group_element(e_2).
% 1.69/1.89 ** KEPT (pick-wt=2): 43 [] group_element(e_3).
% 1.69/1.89 ** KEPT (pick-wt=2): 44 [] group_element(e_4).
% 1.69/1.89 ** KEPT (pick-wt=4): 45 [] product(A,A,A).
% 1.69/1.89
% 1.69/1.89 ======= end of input processing =======
% 1.69/1.92
% 1.69/1.92 =========== start of search ===========
% 1.69/1.92
% 1.69/1.92 -------- PROOF --------
% 1.69/1.92
% 1.69/1.92 ----> UNIT CONFLICT at 0.03 sec ----> 99 [binary,98.1,9.1] $F.
% 1.69/1.92
% 1.69/1.92 Length of proof is 18. Level of proof is 8.
% 1.69/1.92
% 1.69/1.92 ---------------- PROOF ----------------
% 1.69/1.92 % SZS status Unsatisfiable
% 1.69/1.92 % SZS output start Refutation
% See solution above
% 1.74/1.92 ------------ end of proof -------------
% 1.74/1.92
% 1.74/1.92
% 1.74/1.92 Search stopped by max_proofs option.
% 1.74/1.92
% 1.74/1.92
% 1.74/1.92 Search stopped by max_proofs option.
% 1.74/1.92
% 1.74/1.92 ============ end of search ============
% 1.74/1.92
% 1.74/1.92 -------------- statistics -------------
% 1.74/1.92 clauses given 32
% 1.74/1.92 clauses generated 832
% 1.74/1.92 clauses kept 98
% 1.74/1.92 clauses forward subsumed 767
% 1.74/1.92 clauses back subsumed 38
% 1.74/1.92 Kbytes malloced 976
% 1.74/1.92
% 1.74/1.92 ----------- times (seconds) -----------
% 1.74/1.92 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.74/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.92
% 1.74/1.92 That finishes the proof of the theorem.
% 1.74/1.92
% 1.74/1.92 Process 6263 finished Wed Jul 27 04:47:34 2022
% 1.74/1.92 Otter interrupted
% 1.74/1.92 PROOF FOUND
%------------------------------------------------------------------------------