TSTP Solution File: MGT028-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 13:06:04 EDT 2022
% Result : Unsatisfiable 1.69s 1.89s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 28 ( 9 unt; 12 nHn; 28 RR)
% Number of literals : 75 ( 0 equ; 36 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| greater(sk2(A),appear(efficient_producers,A)) ),
file('MGT028-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| greater_or_e_qual(sk1(B,A),B)
| greater(sk2(A),appear(efficient_producers,A)) ),
file('MGT028-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater_or_e_qual(C,sk2(A))
| greater(zero,growth_rate(first_movers,C)) ),
file('MGT028-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| greater_or_e_qual(sk1(B,A),B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater_or_e_qual(C,sk2(A))
| greater(zero,growth_rate(first_movers,C)) ),
file('MGT028-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| greater(sk2(A),appear(efficient_producers,A)) ),
file('MGT028-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater_or_e_qual(C,sk2(A))
| greater(zero,growth_rate(first_movers,C)) ),
file('MGT028-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ environment(A)
| ~ stable(A)
| in_environment(A,sk3(A)) ),
file('MGT028-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_e_qual(B,sk3(A))
| greater(zero,growth_rate(first_movers,B)) ),
file('MGT028-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ greater(A,appear(efficient_producers,sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk5(A)) ),
file('MGT028-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ greater(A,appear(efficient_producers,sk4))
| greater_or_e_qual(sk5(A),A) ),
file('MGT028-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ greater(A,appear(efficient_producers,sk4))
| ~ greater(zero,growth_rate(first_movers,sk5(A))) ),
file('MGT028-1.p',unknown),
[] ).
cnf(13,axiom,
environment(sk4),
file('MGT028-1.p',unknown),
[] ).
cnf(14,axiom,
stable(sk4),
file('MGT028-1.p',unknown),
[] ).
cnf(15,plain,
in_environment(sk4,sk3(sk4)),
inference(hyper,[status(thm)],[14,7,13]),
[iquote('hyper,14,7,13')] ).
cnf(16,plain,
( greater_or_e_qual(sk1(sk3(sk4),sk4),sk3(sk4))
| greater(sk2(sk4),appear(efficient_producers,sk4)) ),
inference(hyper,[status(thm)],[15,2,13,14]),
[iquote('hyper,15,2,13,14')] ).
cnf(17,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(sk2(sk4),appear(efficient_producers,sk4)) ),
inference(hyper,[status(thm)],[15,1,13,14]),
[iquote('hyper,15,1,13,14')] ).
cnf(18,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater_or_e_qual(sk5(sk2(sk4)),sk2(sk4)) ),
inference(hyper,[status(thm)],[17,11]),
[iquote('hyper,17,11')] ).
cnf(19,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(hyper,[status(thm)],[17,10]),
[iquote('hyper,17,10')] ).
cnf(23,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[19,3,13,14,15,18])])]),
[iquote('hyper,19,3,13,14,15,18,factor_simp,factor_simp')] ).
cnf(24,plain,
subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[23,12,17])]),
[iquote('hyper,23,12,17,factor_simp')] ).
cnf(25,plain,
( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(sk2(sk4),appear(efficient_producers,sk4)) ),
inference(hyper,[status(thm)],[24,9,13,14,16]),
[iquote('hyper,24,9,13,14,16')] ).
cnf(27,plain,
greater(sk2(sk4),appear(efficient_producers,sk4)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[25,5,13,14,15])]),
[iquote('hyper,25,5,13,14,15,factor_simp')] ).
cnf(30,plain,
greater_or_e_qual(sk5(sk2(sk4)),sk2(sk4)),
inference(hyper,[status(thm)],[27,11]),
[iquote('hyper,27,11')] ).
cnf(31,plain,
subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
inference(hyper,[status(thm)],[27,10]),
[iquote('hyper,27,10')] ).
cnf(32,plain,
( greater_or_e_qual(sk1(sk3(sk4),sk4),sk3(sk4))
| greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(hyper,[status(thm)],[31,4,13,14,15,30]),
[iquote('hyper,31,4,13,14,15,30')] ).
cnf(33,plain,
( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
| greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(hyper,[status(thm)],[32,9,13,14,24]),
[iquote('hyper,32,9,13,14,24')] ).
cnf(36,plain,
greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[33,6,13,14,15,31,30])]),
[iquote('hyper,33,6,13,14,15,31,30,factor_simp')] ).
cnf(37,plain,
$false,
inference(hyper,[status(thm)],[36,12,27]),
[iquote('hyper,36,12,27')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n010.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 03:54:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.89 ----- Otter 3.3f, August 2004 -----
% 1.69/1.89 The process was started by sandbox on n010.cluster.edu,
% 1.69/1.89 Wed Jul 27 03:54:40 2022
% 1.69/1.89 The command was "./otter". The process ID is 22900.
% 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 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,sk1(B,A))|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89 0 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual(sk1(B,A),B)|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89 0 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,sk1(B,A))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89 0 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual(sk1(B,A),B)| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89 0 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,sk1(B,A)))|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89 0 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,sk1(B,A)))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89 0 [] -environment(A)| -stable(A)|in_environment(A,sk3(A)).
% 1.69/1.89 0 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,sk3(A))|greater(growth_rate(efficient_producers,B),zero).
% 1.69/1.89 0 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,sk3(A))|greater(zero,growth_rate(first_movers,B)).
% 1.69/1.89 0 [] environment(sk4).
% 1.69/1.89 0 [] stable(sk4).
% 1.69/1.89 0 [] -greater(A,appear(efficient_producers,sk4))|subpopulations(first_movers,efficient_producers,sk4,sk5(A)).
% 1.69/1.89 0 [] -greater(A,appear(efficient_producers,sk4))|greater_or_e_qual(sk5(A),A).
% 1.69/1.89 0 [] -greater(A,appear(efficient_producers,sk4))| -greater(zero,growth_rate(first_movers,sk5(A))).
% 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=7.
% 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=20): 1 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,sk1(B,A))|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89 ** KEPT (pick-wt=18): 2 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual(sk1(B,A),B)|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89 ** KEPT (pick-wt=28): 3 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,sk1(B,A))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89 ** KEPT (pick-wt=26): 4 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual(sk1(B,A),B)| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89 ** KEPT (pick-wt=20): 5 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,sk1(B,A)))|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89 ** KEPT (pick-wt=28): 6 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,sk1(B,A)))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89 ** KEPT (pick-wt=8): 7 [] -environment(A)| -stable(A)|in_environment(A,sk3(A)).
% 1.69/1.89 ** KEPT (pick-wt=18): 8 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,sk3(A))|greater(growth_rate(efficient_producers,B),zero).
% 1.69/1.89 ** KEPT (pick-wt=18): 9 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,sk3(A))|greater(zero,growth_rate(first_movers,B)).
% 1.69/1.89 ** KEPT (pick-wt=11): 10 [] -greater(A,appear(efficient_producers,sk4))|subpopulations(first_movers,efficient_producers,sk4,sk5(A)).
% 1.69/1.89 ** KEPT (pick-wt=9): 11 [] -greater(A,appear(efficient_producers,sk4))|greater_or_e_qual(sk5(A),A).
% 1.69/1.89 ** KEPT (pick-wt=11): 12 [] -greater(A,appear(efficient_producers,sk4))| -greater(zero,growth_rate(first_movers,sk5(A))).
% 1.69/1.89
% 1.69/1.89 ------------> process sos:
% 1.69/1.89 ** KEPT (pick-wt=2): 13 [] environment(sk4).
% 1.69/1.89 ** KEPT (pick-wt=2): 14 [] stable(sk4).
% 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 -----> EMPTY CLAUSE at 0.00 sec ----> 37 [hyper,36,12,27] $F.
% 1.69/1.89
% 1.69/1.89 Length of proof is 14. Level of proof is 11.
% 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 17
% 1.69/1.89 clauses generated 27
% 1.69/1.89 clauses kept 36
% 1.69/1.89 clauses forward subsumed 4
% 1.69/1.89 clauses back subsumed 15
% 1.69/1.89 Kbytes malloced 976
% 1.69/1.89
% 1.69/1.89 ----------- times (seconds) -----------
% 1.69/1.89 user CPU time 0.00 (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 22900 finished Wed Jul 27 03:54:41 2022
% 1.69/1.89 Otter interrupted
% 1.69/1.89 PROOF FOUND
%------------------------------------------------------------------------------