TSTP Solution File: MGT028+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 : Theorem 1.75s 1.94s
% Output : Refutation 1.75s
% 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,dollar_f1(A,B))
| greater(dollar_f2(A),appear(efficient_producers,A)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,dollar_f1(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater_or_e_qual(C,dollar_f2(A))
| greater(zero,growth_rate(first_movers,C)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| greater_or_e_qual(dollar_f1(A,B),B)
| greater(dollar_f2(A),appear(efficient_producers,A)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ in_environment(A,B)
| greater_or_e_qual(dollar_f1(A,B),B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater_or_e_qual(C,dollar_f2(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,dollar_f1(A,B)))
| greater(dollar_f2(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,dollar_f1(A,B)))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater_or_e_qual(C,dollar_f2(A))
| greater(zero,growth_rate(first_movers,C)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ environment(A)
| ~ stable(A)
| in_environment(A,dollar_f3(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,dollar_f3(A))
| greater(zero,growth_rate(first_movers,B)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ greater(A,appear(efficient_producers,dollar_c1))
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f4(A)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ greater(A,appear(efficient_producers,dollar_c1))
| greater_or_e_qual(dollar_f4(A),A) ),
file('MGT028+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ greater(A,appear(efficient_producers,dollar_c1))
| ~ greater(zero,growth_rate(first_movers,dollar_f4(A))) ),
file('MGT028+1.p',unknown),
[] ).
cnf(13,axiom,
environment(dollar_c1),
file('MGT028+1.p',unknown),
[] ).
cnf(14,axiom,
stable(dollar_c1),
file('MGT028+1.p',unknown),
[] ).
cnf(15,plain,
in_environment(dollar_c1,dollar_f3(dollar_c1)),
inference(hyper,[status(thm)],[14,7,13]),
[iquote('hyper,14,7,13')] ).
cnf(16,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f3(dollar_c1)),dollar_f3(dollar_c1))
| greater(dollar_f2(dollar_c1),appear(efficient_producers,dollar_c1)) ),
inference(hyper,[status(thm)],[15,3,13,14]),
[iquote('hyper,15,3,13,14')] ).
cnf(17,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f3(dollar_c1)))
| greater(dollar_f2(dollar_c1),appear(efficient_producers,dollar_c1)) ),
inference(hyper,[status(thm)],[15,1,13,14]),
[iquote('hyper,15,1,13,14')] ).
cnf(18,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f3(dollar_c1)))
| greater_or_e_qual(dollar_f4(dollar_f2(dollar_c1)),dollar_f2(dollar_c1)) ),
inference(hyper,[status(thm)],[17,11]),
[iquote('hyper,17,11')] ).
cnf(19,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f3(dollar_c1)))
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f4(dollar_f2(dollar_c1))) ),
inference(hyper,[status(thm)],[17,10]),
[iquote('hyper,17,10')] ).
cnf(23,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f3(dollar_c1)))
| greater(zero,growth_rate(first_movers,dollar_f4(dollar_f2(dollar_c1)))) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[19,2,13,14,15,18])])]),
[iquote('hyper,19,2,13,14,15,18,factor_simp,factor_simp')] ).
cnf(24,plain,
subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f3(dollar_c1))),
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,dollar_f1(dollar_c1,dollar_f3(dollar_c1))))
| greater(dollar_f2(dollar_c1),appear(efficient_producers,dollar_c1)) ),
inference(hyper,[status(thm)],[24,9,13,14,16]),
[iquote('hyper,24,9,13,14,16')] ).
cnf(27,plain,
greater(dollar_f2(dollar_c1),appear(efficient_producers,dollar_c1)),
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(dollar_f4(dollar_f2(dollar_c1)),dollar_f2(dollar_c1)),
inference(hyper,[status(thm)],[27,11]),
[iquote('hyper,27,11')] ).
cnf(31,plain,
subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f4(dollar_f2(dollar_c1))),
inference(hyper,[status(thm)],[27,10]),
[iquote('hyper,27,10')] ).
cnf(32,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f3(dollar_c1)),dollar_f3(dollar_c1))
| greater(zero,growth_rate(first_movers,dollar_f4(dollar_f2(dollar_c1)))) ),
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,dollar_f4(dollar_f2(dollar_c1))))
| greater(zero,growth_rate(first_movers,dollar_f1(dollar_c1,dollar_f3(dollar_c1)))) ),
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,dollar_f4(dollar_f2(dollar_c1)))),
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
% 0.10/0.12 % Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 04:04:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.75/1.93 ----- Otter 3.3f, August 2004 -----
% 1.75/1.93 The process was started by sandbox on n018.cluster.edu,
% 1.75/1.93 Wed Jul 27 04:04:46 2022
% 1.75/1.93 The command was "./otter". The process ID is 15598.
% 1.75/1.93
% 1.75/1.93 set(prolog_style_variables).
% 1.75/1.93 set(auto).
% 1.75/1.93 dependent: set(auto1).
% 1.75/1.93 dependent: set(process_input).
% 1.75/1.93 dependent: clear(print_kept).
% 1.75/1.93 dependent: clear(print_new_demod).
% 1.75/1.93 dependent: clear(print_back_demod).
% 1.75/1.93 dependent: clear(print_back_sub).
% 1.75/1.93 dependent: set(control_memory).
% 1.75/1.93 dependent: assign(max_mem, 12000).
% 1.75/1.93 dependent: assign(pick_given_ratio, 4).
% 1.75/1.93 dependent: assign(stats_level, 1).
% 1.75/1.93 dependent: assign(max_seconds, 10800).
% 1.75/1.93 clear(print_given).
% 1.75/1.93
% 1.75/1.93 formula_list(usable).
% 1.75/1.93 all E (environment(E)&stable(E)& (exists T1 (in_environment(E,T1)& (all T (subpopulations(first_movers,efficient_producers,E,T)&greater_or_e_qual(T,T1)->greater(zero,growth_rate(first_movers,T))))))-> (exists T2 (greater(T2,appear(efficient_producers,E))& (all T (subpopulations(first_movers,efficient_producers,E,T)&greater_or_e_qual(T,T2)->greater(zero,growth_rate(first_movers,T))))))).
% 1.75/1.93 all E (environment(E)&stable(E)-> (exists To (in_environment(E,To)& (all T (subpopulations(first_movers,efficient_producers,E,T)&greater_or_e_qual(T,To)->greater(growth_rate(efficient_producers,T),zero)&greater(zero,growth_rate(first_movers,T))))))).
% 1.75/1.93 -(all E (environment(E)&stable(E)-> (exists To (greater(To,appear(efficient_producers,E))& (all T (subpopulations(first_movers,efficient_producers,E,T)&greater_or_e_qual(T,To)->greater(zero,growth_rate(first_movers,T)))))))).
% 1.75/1.93 end_of_list.
% 1.75/1.93
% 1.75/1.93 -------> usable clausifies to:
% 1.75/1.93
% 1.75/1.93 list(usable).
% 1.75/1.93 0 [] -environment(E)| -stable(E)| -in_environment(E,T1)|subpopulations(first_movers,efficient_producers,E,$f1(E,T1))|greater($f2(E),appear(efficient_producers,E)).
% 1.75/1.93 0 [] -environment(E)| -stable(E)| -in_environment(E,T1)|subpopulations(first_movers,efficient_producers,E,$f1(E,T1))| -subpopulations(first_movers,efficient_producers,E,T)| -greater_or_e_qual(T,$f2(E))|greater(zero,growth_rate(first_movers,T)).
% 1.75/1.93 0 [] -environment(E)| -stable(E)| -in_environment(E,T1)|greater_or_e_qual($f1(E,T1),T1)|greater($f2(E),appear(efficient_producers,E)).
% 1.75/1.93 0 [] -environment(E)| -stable(E)| -in_environment(E,T1)|greater_or_e_qual($f1(E,T1),T1)| -subpopulations(first_movers,efficient_producers,E,T)| -greater_or_e_qual(T,$f2(E))|greater(zero,growth_rate(first_movers,T)).
% 1.75/1.93 0 [] -environment(E)| -stable(E)| -in_environment(E,T1)| -greater(zero,growth_rate(first_movers,$f1(E,T1)))|greater($f2(E),appear(efficient_producers,E)).
% 1.75/1.93 0 [] -environment(E)| -stable(E)| -in_environment(E,T1)| -greater(zero,growth_rate(first_movers,$f1(E,T1)))| -subpopulations(first_movers,efficient_producers,E,T)| -greater_or_e_qual(T,$f2(E))|greater(zero,growth_rate(first_movers,T)).
% 1.75/1.93 0 [] -environment(E)| -stable(E)|in_environment(E,$f3(E)).
% 1.75/1.93 0 [] -environment(E)| -stable(E)| -subpopulations(first_movers,efficient_producers,E,T)| -greater_or_e_qual(T,$f3(E))|greater(growth_rate(efficient_producers,T),zero).
% 1.75/1.93 0 [] -environment(E)| -stable(E)| -subpopulations(first_movers,efficient_producers,E,T)| -greater_or_e_qual(T,$f3(E))|greater(zero,growth_rate(first_movers,T)).
% 1.75/1.93 0 [] environment($c1).
% 1.75/1.93 0 [] stable($c1).
% 1.75/1.93 0 [] -greater(To,appear(efficient_producers,$c1))|subpopulations(first_movers,efficient_producers,$c1,$f4(To)).
% 1.75/1.93 0 [] -greater(To,appear(efficient_producers,$c1))|greater_or_e_qual($f4(To),To).
% 1.75/1.93 0 [] -greater(To,appear(efficient_producers,$c1))| -greater(zero,growth_rate(first_movers,$f4(To))).
% 1.75/1.93 end_of_list.
% 1.75/1.93
% 1.75/1.93 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=7.
% 1.75/1.93
% 1.75/1.93 This is a non-Horn set without equality. The strategy will
% 1.75/1.93 be ordered hyper_res, unit deletion, and factoring, with
% 1.75/1.93 satellites in sos and with nuclei in usable.
% 1.75/1.93
% 1.75/1.93 dependent: set(hyper_res).
% 1.75/1.93 dependent: set(factor).
% 1.75/1.93 dependent: set(unit_deletion).
% 1.75/1.93
% 1.75/1.93 ------------> process usable:
% 1.75/1.93 ** KEPT (pick-wt=20): 1 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,$f1(A,B))|greater($f2(A),appear(efficient_producers,A)).
% 1.75/1.93 ** KEPT (pick-wt=28): 2 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,$f1(A,B))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,$f2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.75/1.94 ** KEPT (pick-wt=18): 3 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual($f1(A,B),B)|greater($f2(A),appear(efficient_producers,A)).
% 1.75/1.94 ** KEPT (pick-wt=26): 4 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual($f1(A,B),B)| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,$f2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.75/1.94 ** KEPT (pick-wt=20): 5 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,$f1(A,B)))|greater($f2(A),appear(efficient_producers,A)).
% 1.75/1.94 ** KEPT (pick-wt=28): 6 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,$f1(A,B)))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,$f2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.75/1.94 ** KEPT (pick-wt=8): 7 [] -environment(A)| -stable(A)|in_environment(A,$f3(A)).
% 1.75/1.94 ** KEPT (pick-wt=18): 8 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,$f3(A))|greater(growth_rate(efficient_producers,B),zero).
% 1.75/1.94 ** KEPT (pick-wt=18): 9 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,$f3(A))|greater(zero,growth_rate(first_movers,B)).
% 1.75/1.94 ** KEPT (pick-wt=11): 10 [] -greater(A,appear(efficient_producers,$c1))|subpopulations(first_movers,efficient_producers,$c1,$f4(A)).
% 1.75/1.94 ** KEPT (pick-wt=9): 11 [] -greater(A,appear(efficient_producers,$c1))|greater_or_e_qual($f4(A),A).
% 1.75/1.94 ** KEPT (pick-wt=11): 12 [] -greater(A,appear(efficient_producers,$c1))| -greater(zero,growth_rate(first_movers,$f4(A))).
% 1.75/1.94
% 1.75/1.94 ------------> process sos:
% 1.75/1.94 ** KEPT (pick-wt=2): 13 [] environment($c1).
% 1.75/1.94 ** KEPT (pick-wt=2): 14 [] stable($c1).
% 1.75/1.94
% 1.75/1.94 ======= end of input processing =======
% 1.75/1.94
% 1.75/1.94 =========== start of search ===========
% 1.75/1.94
% 1.75/1.94 -------- PROOF --------
% 1.75/1.94
% 1.75/1.94 -----> EMPTY CLAUSE at 0.00 sec ----> 37 [hyper,36,12,27] $F.
% 1.75/1.94
% 1.75/1.94 Length of proof is 14. Level of proof is 11.
% 1.75/1.94
% 1.75/1.94 ---------------- PROOF ----------------
% 1.75/1.94 % SZS status Theorem
% 1.75/1.94 % SZS output start Refutation
% See solution above
% 1.75/1.94 ------------ end of proof -------------
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Search stopped by max_proofs option.
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Search stopped by max_proofs option.
% 1.75/1.94
% 1.75/1.94 ============ end of search ============
% 1.75/1.94
% 1.75/1.94 -------------- statistics -------------
% 1.75/1.94 clauses given 17
% 1.75/1.94 clauses generated 27
% 1.75/1.94 clauses kept 36
% 1.75/1.94 clauses forward subsumed 4
% 1.75/1.94 clauses back subsumed 15
% 1.75/1.94 Kbytes malloced 976
% 1.75/1.94
% 1.75/1.94 ----------- times (seconds) -----------
% 1.75/1.94 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.94
% 1.75/1.94 That finishes the proof of the theorem.
% 1.75/1.94
% 1.75/1.94 Process 15598 finished Wed Jul 27 04:04:47 2022
% 1.75/1.94 Otter interrupted
% 1.75/1.94 PROOF FOUND
%------------------------------------------------------------------------------