TSTP Solution File: MGT023+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:06:02 EDT 2022
% Result : Theorem 1.80s 2.02s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 10 unt; 8 nHn; 21 RR)
% Number of literals : 48 ( 9 equ; 18 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,dollar_f1(A,B))
| B = critical_point(A) ),
file('MGT023+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| greater(dollar_f1(A,B),B)
| B = critical_point(A) ),
file('MGT023+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,dollar_f1(A,B)),growth_rate(first_movers,dollar_f1(A,B)))
| B = critical_point(A) ),
file('MGT023+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ environment(A)
| ~ stable(A)
| in_environment(A,dollar_f2(A)) ),
file('MGT023+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ greater(growth_rate(efficient_producers,dollar_f2(A)),growth_rate(first_movers,dollar_f2(A))) ),
file('MGT023+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater(B,dollar_f2(A))
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) ),
file('MGT023+1.p',unknown),
[] ).
cnf(7,axiom,
~ in_environment(dollar_c1,critical_point(dollar_c1)),
file('MGT023+1.p',unknown),
[] ).
cnf(9,axiom,
environment(dollar_c1),
file('MGT023+1.p',unknown),
[] ).
cnf(10,axiom,
stable(dollar_c1),
file('MGT023+1.p',unknown),
[] ).
cnf(14,plain,
in_environment(dollar_c1,dollar_f2(dollar_c1)),
inference(hyper,[status(thm)],[10,4,9]),
[iquote('hyper,10,4,9')] ).
cnf(18,plain,
( greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f1(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[14,2,9])]),
[iquote('hyper,14,2,9,flip.3')] ).
cnf(19,plain,
( greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f2(dollar_c1)))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[14,1,9])]),
[iquote('hyper,14,1,9,flip.3')] ).
cnf(185,plain,
( greater(dollar_f1(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(hyper,[status(thm)],[18,5,9,10]),
[iquote('hyper,18,5,9,10')] ).
cnf(213,plain,
greater(dollar_f1(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[185,7]),14]),
[iquote('para_from,185.2.1,7.1.2,unit_del,14')] ).
cnf(334,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f2(dollar_c1)))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(hyper,[status(thm)],[19,5,9,10]),
[iquote('hyper,19,5,9,10')] ).
cnf(367,plain,
subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f2(dollar_c1))),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[334,7]),14]),
[iquote('para_from,334.2.1,7.1.2,unit_del,14')] ).
cnf(368,plain,
greater(growth_rate(efficient_producers,dollar_f1(dollar_c1,dollar_f2(dollar_c1))),growth_rate(first_movers,dollar_f1(dollar_c1,dollar_f2(dollar_c1)))),
inference(hyper,[status(thm)],[367,6,9,10,213]),
[iquote('hyper,367,6,9,10,213')] ).
cnf(459,plain,
( greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[368,3,9,14])]),
[iquote('hyper,368,3,9,14,flip.2')] ).
cnf(491,plain,
critical_point(dollar_c1) = dollar_f2(dollar_c1),
inference(hyper,[status(thm)],[459,5,9,10]),
[iquote('hyper,459,5,9,10')] ).
cnf(492,plain,
~ in_environment(dollar_c1,dollar_f2(dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),491]),
[iquote('back_demod,7,demod,491')] ).
cnf(493,plain,
$false,
inference(binary,[status(thm)],[492,14]),
[iquote('binary,492.1,14.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n012.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 04:00:50 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 sandbox2 on n012.cluster.edu,
% 1.69/1.89 Wed Jul 27 04:00:50 2022
% 1.69/1.89 The command was "./otter". The process ID is 25776.
% 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 formula_list(usable).
% 1.69/1.89 all A (A=A).
% 1.69/1.89 all E To (environment(E)& -greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))&in_environment(E,To)& (all T (subpopulations(first_movers,efficient_producers,E,T)&greater(T,To)->greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))))->To=critical_point(E)).
% 1.69/1.89 all E (environment(E)&stable(E)-> (exists To (in_environment(E,To)& -greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))& (all T (subpopulations(first_movers,efficient_producers,E,T)&greater(T,To)->greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))))))).
% 1.69/1.89 -(all E (environment(E)&stable(E)->in_environment(E,critical_point(E)))).
% 1.69/1.89 end_of_list.
% 1.69/1.89
% 1.69/1.89 -------> usable clausifies to:
% 1.69/1.89
% 1.69/1.89 list(usable).
% 1.69/1.89 0 [] A=A.
% 1.69/1.89 0 [] -environment(E)|greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))| -in_environment(E,To)|subpopulations(first_movers,efficient_producers,E,$f1(E,To))|To=critical_point(E).
% 1.69/1.89 0 [] -environment(E)|greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))| -in_environment(E,To)|greater($f1(E,To),To)|To=critical_point(E).
% 1.69/1.89 0 [] -environment(E)|greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))| -in_environment(E,To)| -greater(growth_rate(efficient_producers,$f1(E,To)),growth_rate(first_movers,$f1(E,To)))|To=critical_point(E).
% 1.69/1.89 0 [] -environment(E)| -stable(E)|in_environment(E,$f2(E)).
% 1.69/1.89 0 [] -environment(E)| -stable(E)| -greater(growth_rate(efficient_producers,$f2(E)),growth_rate(first_movers,$f2(E))).
% 1.69/1.89 0 [] -environment(E)| -stable(E)| -subpopulations(first_movers,efficient_producers,E,T)| -greater(T,$f2(E))|greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)).
% 1.69/1.89 0 [] environment($c1).
% 1.69/1.89 0 [] stable($c1).
% 1.69/1.89 0 [] -in_environment($c1,critical_point($c1)).
% 1.69/1.89 end_of_list.
% 1.69/1.89
% 1.69/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.69/1.89
% 1.69/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.69/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.69/1.89 deletion, with positive clauses in sos and nonpositive
% 1.69/1.89 clauses in usable.
% 1.69/1.89
% 1.69/1.89 dependent: set(knuth_bendix).
% 1.69/1.89 dependent: set(anl_eq).
% 1.69/1.89 dependent: set(para_from).
% 1.69/1.89 dependent: set(para_into).
% 1.69/1.89 dependent: clear(para_from_right).
% 1.69/1.89 dependent: clear(para_into_right).
% 1.69/1.89 dependent: set(para_from_vars).
% 1.69/1.89 dependent: set(eq_units_both_ways).
% 1.69/1.89 dependent: set(dynamic_demod_all).
% 1.69/1.89 dependent: set(dynamic_demod).
% 1.69/1.89 dependent: set(order_eq).
% 1.69/1.89 dependent: set(back_demod).
% 1.69/1.89 dependent: set(lrpo).
% 1.69/1.89 dependent: set(hyper_res).
% 1.69/1.89 dependent: set(unit_deletion).
% 1.69/1.89 dependent: set(factor).
% 1.69/1.89
% 1.69/1.89 ------------> process usable:
% 1.69/1.89 ** KEPT (pick-wt=23): 1 [] -environment(A)|greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,$f1(A,B))|B=critical_point(A).
% 1.69/1.89 ** KEPT (pick-wt=21): 2 [] -environment(A)|greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))| -in_environment(A,B)|greater($f1(A,B),B)|B=critical_point(A).
% 1.69/1.89 ** KEPT (pick-wt=27): 3 [] -environment(A)|greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))| -in_environment(A,B)| -greater(growth_rate(efficient_producers,$f1(A,B)),growth_rate(first_movers,$f1(A,B)))|B=critical_point(A).
% 1.69/1.89 ** KEPT (pick-wt=8): 4 [] -environment(A)| -stable(A)|in_environment(A,$f2(A)).
% 1.69/1.89 ** KEPT (pick-wt=13): 5 [] -environment(A)| -stable(A)| -greater(growth_rate(efficient_producers,$f2(A)),growth_rate(first_movers,$f2(A))).
% 1.80/2.02 ** KEPT (pick-wt=20): 6 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater(B,$f2(A))|greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)).
% 1.80/2.02 ** KEPT (pick-wt=4): 7 [] -in_environment($c1,critical_point($c1)).
% 1.80/2.02
% 1.80/2.02 ------------> process sos:
% 1.80/2.02 ** KEPT (pick-wt=3): 8 [] A=A.
% 1.80/2.02 ** KEPT (pick-wt=2): 9 [] environment($c1).
% 1.80/2.02 ** KEPT (pick-wt=2): 10 [] stable($c1).
% 1.80/2.02 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.80/2.02
% 1.80/2.02 ======= end of input processing =======
% 1.80/2.02
% 1.80/2.02 =========== start of search ===========
% 1.80/2.02
% 1.80/2.02 -------- PROOF --------
% 1.80/2.02
% 1.80/2.02 ----> UNIT CONFLICT at 0.13 sec ----> 493 [binary,492.1,14.1] $F.
% 1.80/2.02
% 1.80/2.02 Length of proof is 11. Level of proof is 8.
% 1.80/2.02
% 1.80/2.02 ---------------- PROOF ----------------
% 1.80/2.02 % SZS status Theorem
% 1.80/2.02 % SZS output start Refutation
% See solution above
% 1.80/2.02 ------------ end of proof -------------
% 1.80/2.02
% 1.80/2.02
% 1.80/2.02 Search stopped by max_proofs option.
% 1.80/2.02
% 1.80/2.02
% 1.80/2.02 Search stopped by max_proofs option.
% 1.80/2.02
% 1.80/2.02 ============ end of search ============
% 1.80/2.02
% 1.80/2.02 -------------- statistics -------------
% 1.80/2.02 clauses given 18
% 1.80/2.02 clauses generated 631
% 1.80/2.02 clauses kept 491
% 1.80/2.02 clauses forward subsumed 153
% 1.80/2.02 clauses back subsumed 66
% 1.80/2.02 Kbytes malloced 1953
% 1.80/2.02
% 1.80/2.02 ----------- times (seconds) -----------
% 1.80/2.02 user CPU time 0.13 (0 hr, 0 min, 0 sec)
% 1.80/2.02 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/2.02 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.80/2.02
% 1.80/2.02 That finishes the proof of the theorem.
% 1.80/2.02
% 1.80/2.02 Process 25776 finished Wed Jul 27 04:00:52 2022
% 1.80/2.02 Otter interrupted
% 1.80/2.02 PROOF FOUND
%------------------------------------------------------------------------------