TSTP Solution File: MGT023+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT023+2 : 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 13:06:03 EDT 2022
% Result : Theorem 3.35s 3.62s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 17
% Syntax : Number of clauses : 70 ( 12 unt; 48 nHn; 70 RR)
% Number of literals : 202 ( 13 equ; 60 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,dollar_f1(A,B))
| in_environment(A,dollar_f2(A)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,dollar_f1(A,B))
| ~ greater(growth_rate(efficient_producers,dollar_f2(A)),growth_rate(first_movers,dollar_f2(A))) ),
file('MGT023+2.p',unknown),
[] ).
cnf(3,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,dollar_f1(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(C,dollar_f2(A))
| greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| greater_or_e_qual(dollar_f1(A,B),B)
| in_environment(A,dollar_f2(A)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| greater_or_e_qual(dollar_f1(A,B),B)
| ~ greater(growth_rate(efficient_producers,dollar_f2(A)),growth_rate(first_movers,dollar_f2(A))) ),
file('MGT023+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| greater_or_e_qual(dollar_f1(A,B),B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(C,dollar_f2(A))
| greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,dollar_f1(A,B)),growth_rate(first_movers,dollar_f1(A,B)))
| in_environment(A,dollar_f2(A)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,dollar_f1(A,B)),growth_rate(first_movers,dollar_f1(A,B)))
| ~ greater(growth_rate(efficient_producers,dollar_f2(A)),growth_rate(first_movers,dollar_f2(A))) ),
file('MGT023+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,dollar_f1(A,B)),growth_rate(first_movers,dollar_f1(A,B)))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(C,dollar_f2(A))
| greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(10,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_f3(A,B))
| B = critical_point(A) ),
file('MGT023+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| greater(dollar_f3(A,B),B)
| B = critical_point(A) ),
file('MGT023+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,dollar_f3(A,B)),growth_rate(first_movers,dollar_f3(A,B)))
| B = critical_point(A) ),
file('MGT023+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ environment(A)
| ~ stable(A)
| in_environment(A,dollar_f4(A)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(14,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_e_qual(B,dollar_f4(A))
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(15,axiom,
~ in_environment(dollar_c1,critical_point(dollar_c1)),
file('MGT023+2.p',unknown),
[] ).
cnf(17,axiom,
environment(dollar_c1),
file('MGT023+2.p',unknown),
[] ).
cnf(18,axiom,
stable(dollar_c1),
file('MGT023+2.p',unknown),
[] ).
cnf(22,plain,
in_environment(dollar_c1,dollar_f4(dollar_c1)),
inference(hyper,[status(thm)],[18,13,17]),
[iquote('hyper,18,13,17')] ).
cnf(28,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| in_environment(dollar_c1,dollar_f2(dollar_c1)) ),
inference(hyper,[status(thm)],[22,4,17]),
[iquote('hyper,22,4,17')] ).
cnf(29,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| in_environment(dollar_c1,dollar_f2(dollar_c1)) ),
inference(hyper,[status(thm)],[22,1,17]),
[iquote('hyper,22,1,17')] ).
cnf(39,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f3(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)],[28,11,17])]),
[iquote('hyper,28,11,17,flip.4')] ).
cnf(40,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| 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_f3(dollar_c1,dollar_f2(dollar_c1)))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[28,10,17])]),
[iquote('hyper,28,10,17,flip.4')] ).
cnf(65,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| in_environment(dollar_c1,critical_point(A))
| ~ environment(A)
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| ~ in_environment(A,dollar_f2(dollar_c1))
| ~ greater(growth_rate(efficient_producers,dollar_f3(A,dollar_f2(dollar_c1))),growth_rate(first_movers,dollar_f3(A,dollar_f2(dollar_c1)))) ),
inference(para_into,[status(thm),theory(equality)],[28,12]),
[iquote('para_into,28.2.2,12.5.1')] ).
cnf(140,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f3(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)],[29,11,17])]),
[iquote('hyper,29,11,17,flip.4')] ).
cnf(141,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| 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_f3(dollar_c1,dollar_f2(dollar_c1)))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[29,10,17])]),
[iquote('hyper,29,10,17,flip.4')] ).
cnf(1320,plain,
( ~ in_environment(dollar_c1,dollar_f2(dollar_c1))
| greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1)) ),
inference(para_from,[status(thm),theory(equality)],[39,15]),
[iquote('para_from,39.4.1,15.1.2')] ).
cnf(1322,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1320,28])]),
[iquote('hyper,1320,28,factor_simp')] ).
cnf(1456,plain,
( ~ in_environment(dollar_c1,dollar_f2(dollar_c1))
| greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| 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_f3(dollar_c1,dollar_f2(dollar_c1))) ),
inference(para_from,[status(thm),theory(equality)],[40,15]),
[iquote('para_from,40.4.1,15.1.2')] ).
cnf(1560,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| 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_f3(dollar_c1,dollar_f2(dollar_c1))) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1456,28])]),
[iquote('hyper,1456,28,factor_simp')] ).
cnf(2129,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[140,2,17,22])]),
[iquote('hyper,140,2,17,22,factor_simp')] ).
cnf(2280,plain,
( ~ in_environment(dollar_c1,dollar_f2(dollar_c1))
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1)) ),
inference(para_from,[status(thm),theory(equality)],[2129,15]),
[iquote('para_from,2129.3.1,15.1.2')] ).
cnf(2281,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2280,29])]),
[iquote('hyper,2280,29,factor_simp')] ).
cnf(2618,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[141,2,17,22])]),
[iquote('hyper,141,2,17,22,factor_simp')] ).
cnf(2621,plain,
( ~ in_environment(dollar_c1,dollar_f2(dollar_c1))
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1))) ),
inference(para_from,[status(thm),theory(equality)],[2618,15]),
[iquote('para_from,2618.3.1,15.1.2')] ).
cnf(2622,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1))) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2621,29])]),
[iquote('hyper,2621,29,factor_simp')] ).
cnf(2623,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))
| greater(growth_rate(efficient_producers,dollar_f1(dollar_c1,dollar_f4(dollar_c1))),growth_rate(first_movers,dollar_f1(dollar_c1,dollar_f4(dollar_c1))))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1))) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2622,14,17,18,1560])]),
[iquote('hyper,2622,14,17,18,1560,factor_simp')] ).
cnf(2627,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| greater(growth_rate(efficient_producers,dollar_f3(dollar_c1,dollar_f2(dollar_c1))),growth_rate(first_movers,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2622,3,17,22,2281])])]),
[iquote('hyper,2622,3,17,22,2281,factor_simp,factor_simp')] ).
cnf(2638,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| 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(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2627,12,17,29])]),
[iquote('hyper,2627,12,17,29,factor_simp')] ).
cnf(2642,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))
| critical_point(dollar_c1) = dollar_f2(dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2638,2,17,22])]),
[iquote('hyper,2638,2,17,22,factor_simp')] ).
cnf(2677,plain,
( ~ in_environment(dollar_c1,dollar_f2(dollar_c1))
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1))) ),
inference(para_from,[status(thm),theory(equality)],[2642,15]),
[iquote('para_from,2642.2.1,15.1.2')] ).
cnf(2678,plain,
subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f1(dollar_c1,dollar_f4(dollar_c1))),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2677,29])]),
[iquote('hyper,2677,29,factor_simp')] ).
cnf(2679,plain,
( greater(growth_rate(efficient_producers,dollar_f1(dollar_c1,dollar_f4(dollar_c1))),growth_rate(first_movers,dollar_f1(dollar_c1,dollar_f4(dollar_c1))))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1)) ),
inference(hyper,[status(thm)],[2678,14,17,18,1322]),
[iquote('hyper,2678,14,17,18,1322')] ).
cnf(2697,plain,
( greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1))
| in_environment(dollar_c1,dollar_f2(dollar_c1)) ),
inference(hyper,[status(thm)],[2679,7,17,22]),
[iquote('hyper,2679,7,17,22')] ).
cnf(2705,plain,
( greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1))
| in_environment(dollar_c1,critical_point(A))
| ~ environment(A)
| ~ in_environment(A,dollar_f2(dollar_c1))
| greater(dollar_f3(A,dollar_f2(dollar_c1)),dollar_f2(dollar_c1)) ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[2697,11])]),
[iquote('para_into,2697.3.2,11.5.1,factor_simp')] ).
cnf(2707,plain,
( greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1))
| ~ in_environment(dollar_c1,dollar_f2(dollar_c1)) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[2705]),15,17]),
[iquote('factor,2705.2.6,unit_del,15,17')] ).
cnf(2708,plain,
( greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1)) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2707,2697])])]),
[iquote('hyper,2707,2697,factor_simp,factor_simp')] ).
cnf(2710,plain,
( greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1))
| greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1)) ),
inference(hyper,[status(thm)],[2708,5,17,22]),
[iquote('hyper,2708,5,17,22')] ).
cnf(2724,plain,
( greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1))
| greater(growth_rate(efficient_producers,dollar_f1(dollar_c1,dollar_f4(dollar_c1))),growth_rate(first_movers,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))) ),
inference(hyper,[status(thm)],[2710,14,17,18,2678]),
[iquote('hyper,2710,14,17,18,2678')] ).
cnf(2737,plain,
greater(dollar_f3(dollar_c1,dollar_f2(dollar_c1)),dollar_f2(dollar_c1)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2724,8,17,22,2708])]),
[iquote('hyper,2724,8,17,22,2708,factor_simp')] ).
cnf(2747,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| in_environment(dollar_c1,dollar_f2(dollar_c1)) ),
inference(hyper,[status(thm)],[2623,7,17,22]),
[iquote('hyper,2623,7,17,22')] ).
cnf(2754,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| in_environment(dollar_c1,critical_point(A))
| ~ environment(A)
| ~ in_environment(A,dollar_f2(dollar_c1))
| subpopulations(first_movers,efficient_producers,A,dollar_f3(A,dollar_f2(dollar_c1))) ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[2747,10])]),
[iquote('para_into,2747.3.2,10.5.1,factor_simp')] ).
cnf(2755,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| ~ in_environment(dollar_c1,dollar_f2(dollar_c1)) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[2754]),15,17]),
[iquote('factor,2754.1.6,unit_del,15,17')] ).
cnf(2756,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1))) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2755,2747])])]),
[iquote('hyper,2755,2747,factor_simp,factor_simp')] ).
cnf(2758,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))
| greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1)) ),
inference(hyper,[status(thm)],[2756,5,17,22]),
[iquote('hyper,2756,5,17,22')] ).
cnf(2770,plain,
( subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))
| greater(growth_rate(efficient_producers,dollar_f1(dollar_c1,dollar_f4(dollar_c1))),growth_rate(first_movers,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))) ),
inference(hyper,[status(thm)],[2758,14,17,18,2678]),
[iquote('hyper,2758,14,17,18,2678')] ).
cnf(2787,plain,
subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f3(dollar_c1,dollar_f2(dollar_c1))),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2770,8,17,22,2756])]),
[iquote('hyper,2770,8,17,22,2756,factor_simp')] ).
cnf(2789,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| greater(growth_rate(efficient_producers,dollar_f3(dollar_c1,dollar_f2(dollar_c1))),growth_rate(first_movers,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))) ),
inference(hyper,[status(thm)],[2787,6,17,22,2737]),
[iquote('hyper,2787,6,17,22,2737')] ).
cnf(2805,plain,
( greater(growth_rate(efficient_producers,dollar_f3(dollar_c1,dollar_f2(dollar_c1))),growth_rate(first_movers,dollar_f3(dollar_c1,dollar_f2(dollar_c1))))
| greater(growth_rate(efficient_producers,dollar_f1(dollar_c1,dollar_f4(dollar_c1))),growth_rate(first_movers,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))) ),
inference(hyper,[status(thm)],[2789,14,17,18,2678]),
[iquote('hyper,2789,14,17,18,2678')] ).
cnf(2807,plain,
greater(growth_rate(efficient_producers,dollar_f3(dollar_c1,dollar_f2(dollar_c1))),growth_rate(first_movers,dollar_f3(dollar_c1,dollar_f2(dollar_c1)))),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2805,9,17,22,2787,2737])]),
[iquote('hyper,2805,9,17,22,2787,2737,factor_simp')] ).
cnf(2827,plain,
( greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1))) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[65,17,28,2807]),15])]),
[iquote('hyper,65,17,28,2807,unit_del,15,factor_simp')] ).
cnf(2828,plain,
( greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| greater(growth_rate(efficient_producers,dollar_f1(dollar_c1,dollar_f4(dollar_c1))),growth_rate(first_movers,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))) ),
inference(hyper,[status(thm)],[2827,14,17,18,2678]),
[iquote('hyper,2827,14,17,18,2678')] ).
cnf(2838,plain,
( greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1)))
| in_environment(dollar_c1,dollar_f2(dollar_c1)) ),
inference(hyper,[status(thm)],[2828,7,17,22]),
[iquote('hyper,2828,7,17,22')] ).
cnf(2839,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(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2838,12,17,2807])]),
[iquote('hyper,2838,12,17,2807,factor_simp')] ).
cnf(2856,plain,
( critical_point(dollar_c1) = dollar_f2(dollar_c1)
| greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1)) ),
inference(hyper,[status(thm)],[2839,5,17,22]),
[iquote('hyper,2839,5,17,22')] ).
cnf(2904,plain,
( ~ in_environment(dollar_c1,dollar_f2(dollar_c1))
| greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1))) ),
inference(para_from,[status(thm),theory(equality)],[2839,15]),
[iquote('para_from,2839.2.1,15.1.2')] ).
cnf(2979,plain,
( ~ in_environment(dollar_c1,dollar_f2(dollar_c1))
| greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1)) ),
inference(para_from,[status(thm),theory(equality)],[2856,15]),
[iquote('para_from,2856.1.1,15.1.2')] ).
cnf(2980,plain,
greater_or_e_qual(dollar_f1(dollar_c1,dollar_f4(dollar_c1)),dollar_f4(dollar_c1)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2979,28])]),
[iquote('hyper,2979,28,factor_simp')] ).
cnf(2981,plain,
greater(growth_rate(efficient_producers,dollar_f1(dollar_c1,dollar_f4(dollar_c1))),growth_rate(first_movers,dollar_f1(dollar_c1,dollar_f4(dollar_c1)))),
inference(hyper,[status(thm)],[2980,14,17,18,2678]),
[iquote('hyper,2980,14,17,18,2678')] ).
cnf(2997,plain,
greater(growth_rate(efficient_producers,dollar_f2(dollar_c1)),growth_rate(first_movers,dollar_f2(dollar_c1))),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2904,2838])]),
[iquote('hyper,2904,2838,factor_simp')] ).
cnf(3010,plain,
$false,
inference(hyper,[status(thm)],[2981,8,17,22,2997]),
[iquote('hyper,2981,8,17,22,2997')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT023+2 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.32 % Computer : n018.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Wed Jul 27 04:04:46 EDT 2022
% 0.13/0.32 % CPUTime :
% 1.61/1.84 ----- Otter 3.3f, August 2004 -----
% 1.61/1.84 The process was started by sandbox2 on n018.cluster.edu,
% 1.61/1.84 Wed Jul 27 04:04:46 2022
% 1.61/1.84 The command was "./otter". The process ID is 15763.
% 1.61/1.84
% 1.61/1.84 set(prolog_style_variables).
% 1.61/1.84 set(auto).
% 1.61/1.84 dependent: set(auto1).
% 1.61/1.84 dependent: set(process_input).
% 1.61/1.84 dependent: clear(print_kept).
% 1.61/1.84 dependent: clear(print_new_demod).
% 1.61/1.84 dependent: clear(print_back_demod).
% 1.61/1.84 dependent: clear(print_back_sub).
% 1.61/1.84 dependent: set(control_memory).
% 1.61/1.84 dependent: assign(max_mem, 12000).
% 1.61/1.84 dependent: assign(pick_given_ratio, 4).
% 1.61/1.84 dependent: assign(stats_level, 1).
% 1.61/1.84 dependent: assign(max_seconds, 10800).
% 1.61/1.84 clear(print_given).
% 1.61/1.84
% 1.61/1.84 formula_list(usable).
% 1.61/1.84 all A (A=A).
% 1.61/1.84 all E (environment(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),growth_rate(first_movers,T))))))-> (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))))))).
% 1.61/1.84 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)).
% 1.61/1.84 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),growth_rate(first_movers,T))))))).
% 1.61/1.84 -(all E (environment(E)&stable(E)->in_environment(E,critical_point(E)))).
% 1.61/1.84 end_of_list.
% 1.61/1.84
% 1.61/1.84 -------> usable clausifies to:
% 1.61/1.84
% 1.61/1.84 list(usable).
% 1.61/1.84 0 [] A=A.
% 1.61/1.84 0 [] -environment(E)| -in_environment(E,To)|subpopulations(first_movers,efficient_producers,E,$f1(E,To))|in_environment(E,$f2(E)).
% 1.61/1.84 0 [] -environment(E)| -in_environment(E,To)|subpopulations(first_movers,efficient_producers,E,$f1(E,To))| -greater(growth_rate(efficient_producers,$f2(E)),growth_rate(first_movers,$f2(E))).
% 1.61/1.84 0 [] -environment(E)| -in_environment(E,To)|subpopulations(first_movers,efficient_producers,E,$f1(E,To))| -subpopulations(first_movers,efficient_producers,E,T)| -greater(T,$f2(E))|greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)).
% 1.61/1.84 0 [] -environment(E)| -in_environment(E,To)|greater_or_e_qual($f1(E,To),To)|in_environment(E,$f2(E)).
% 1.61/1.84 0 [] -environment(E)| -in_environment(E,To)|greater_or_e_qual($f1(E,To),To)| -greater(growth_rate(efficient_producers,$f2(E)),growth_rate(first_movers,$f2(E))).
% 1.61/1.84 0 [] -environment(E)| -in_environment(E,To)|greater_or_e_qual($f1(E,To),To)| -subpopulations(first_movers,efficient_producers,E,T)| -greater(T,$f2(E))|greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)).
% 1.61/1.84 0 [] -environment(E)| -in_environment(E,To)| -greater(growth_rate(efficient_producers,$f1(E,To)),growth_rate(first_movers,$f1(E,To)))|in_environment(E,$f2(E)).
% 1.61/1.84 0 [] -environment(E)| -in_environment(E,To)| -greater(growth_rate(efficient_producers,$f1(E,To)),growth_rate(first_movers,$f1(E,To)))| -greater(growth_rate(efficient_producers,$f2(E)),growth_rate(first_movers,$f2(E))).
% 1.61/1.84 0 [] -environment(E)| -in_environment(E,To)| -greater(growth_rate(efficient_producers,$f1(E,To)),growth_rate(first_movers,$f1(E,To)))| -subpopulations(first_movers,efficient_producers,E,T)| -greater(T,$f2(E))|greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)).
% 1.61/1.84 0 [] -environment(E)|greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))| -in_environment(E,To)|subpopulations(first_movers,efficient_producers,E,$f3(E,To))|To=critical_point(E).
% 1.61/1.84 0 [] -environment(E)|greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))| -in_environment(E,To)|greater($f3(E,To),To)|To=critical_point(E).
% 1.61/1.84 0 [] -environment(E)|greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))| -in_environment(E,To)| -greater(growth_rate(efficient_producers,$f3(E,To)),growth_rate(first_movers,$f3(E,To)))|To=critical_point(E).
% 1.61/1.84 0 [] -environment(E)| -stable(E)|in_environment(E,$f4(E)).
% 1.61/1.84 0 [] -environment(E)| -stable(E)| -subpopulations(first_movers,efficient_producers,E,T)| -greater_or_e_qual(T,$f4(E))|greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)).
% 1.61/1.84 0 [] environment($c1).
% 1.61/1.84 0 [] stable($c1).
% 1.61/1.84 0 [] -in_environment($c1,critical_point($c1)).
% 1.61/1.84 end_of_list.
% 1.61/1.84
% 1.61/1.84 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.61/1.84
% 1.61/1.84 This ia a non-Horn set with equality. The strategy will be
% 1.61/1.84 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.61/1.84 deletion, with positive clauses in sos and nonpositive
% 1.61/1.84 clauses in usable.
% 1.61/1.84
% 1.61/1.84 dependent: set(knuth_bendix).
% 1.61/1.84 dependent: set(anl_eq).
% 1.61/1.84 dependent: set(para_from).
% 1.61/1.84 dependent: set(para_into).
% 1.61/1.84 dependent: clear(para_from_right).
% 1.61/1.84 dependent: clear(para_into_right).
% 1.61/1.84 dependent: set(para_from_vars).
% 1.61/1.84 dependent: set(eq_units_both_ways).
% 1.61/1.84 dependent: set(dynamic_demod_all).
% 1.61/1.84 dependent: set(dynamic_demod).
% 1.61/1.84 dependent: set(order_eq).
% 1.61/1.84 dependent: set(back_demod).
% 1.61/1.84 dependent: set(lrpo).
% 1.61/1.84 dependent: set(hyper_res).
% 1.61/1.84 dependent: set(unit_deletion).
% 1.61/1.84 dependent: set(factor).
% 1.61/1.84
% 1.61/1.84 ------------> process usable:
% 1.61/1.84 ** KEPT (pick-wt=16): 1 [] -environment(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,$f1(A,B))|in_environment(A,$f2(A)).
% 1.61/1.84 ** KEPT (pick-wt=21): 2 [] -environment(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,$f1(A,B))| -greater(growth_rate(efficient_producers,$f2(A)),growth_rate(first_movers,$f2(A))).
% 1.61/1.84 ** KEPT (pick-wt=28): 3 [] -environment(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,$f1(A,B))| -subpopulations(first_movers,efficient_producers,A,C)| -greater(C,$f2(A))|greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)).
% 1.61/1.84 ** KEPT (pick-wt=14): 4 [] -environment(A)| -in_environment(A,B)|greater_or_e_qual($f1(A,B),B)|in_environment(A,$f2(A)).
% 1.61/1.84 ** KEPT (pick-wt=19): 5 [] -environment(A)| -in_environment(A,B)|greater_or_e_qual($f1(A,B),B)| -greater(growth_rate(efficient_producers,$f2(A)),growth_rate(first_movers,$f2(A))).
% 1.61/1.84 ** KEPT (pick-wt=26): 6 [] -environment(A)| -in_environment(A,B)|greater_or_e_qual($f1(A,B),B)| -subpopulations(first_movers,efficient_producers,A,C)| -greater(C,$f2(A))|greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)).
% 1.61/1.84 ** KEPT (pick-wt=20): 7 [] -environment(A)| -in_environment(A,B)| -greater(growth_rate(efficient_producers,$f1(A,B)),growth_rate(first_movers,$f1(A,B)))|in_environment(A,$f2(A)).
% 1.61/1.84 ** KEPT (pick-wt=25): 8 [] -environment(A)| -in_environment(A,B)| -greater(growth_rate(efficient_producers,$f1(A,B)),growth_rate(first_movers,$f1(A,B)))| -greater(growth_rate(efficient_producers,$f2(A)),growth_rate(first_movers,$f2(A))).
% 1.61/1.84 ** KEPT (pick-wt=32): 9 [] -environment(A)| -in_environment(A,B)| -greater(growth_rate(efficient_producers,$f1(A,B)),growth_rate(first_movers,$f1(A,B)))| -subpopulations(first_movers,efficient_producers,A,C)| -greater(C,$f2(A))|greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)).
% 1.61/1.84 ** KEPT (pick-wt=23): 10 [] -environment(A)|greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,$f3(A,B))|B=critical_point(A).
% 1.61/1.84 ** KEPT (pick-wt=21): 11 [] -environment(A)|greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))| -in_environment(A,B)|greater($f3(A,B),B)|B=critical_point(A).
% 1.61/1.84 ** KEPT (pick-wt=27): 12 [] -environment(A)|greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))| -in_environment(A,B)| -greater(growth_rate(efficient_producers,$f3(A,B)),growth_rate(first_movers,$f3(A,B)))|B=critical_point(A).
% 1.61/1.84 ** KEPT (pick-wt=8): 13 [] -environment(A)| -stable(A)|in_environment(A,$f4(A)).
% 1.61/1.84 ** KEPT (pick-wt=20): 14 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,$f4(A))|greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)).
% 1.61/1.84 ** KEPT (pick-wt=4): 15 [] -in_environment($c1,critical_point($c1)).
% 3.35/3.62
% 3.35/3.62 ------------> process sos:
% 3.35/3.62 ** KEPT (pick-wt=3): 16 [] A=A.
% 3.35/3.62 ** KEPT (pick-wt=2): 17 [] environment($c1).
% 3.35/3.62 ** KEPT (pick-wt=2): 18 [] stable($c1).
% 3.35/3.62 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 3.35/3.62
% 3.35/3.62 ======= end of input processing =======
% 3.35/3.62
% 3.35/3.62 =========== start of search ===========
% 3.35/3.62
% 3.35/3.62
% 3.35/3.62 Resetting weight limit to 35.
% 3.35/3.62
% 3.35/3.62
% 3.35/3.62 Resetting weight limit to 35.
% 3.35/3.62
% 3.35/3.62 sos_size=2216
% 3.35/3.62
% 3.35/3.62 -------- PROOF --------
% 3.35/3.62
% 3.35/3.62 -----> EMPTY CLAUSE at 1.78 sec ----> 3010 [hyper,2981,8,17,22,2997] $F.
% 3.35/3.62
% 3.35/3.62 Length of proof is 52. Level of proof is 30.
% 3.35/3.62
% 3.35/3.62 ---------------- PROOF ----------------
% 3.35/3.62 % SZS status Theorem
% 3.35/3.62 % SZS output start Refutation
% See solution above
% 3.35/3.62 ------------ end of proof -------------
% 3.35/3.62
% 3.35/3.62
% 3.35/3.62 Search stopped by max_proofs option.
% 3.35/3.62
% 3.35/3.62
% 3.35/3.62 Search stopped by max_proofs option.
% 3.35/3.62
% 3.35/3.62 ============ end of search ============
% 3.35/3.62
% 3.35/3.62 -------------- statistics -------------
% 3.35/3.62 clauses given 143
% 3.35/3.62 clauses generated 8651
% 3.35/3.62 clauses kept 3009
% 3.35/3.62 clauses forward subsumed 1068
% 3.35/3.62 clauses back subsumed 1098
% 3.35/3.62 Kbytes malloced 4882
% 3.35/3.62
% 3.35/3.62 ----------- times (seconds) -----------
% 3.35/3.62 user CPU time 1.78 (0 hr, 0 min, 1 sec)
% 3.35/3.62 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.35/3.62 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.35/3.62
% 3.35/3.62 That finishes the proof of the theorem.
% 3.35/3.62
% 3.35/3.62 Process 15763 finished Wed Jul 27 04:04:49 2022
% 3.35/3.62 Otter interrupted
% 3.35/3.62 PROOF FOUND
%------------------------------------------------------------------------------