%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:02:32 AM UTC 2026
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 98 ( 24 unt; 0 def)
% Number of atoms : 272 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 292 ( 118 ~; 110 |; 43 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 41 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp1_high_growth_rates,axiom,
! [E,S1,S2,T] :
( ( greater(growth_rate(S2,T),growth_rate(S1,T))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> selection_favors(S2,S1,T) ),
file('theBenchmark.p',mp1_high_growth_rates) ).
fof(l3,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
file('theBenchmark.p',l3) ).
fof(mp_critical_point_means_FM_and_EP,axiom,
! [E] :
( ( in_environment(E,critical_point(E))
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,critical_point(E)) ),
file('theBenchmark.p',mp_critical_point_means_FM_and_EP) ).
fof(mp_FM_and_EP_when_EP_appears,axiom,
! [E] :
( ( in_environment(E,appear(efficient_producers,E))
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,appear(efficient_producers,E)) ),
file('theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
fof(mp_difference_between_founding_rates,axiom,
! [T] :
( ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) )
=> decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) ),
file('theBenchmark.p',mp_difference_between_founding_rates) ).
fof(mp_decreasing_function,axiom,
! [E,T,To] :
( ( greater(To,T)
& greater_or_equal(T,appear(efficient_producers,E))
& greater_or_equal(difference(growth_rate(first_movers,To),growth_rate(efficient_producers,To)),zero)
& in_environment(E,To)
& environment(E) )
=> ( decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
=> greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ) ),
file('theBenchmark.p',mp_decreasing_function) ).
fof(mp_negative_growth_rate_difference,axiom,
! [T] :
( greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
<=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
file('theBenchmark.p',mp_negative_growth_rate_difference) ).
fof(mp_positive_growth_rate_difference,axiom,
! [T] :
( greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
<=> greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T)) ),
file('theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(mp_durations_are_time_intervals,axiom,
! [E,T1,T2,T] :
( ( greater_or_equal(T,T1)
& greater_or_equal(T2,T)
& in_environment(E,T2)
& in_environment(E,T1)
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_durations_are_time_intervals) ).
fof(mp_critical_time_points,axiom,
! [E,T] :
( ( greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_critical_time_points) ).
fof(mp_symmetry_of_subpopulations,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> subpopulations(efficient_producers,first_movers,E,T) ),
file('theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(mp_FM_and_EP_members_EP_appeared,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater_or_equal(T,appear(efficient_producers,E)) ),
file('theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
fof(mp_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('theBenchmark.p',mp_greater_or_equal) ).
fof(mp_relationship_of_growth_rates,axiom,
! [E,T] :
( ( ~ greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater_or_equal(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ),
file('theBenchmark.p',mp_relationship_of_growth_rates) ).
fof(d1,axiom,
! [E,Tc] :
( ( Tc = critical_point(E)
& environment(E) )
=> ( ! [T] :
( ( greater(T,Tc)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) ) ),
file('theBenchmark.p',d1) ).
fof(a10,axiom,
! [E,T1,T2,T] :
( ( greater_or_equal(T2,T)
& greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T2)
& subpopulations(first_movers,efficient_producers,E,T1)
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('theBenchmark.p',a10) ).
fof(a12,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) ),
file('theBenchmark.p',a12) ).
fof(prove_t3,conjecture,
! [E,T] :
( ( greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) )
=> selection_favors(first_movers,efficient_producers,T) ),
file('theBenchmark.p',prove_t3) ).
fof(prove_t3_neg,negated_conjecture,
~ ! [E,T] :
( ( greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) )
=> selection_favors(first_movers,efficient_producers,T) ),
inference(assume_negation,[status(cth)],[prove_t3]) ).
fof(nnf_21,plain,
? [E,T] :
( ~ selection_favors(first_movers,efficient_producers,T)
& greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_t3_neg]) ).
fof(sk_prove_t3_neg,plain,
( ~ selection_favors(first_movers,efficient_producers,sK1)
& greater(critical_point(sK0),sK1)
& greater_or_equal(sK1,appear(efficient_producers,sK0))
& in_environment(sK0,critical_point(sK0))
& environment(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(E,sK0),skolemize(T,sK1)],[nnf_21]) ).
cnf(c_22,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_t3_neg]) ).
cnf(c_23,plain,
( decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a12]) ).
cnf(c_24,plain,
( subpopulations(first_movers,efficient_producers,A,D)
| ~ greater_or_equal(C,D)
| ~ greater_or_equal(D,B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a10]) ).
cnf(c_26,plain,
( ~ greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| critical_point(A) != B
| ~ environment(A) ),
inference(clausify,[status(thm)],[d1]) ).
cnf(c_27,plain,
( greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| greater(zero,difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_relationship_of_growth_rates]) ).
cnf(c_28,plain,
( greater_or_equal(B,appear(efficient_producers,A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_FM_and_EP_members_EP_appeared]) ).
cnf(c_29,plain,
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_symmetry_of_subpopulations]) ).
cnf(c_31,plain,
( in_environment(A,B)
| ~ greater(critical_point(A),B)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_critical_time_points]) ).
cnf(c_34,plain,
( in_environment(A,D)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(C,D)
| ~ in_environment(A,C)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_durations_are_time_intervals]) ).
cnf(c_35,plain,
( greater(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)),zero)
| ~ decreases(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)))
| ~ greater(B,C)
| ~ greater_or_equal(C,appear(efficient_producers,A))
| ~ greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_decreasing_function]) ).
cnf(c_36,plain,
( subpopulations(first_movers,efficient_producers,A,appear(efficient_producers,A))
| ~ in_environment(A,appear(efficient_producers,A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_FM_and_EP_when_EP_appears]) ).
cnf(c_37,plain,
( subpopulations(first_movers,efficient_producers,A,critical_point(A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_critical_point_means_FM_and_EP]) ).
cnf(c_38,plain,
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l3]) ).
cnf(c_39,plain,
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp1_high_growth_rates]) ).
cnf(c_40,negated_conjecture,
( selection_favors(B,A,C)
| ~ greater(growth_rate(B,C),growth_rate(A,C))
| ~ subpopulations(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_22,c_39]) ).
cnf(c_41,negated_conjecture,
( ~ decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_38]) ).
cnf(c_42,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ in_environment(sK0,critical_point(sK0)) ),
inference(resolve,[status(thm)],[c_22,c_37]) ).
cnf(c_43,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0))
| ~ in_environment(sK0,appear(efficient_producers,sK0)) ),
inference(resolve,[status(thm)],[c_22,c_36]) ).
cnf(c_44,negated_conjecture,
( greater(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| ~ decreases(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)))
| ~ greater(A,B)
| ~ greater_or_equal(B,appear(efficient_producers,sK0))
| ~ greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_35]) ).
cnf(c_45,negated_conjecture,
( in_environment(sK0,C)
| ~ greater_or_equal(C,A)
| ~ greater_or_equal(B,C)
| ~ in_environment(sK0,B)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_34]) ).
cnf(c_48,negated_conjecture,
( in_environment(sK0,A)
| ~ greater(critical_point(sK0),A)
| ~ greater_or_equal(A,appear(efficient_producers,sK0))
| ~ in_environment(sK0,critical_point(sK0)) ),
inference(resolve,[status(thm)],[c_22,c_31]) ).
cnf(c_50,negated_conjecture,
( subpopulations(efficient_producers,first_movers,sK0,A)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_29]) ).
cnf(c_51,negated_conjecture,
( greater_or_equal(A,appear(efficient_producers,sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_28]) ).
cnf(c_52,negated_conjecture,
( greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero)
| greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_27]) ).
cnf(c_53,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| critical_point(sK0) != A ),
inference(resolve,[status(thm)],[c_22,c_26]) ).
cnf(c_55,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK0,C)
| ~ greater_or_equal(B,C)
| ~ greater_or_equal(C,A)
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_24]) ).
cnf(c_56,negated_conjecture,
( decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A)))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_22,c_23]) ).
cnf(c_57,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_t3_neg]) ).
cnf(c_58,negated_conjecture,
greater(critical_point(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_prove_t3_neg]) ).
cnf(c_59,negated_conjecture,
greater_or_equal(sK1,appear(efficient_producers,sK0)),
inference(split_conjunct,[status(thm)],[sk_prove_t3_neg]) ).
cnf(c_60,negated_conjecture,
in_environment(sK0,critical_point(sK0)),
inference(split_conjunct,[status(thm)],[sk_prove_t3_neg]) ).
cnf(c_61,plain,
( B != A
| greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal]) ).
cnf(c_62,plain,
( ~ greater(A,B)
| greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal]) ).
cnf(c_63,plain,
( B = A
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal]) ).
cnf(c_65,plain,
( greater(growth_rate(first_movers,A),growth_rate(efficient_producers,A))
| ~ greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) ),
inference(clausify,[status(thm)],[mp_positive_growth_rate_difference]) ).
cnf(c_67,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) ),
inference(clausify,[status(thm)],[mp_negative_growth_rate_difference]) ).
cnf(c_68,plain,
( decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))) ),
inference(clausify,[status(thm)],[mp_difference_between_founding_rates]) ).
cnf(c_71,negated_conjecture,
( in_environment(sK0,A)
| ~ greater(critical_point(sK0),A)
| ~ greater_or_equal(A,appear(efficient_producers,sK0)) ),
inference(resolve,[status(thm)],[c_60,c_48]) ).
cnf(c_72,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0)),
inference(resolve,[status(thm)],[c_60,c_42]) ).
cnf(c_77,plain,
~ greater(growth_rate(efficient_producers,critical_point(sK0)),growth_rate(first_movers,critical_point(sK0))),
inference(xxres,[status(thm)],[c_53]) ).
cnf(c_80,plain,
( greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero)
| ~ decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| ~ greater(critical_point(sK0),A)
| ~ greater_or_equal(A,appear(efficient_producers,sK0))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sK0)),growth_rate(efficient_producers,critical_point(sK0))),zero) ),
inference(resolve,[status(thm)],[c_60,c_44]) ).
cnf(c_81,plain,
greater_or_equal(A,A),
inference(xxres,[status(thm)],[c_61]) ).
cnf(c_82,plain,
greater_or_equal(critical_point(sK0),sK1),
inference(resolve,[status(thm)],[c_62,c_58]) ).
cnf(c_233,negated_conjecture,
( in_environment(sK0,sK1)
| ~ greater(critical_point(sK0),sK1) ),
inference(resolve,[status(thm)],[c_71,c_59]) ).
cnf(c_87,negated_conjecture,
in_environment(sK0,sK1),
inference(resolve,[status(thm)],[c_58,c_233]) ).
cnf(c_90,plain,
( subpopulations(first_movers,efficient_producers,sK0,B)
| ~ greater_or_equal(critical_point(sK0),B)
| ~ greater_or_equal(B,A)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_72,c_55]) ).
cnf(c_93,plain,
( greater_or_equal(difference(growth_rate(first_movers,critical_point(sK0)),growth_rate(efficient_producers,critical_point(sK0))),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(sK0)),growth_rate(efficient_producers,critical_point(sK0)))) ),
inference(resolve,[status(thm)],[c_72,c_52]) ).
cnf(c_94,plain,
greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0)),
inference(resolve,[status(thm)],[c_72,c_51]) ).
cnf(c_101,plain,
~ greater(zero,difference(growth_rate(first_movers,critical_point(sK0)),growth_rate(efficient_producers,critical_point(sK0)))),
inference(resolve,[status(thm)],[c_67,c_77]) ).
cnf(c_102,plain,
greater_or_equal(difference(growth_rate(first_movers,critical_point(sK0)),growth_rate(efficient_producers,critical_point(sK0))),zero),
inference(resolve,[status(thm)],[c_101,c_93]) ).
cnf(c_103,plain,
( greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero)
| ~ decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| ~ greater(critical_point(sK0),A)
| ~ greater_or_equal(A,appear(efficient_producers,sK0)) ),
inference(resolve,[status(thm)],[c_102,c_80]) ).
cnf(c_104,plain,
( in_environment(sK0,appear(efficient_producers,sK0))
| ~ greater(critical_point(sK0),appear(efficient_producers,sK0)) ),
inference(resolve,[status(thm)],[c_81,c_71]) ).
cnf(c_109,plain,
( in_environment(sK0,B)
| ~ greater_or_equal(B,A)
| ~ greater_or_equal(sK1,B)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_87,c_45]) ).
cnf(c_234,plain,
( appear(efficient_producers,sK0) = critical_point(sK0)
| greater(critical_point(sK0),appear(efficient_producers,sK0)) ),
inference(resolve,[status(thm)],[c_94,c_63]) ).
cnf(c_113,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| greater(critical_point(sK0),appear(efficient_producers,sK0)) ),
inference(copy,[status(thm)],[c_234]) ).
cnf(c_118,plain,
( in_environment(sK0,A)
| ~ greater_or_equal(A,critical_point(sK0))
| ~ greater_or_equal(sK1,A) ),
inference(resolve,[status(thm)],[c_109,c_60]) ).
cnf(c_123,plain,
( in_environment(sK0,appear(efficient_producers,sK0))
| ~ greater_or_equal(appear(efficient_producers,sK0),critical_point(sK0)) ),
inference(resolve,[status(thm)],[c_118,c_59]) ).
cnf(c_144,plain,
( in_environment(sK0,appear(efficient_producers,sK0))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolve,[status(thm)],[c_113,c_104]) ).
cnf(c_146,plain,
( greater_or_equal(appear(efficient_producers,sK0),critical_point(sK0))
| in_environment(sK0,appear(efficient_producers,sK0)) ),
inference(resolve,[status(thm)],[c_144,c_61]) ).
cnf(c_235,plain,
( in_environment(sK0,appear(efficient_producers,sK0))
| in_environment(sK0,appear(efficient_producers,sK0)) ),
inference(resolve,[status(thm)],[c_146,c_123]) ).
cnf(c_171,plain,
in_environment(sK0,appear(efficient_producers,sK0)),
inference(copy,[status(thm)],[c_235]) ).
cnf(c_172,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0)),
inference(resolve,[status(thm)],[c_171,c_43]) ).
cnf(c_184,plain,
( subpopulations(first_movers,efficient_producers,sK0,A)
| ~ greater_or_equal(critical_point(sK0),A)
| ~ greater_or_equal(A,appear(efficient_producers,sK0)) ),
inference(resolve,[status(thm)],[c_172,c_90]) ).
cnf(c_236,negated_conjecture,
( greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| ~ greater(critical_point(sK0),sK1) ),
inference(resolve,[status(thm)],[c_103,c_59]) ).
cnf(c_209,negated_conjecture,
( greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))) ),
inference(resolve,[status(thm)],[c_58,c_236]) ).
cnf(c_237,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ greater_or_equal(critical_point(sK0),sK1) ),
inference(resolve,[status(thm)],[c_184,c_59]) ).
cnf(c_215,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(resolve,[status(thm)],[c_82,c_237]) ).
cnf(c_219,plain,
decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1))),
inference(resolve,[status(thm)],[c_215,c_56]) ).
cnf(c_224,plain,
subpopulations(efficient_producers,first_movers,sK0,sK1),
inference(resolve,[status(thm)],[c_215,c_50]) ).
cnf(c_225,plain,
~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(resolve,[status(thm)],[c_215,c_41]) ).
cnf(c_238,negated_conjecture,
( selection_favors(first_movers,efficient_producers,sK1)
| ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_224,c_40]) ).
cnf(c_227,negated_conjecture,
~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),
inference(resolve,[status(thm)],[c_57,c_238]) ).
cnf(c_230,plain,
~ greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero),
inference(resolve,[status(thm)],[c_65,c_227]) ).
cnf(c_231,negated_conjecture,
~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))),
inference(resolve,[status(thm)],[c_230,c_209]) ).
cnf(c_239,plain,
( decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| ~ decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1))) ),
inference(resolve,[status(thm)],[c_68,c_225]) ).
cnf(c_240,plain,
~ decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1))),
inference(resolve,[status(thm)],[c_239,c_231]) ).
cnf(c_232,plain,
$false,
inference(resolve,[status(thm)],[c_219,c_240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n007.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 00:03:39 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2237713 was started by sandbox on n007,
% 0.19/0.45 % Sat Sep 26 00:03:39 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 0.19/0.51
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51
% 0.19/0.51 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.19/0.51 % Length of proof is 87.
% 0.19/0.51 % Level of proof is 16.
% 0.19/0.51 % Maximum clause weight is 57.000.
% 0.19/0.51 % Given clauses 114.
% 0.19/0.51
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------