%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT023+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 : n002.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 08:02:09 AM UTC 2026
% Result : Theorem 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 4
% Syntax : Number of formulae : 126 ( 8 unt; 0 def)
% Number of atoms : 586 ( 102 equ)
% Maximal formula atoms : 42 ( 4 avg)
% Number of connectives : 644 ( 184 ~; 407 |; 44 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 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 : 113 ( 0 sgn 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_earliest_time_growth_rate_exceeds,axiom,
! [E] :
( ( ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) )
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) ) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
fof(d1,axiom,
! [E,To] :
( ( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& environment(E) )
=> To = critical_point(E) ),
file('theBenchmark.p',d1) ).
fof(l1,axiom,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) ) ),
file('theBenchmark.p',l1) ).
fof(prove_l5,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
file('theBenchmark.p',prove_l5) ).
fof(prove_l5_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
inference(assume_negation,[status(cth)],[prove_l5]) ).
fof(nnf_4,plain,
? [E] :
( ~ in_environment(E,critical_point(E))
& stable(E)
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_l5_neg]) ).
fof(sk_prove_l5_neg,plain,
( ~ in_environment(sK0,critical_point(sK0))
& stable(sK0)
& environment(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(E,sK0)],[nnf_4]) ).
cnf(c_5,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l5_neg]) ).
fof(nnf_3,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[l1]) ).
fof(sk_l1_sk,plain,
! [E] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,sK1(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,sK1(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(To,sK1(E))],[nnf_3]) ).
fof(sk_l1,plain,
( ! [VAR_0,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ greater_or_equal(VAR_1,sK1(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) )
& ! [VAR_0] :
( in_environment(VAR_0,sK1(VAR_0))
| ~ stable(VAR_0)
| ~ environment(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_l1_sk]) ).
cnf(c_6,plain,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sK1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_l1]) ).
cnf(c_7,plain,
( in_environment(A,sK1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_l1]) ).
fof(nnf_2,plain,
! [E,To] :
( critical_point(E) = To
| ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[d1]) ).
fof(sk_d1_sk,plain,
! [E,To] :
( critical_point(E) = To
| ( ~ greater(growth_rate(efficient_producers,sK2(E,To)),growth_rate(first_movers,sK2(E,To)))
& greater(sK2(E,To),To)
& subpopulations(first_movers,efficient_producers,E,sK2(E,To)) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(T,sK2(E,To))],[nnf_2]) ).
fof(sk_d1,plain,
( ! [VAR_0,VAR_1] :
( critical_point(VAR_0) = VAR_1
| ~ greater(growth_rate(efficient_producers,sK2(VAR_0,VAR_1)),growth_rate(first_movers,sK2(VAR_0,VAR_1)))
| ~ in_environment(VAR_0,VAR_1)
| greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( critical_point(VAR_0) = VAR_1
| greater(sK2(VAR_0,VAR_1),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( critical_point(VAR_0) = VAR_1
| subpopulations(first_movers,efficient_producers,VAR_0,sK2(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ environment(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_sk]) ).
cnf(c_8,plain,
( critical_point(A) = B
| ~ greater(growth_rate(efficient_producers,sK2(A,B)),growth_rate(first_movers,sK2(A,B)))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_d1]) ).
cnf(c_9,plain,
( critical_point(A) = B
| greater(sK2(A,B),B)
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_d1]) ).
cnf(c_10,plain,
( critical_point(A) = B
| subpopulations(first_movers,efficient_producers,A,sK2(A,B))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_d1]) ).
fof(nnf_1,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) )
| ! [X0] :
( ? [X1] :
( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& greater_or_equal(X1,X0)
& subpopulations(first_movers,efficient_producers,E,X1) )
| ~ in_environment(E,X0) )
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_earliest_time_growth_rate_exceeds]) ).
fof(sk_mp_earliest_time_growth_rate_exceeds_sk,plain,
! [E] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,sK4(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,sK4(E)),growth_rate(first_movers,sK4(E)))
& in_environment(E,sK4(E)) )
| ! [X0] :
( ( ~ greater(growth_rate(efficient_producers,sK3(E,X0)),growth_rate(first_movers,sK3(E,X0)))
& greater_or_equal(sK3(E,X0),X0)
& subpopulations(first_movers,efficient_producers,E,sK3(E,X0)) )
| ~ in_environment(E,X0) )
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(E,X0)),skolemize(To,sK4(E))],[nnf_1]) ).
fof(sk_mp_earliest_time_growth_rate_exceeds,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( greater(growth_rate(efficient_producers,VAR_2),growth_rate(first_movers,VAR_2))
| ~ greater(VAR_2,sK4(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| ~ greater(growth_rate(efficient_producers,sK3(VAR_0,VAR_1)),growth_rate(first_movers,sK3(VAR_0,VAR_1)))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,sK4(VAR_0)),growth_rate(first_movers,sK4(VAR_0)))
| ~ greater(growth_rate(efficient_producers,sK3(VAR_0,VAR_1)),growth_rate(first_movers,sK3(VAR_0,VAR_1)))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( in_environment(VAR_0,sK4(VAR_0))
| ~ greater(growth_rate(efficient_producers,sK3(VAR_0,VAR_1)),growth_rate(first_movers,sK3(VAR_0,VAR_1)))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( greater(growth_rate(efficient_producers,VAR_2),growth_rate(first_movers,VAR_2))
| ~ greater(VAR_2,sK4(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| greater_or_equal(sK3(VAR_0,VAR_1),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,sK4(VAR_0)),growth_rate(first_movers,sK4(VAR_0)))
| greater_or_equal(sK3(VAR_0,VAR_1),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( in_environment(VAR_0,sK4(VAR_0))
| greater_or_equal(sK3(VAR_0,VAR_1),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( greater(growth_rate(efficient_producers,VAR_2),growth_rate(first_movers,VAR_2))
| ~ greater(VAR_2,sK4(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| subpopulations(first_movers,efficient_producers,VAR_0,sK3(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,sK4(VAR_0)),growth_rate(first_movers,sK4(VAR_0)))
| subpopulations(first_movers,efficient_producers,VAR_0,sK3(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( in_environment(VAR_0,sK4(VAR_0))
| subpopulations(first_movers,efficient_producers,VAR_0,sK3(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds_sk]) ).
cnf(c_11,plain,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sK4(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(growth_rate(efficient_producers,sK3(A,B)),growth_rate(first_movers,sK3(A,B)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_12,plain,
( ~ greater(growth_rate(efficient_producers,sK4(A)),growth_rate(first_movers,sK4(A)))
| ~ greater(growth_rate(efficient_producers,sK3(A,B)),growth_rate(first_movers,sK3(A,B)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_13,plain,
( in_environment(A,sK4(A))
| ~ greater(growth_rate(efficient_producers,sK3(A,B)),growth_rate(first_movers,sK3(A,B)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_14,plain,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sK4(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sK3(A,B),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_15,plain,
( ~ greater(growth_rate(efficient_producers,sK4(A)),growth_rate(first_movers,sK4(A)))
| greater_or_equal(sK3(A,B),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_16,plain,
( in_environment(A,sK4(A))
| greater_or_equal(sK3(A,B),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_17,plain,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sK4(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sK3(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_18,plain,
( ~ greater(growth_rate(efficient_producers,sK4(A)),growth_rate(first_movers,sK4(A)))
| subpopulations(first_movers,efficient_producers,A,sK3(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_19,plain,
( in_environment(A,sK4(A))
| subpopulations(first_movers,efficient_producers,A,sK3(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_20,negated_conjecture,
( in_environment(sK0,sK4(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,A))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_19]) ).
cnf(c_21,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,A))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_18]) ).
cnf(c_22,negated_conjecture,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sK4(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,A))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_17]) ).
cnf(c_23,negated_conjecture,
( in_environment(sK0,sK4(sK0))
| greater_or_equal(sK3(sK0,A),A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_16]) ).
cnf(c_24,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater_or_equal(sK3(sK0,A),A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_15]) ).
cnf(c_25,negated_conjecture,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sK4(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| greater_or_equal(sK3(sK0,A),A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_14]) ).
cnf(c_26,negated_conjecture,
( in_environment(sK0,sK4(sK0))
| ~ greater(growth_rate(efficient_producers,sK3(sK0,A)),growth_rate(first_movers,sK3(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_13]) ).
cnf(c_27,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| ~ greater(growth_rate(efficient_producers,sK3(sK0,A)),growth_rate(first_movers,sK3(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_12]) ).
cnf(c_28,negated_conjecture,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sK4(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| ~ greater(growth_rate(efficient_producers,sK3(sK0,A)),growth_rate(first_movers,sK3(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_5,c_11]) ).
cnf(c_29,negated_conjecture,
( critical_point(sK0) = A
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,A))
| ~ in_environment(sK0,A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
inference(resolve,[status(thm)],[c_5,c_10]) ).
cnf(c_30,negated_conjecture,
( critical_point(sK0) = A
| greater(sK2(sK0,A),A)
| ~ in_environment(sK0,A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
inference(resolve,[status(thm)],[c_5,c_9]) ).
cnf(c_31,negated_conjecture,
( critical_point(sK0) = A
| ~ greater(growth_rate(efficient_producers,sK2(sK0,A)),growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) ),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_32,negated_conjecture,
( in_environment(sK0,sK1(sK0))
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_33,negated_conjecture,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater_or_equal(A,sK1(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_34,negated_conjecture,
~ in_environment(sK0,critical_point(sK0)),
inference(split_conjunct,[status(thm)],[sk_prove_l5_neg]) ).
cnf(c_35,negated_conjecture,
stable(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l5_neg]) ).
cnf(c_36,negated_conjecture,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater_or_equal(A,sK1(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_35,c_33]) ).
cnf(c_37,negated_conjecture,
in_environment(sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_35,c_32]) ).
cnf(c_41,plain,
( ~ greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| ~ greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_37,c_27]) ).
cnf(c_42,plain,
( in_environment(sK0,sK4(sK0))
| ~ greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_37,c_26]) ).
cnf(c_43,plain,
( ~ greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0)) ),
inference(resolve,[status(thm)],[c_37,c_24]) ).
cnf(c_44,plain,
( in_environment(sK0,sK4(sK0))
| greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0)) ),
inference(resolve,[status(thm)],[c_37,c_23]) ).
cnf(c_45,plain,
( ~ greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_37,c_21]) ).
cnf(c_46,plain,
( in_environment(sK0,sK4(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_37,c_20]) ).
cnf(c_47,plain,
( greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| ~ greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0))
| in_environment(sK0,sK4(sK0)) ),
inference(resolve,[status(thm)],[c_46,c_36]) ).
cnf(c_160,plain,
( in_environment(sK0,sK4(sK0))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| in_environment(sK0,sK4(sK0)) ),
inference(resolve,[status(thm)],[c_47,c_44]) ).
cnf(c_52,plain,
( greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| in_environment(sK0,sK4(sK0)) ),
inference(copy,[status(thm)],[c_160]) ).
cnf(c_161,negated_conjecture,
( critical_point(sK0) = sK4(sK0)
| ~ greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_52,c_31]) ).
cnf(c_53,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| ~ greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_161]) ).
cnf(c_162,negated_conjecture,
( critical_point(sK0) = sK4(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_52,c_30]) ).
cnf(c_54,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_163,negated_conjecture,
( critical_point(sK0) = sK4(sK0)
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_52,c_29]) ).
cnf(c_55,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_163]) ).
cnf(c_59,plain,
( in_environment(sK0,sK4(sK0))
| sK4(sK0) = critical_point(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_54,c_42]) ).
cnf(c_164,negated_conjecture,
( critical_point(sK0) = sK4(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| sK4(sK0) = critical_point(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_59,c_30]) ).
cnf(c_165,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| sK4(sK0) = critical_point(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_166,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| sK4(sK0) = critical_point(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_167,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| sK4(sK0) = critical_point(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_166]) ).
cnf(c_61,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_167]) ).
cnf(c_66,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater_or_equal(sK3(sK0,A),A)
| ~ in_environment(sK0,A)
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_55,c_25]) ).
cnf(c_67,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,A))
| ~ in_environment(sK0,A)
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_55,c_22]) ).
cnf(c_73,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_66,c_37]) ).
cnf(c_168,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_73,c_61]) ).
cnf(c_169,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_168]) ).
cnf(c_76,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_169]) ).
cnf(c_78,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,sK1(sK0)))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_67,c_37]) ).
cnf(c_170,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,sK1(sK0)))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_78,c_61]) ).
cnf(c_171,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,sK1(sK0)))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_170]) ).
cnf(c_84,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,sK1(sK0)))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_171]) ).
cnf(c_172,negated_conjecture,
( greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| ~ greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_84,c_36]) ).
cnf(c_85,negated_conjecture,
( ~ greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_172]) ).
cnf(c_173,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_85,c_76]) ).
cnf(c_174,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_173]) ).
cnf(c_175,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_174]) ).
cnf(c_176,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_90,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_176]) ).
cnf(c_91,plain,
( in_environment(sK0,sK4(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_90,c_42]) ).
cnf(c_177,negated_conjecture,
( critical_point(sK0) = sK4(sK0)
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_91,c_29]) ).
cnf(c_178,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_179,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_95,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_179]) ).
cnf(c_180,negated_conjecture,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| ~ greater(growth_rate(efficient_producers,sK3(sK0,A)),growth_rate(first_movers,sK3(sK0,A)))
| ~ in_environment(sK0,A)
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_95,c_28]) ).
cnf(c_97,negated_conjecture,
( ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| ~ greater(growth_rate(efficient_producers,sK3(sK0,A)),growth_rate(first_movers,sK3(sK0,A)))
| ~ in_environment(sK0,A)
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_180]) ).
cnf(c_108,plain,
( ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| ~ greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_97,c_37]) ).
cnf(c_181,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_108,c_90]) ).
cnf(c_182,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_181]) ).
cnf(c_183,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_182]) ).
cnf(c_115,plain,
( ~ greater(sK2(sK0,sK4(sK0)),sK4(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_183]) ).
cnf(c_184,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_115,c_61]) ).
cnf(c_185,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_184]) ).
cnf(c_116,plain,
( greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_186,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_116,c_53]) ).
cnf(c_187,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_186]) ).
cnf(c_117,plain,
( greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_187]) ).
cnf(c_118,plain,
( in_environment(sK0,sK4(sK0))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_117,c_42]) ).
cnf(c_188,negated_conjecture,
( critical_point(sK0) = sK4(sK0)
| ~ greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_118,c_31]) ).
cnf(c_189,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| ~ greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_188]) ).
cnf(c_190,negated_conjecture,
( sK4(sK0) = critical_point(sK0)
| ~ greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_189]) ).
cnf(c_122,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK2(sK0,sK4(sK0))),growth_rate(first_movers,sK2(sK0,sK4(sK0))))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_191,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(resolve,[status(thm)],[c_122,c_116]) ).
cnf(c_192,plain,
( sK4(sK0) = critical_point(sK0)
| sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_124,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0))) ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_127,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK3(sK0,sK1(sK0)))
| sK4(sK0) = critical_point(sK0) ),
inference(resolve,[status(thm)],[c_124,c_45]) ).
cnf(c_128,plain,
( greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0))
| sK4(sK0) = critical_point(sK0) ),
inference(resolve,[status(thm)],[c_124,c_43]) ).
cnf(c_133,plain,
( greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| ~ greater_or_equal(sK3(sK0,sK1(sK0)),sK1(sK0))
| sK4(sK0) = critical_point(sK0) ),
inference(resolve,[status(thm)],[c_127,c_36]) ).
cnf(c_193,plain,
( sK4(sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| sK4(sK0) = critical_point(sK0) ),
inference(resolve,[status(thm)],[c_133,c_128]) ).
cnf(c_137,plain,
( greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| sK4(sK0) = critical_point(sK0) ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_139,plain,
( ~ greater(growth_rate(efficient_producers,sK4(sK0)),growth_rate(first_movers,sK4(sK0)))
| sK4(sK0) = critical_point(sK0) ),
inference(resolve,[status(thm)],[c_137,c_41]) ).
cnf(c_194,plain,
( sK4(sK0) = critical_point(sK0)
| sK4(sK0) = critical_point(sK0) ),
inference(resolve,[status(thm)],[c_139,c_124]) ).
cnf(c_143,plain,
sK4(sK0) = critical_point(sK0),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_195,plain,
( greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0))))
| in_environment(sK0,critical_point(sK0)) ),
inference(paramod,[status(thm)],[c_143,c_52]) ).
cnf(c_153,negated_conjecture,
greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))),
inference(resolve,[status(thm)],[c_34,c_195]) ).
cnf(c_196,plain,
( in_environment(sK0,critical_point(sK0))
| ~ greater(growth_rate(efficient_producers,sK3(sK0,sK1(sK0))),growth_rate(first_movers,sK3(sK0,sK1(sK0)))) ),
inference(paramod,[status(thm)],[c_143,c_42]) ).
cnf(c_197,plain,
in_environment(sK0,critical_point(sK0)),
inference(resolve,[status(thm)],[c_153,c_196]) ).
cnf(c_159,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_34,c_197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 00:07:20 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 317381 was started by sandbox on n002,
% 0.10/0.38 % Sat Sep 26 00:07:20 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.42
% 0.10/0.42 % SZS status Theorem for theBenchmark
% 0.10/0.42
% 0.10/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.42 % Length of proof is 76.
% 0.10/0.42 % Level of proof is 29.
% 0.10/0.42 % Maximum clause weight is 57.000.
% 0.10/0.42 % Given clauses 94.
% 0.10/0.42
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------