%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:02:31 AM UTC 2026
% Result : Theorem 0.15s 15.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 3
% Syntax : Number of formulae : 92 ( 12 unt; 0 def)
% Number of atoms : 369 ( 0 equ)
% Maximal formula atoms : 42 ( 4 avg)
% Number of connectives : 460 ( 183 ~; 220 |; 48 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 48 !; 10 ?)
% 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(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_l12,conjecture,
! [E] :
( ( stable(E)
& 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',prove_l12) ).
fof(prove_l12_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& 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) ) ),
inference(assume_negation,[status(cth)],[prove_l12]) ).
fof(nnf_3,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) )
& stable(E)
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_l12_neg]) ).
fof(sk_prove_l12_neg_sk,plain,
( ! [To] :
( ( ~ greater(growth_rate(efficient_producers,sK4(To)),growth_rate(first_movers,sK4(To)))
& greater(sK4(To),To)
& subpopulations(first_movers,efficient_producers,sK0,sK4(To)) )
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ in_environment(sK0,To) )
& stable(sK0)
& environment(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4]),skolemize(E,sK0),skolemize(T,sK4(To))],[nnf_3]) ).
fof(sk_prove_l12_neg,plain,
( ! [VAR_0] :
( ~ greater(growth_rate(efficient_producers,sK4(VAR_0)),growth_rate(first_movers,sK4(VAR_0)))
| greater(growth_rate(efficient_producers,VAR_0),growth_rate(first_movers,VAR_0))
| ~ in_environment(sK0,VAR_0) )
& ! [VAR_0] :
( greater(sK4(VAR_0),VAR_0)
| greater(growth_rate(efficient_producers,VAR_0),growth_rate(first_movers,VAR_0))
| ~ in_environment(sK0,VAR_0) )
& ! [VAR_0] :
( subpopulations(first_movers,efficient_producers,sK0,sK4(VAR_0))
| greater(growth_rate(efficient_producers,VAR_0),growth_rate(first_movers,VAR_0))
| ~ in_environment(sK0,VAR_0) )
& stable(sK0)
& environment(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_prove_l12_neg_sk]) ).
cnf(c_4,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l12_neg]) ).
fof(nnf_2,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_2]) ).
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_5,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_6,plain,
( in_environment(A,sK1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_l1]) ).
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,sK3(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,sK3(E)),growth_rate(first_movers,sK3(E)))
& in_environment(E,sK3(E)) )
| ! [X0] :
( ( ~ greater(growth_rate(efficient_producers,sK2(E,X0)),growth_rate(first_movers,sK2(E,X0)))
& greater_or_equal(sK2(E,X0),X0)
& subpopulations(first_movers,efficient_producers,E,sK2(E,X0)) )
| ~ in_environment(E,X0) )
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X1,sK2(E,X0)),skolemize(To,sK3(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,sK3(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| ~ 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)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,sK3(VAR_0)),growth_rate(first_movers,sK3(VAR_0)))
| ~ 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)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( in_environment(VAR_0,sK3(VAR_0))
| ~ 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)
| ~ 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,sK3(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| greater_or_equal(sK2(VAR_0,VAR_1),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,sK3(VAR_0)),growth_rate(first_movers,sK3(VAR_0)))
| greater_or_equal(sK2(VAR_0,VAR_1),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( in_environment(VAR_0,sK3(VAR_0))
| greater_or_equal(sK2(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,sK3(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| subpopulations(first_movers,efficient_producers,VAR_0,sK2(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,sK3(VAR_0)),growth_rate(first_movers,sK3(VAR_0)))
| subpopulations(first_movers,efficient_producers,VAR_0,sK2(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( in_environment(VAR_0,sK3(VAR_0))
| subpopulations(first_movers,efficient_producers,VAR_0,sK2(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_7,plain,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sK3(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(growth_rate(efficient_producers,sK2(A,B)),growth_rate(first_movers,sK2(A,B)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_8,plain,
( ~ greater(growth_rate(efficient_producers,sK3(A)),growth_rate(first_movers,sK3(A)))
| ~ greater(growth_rate(efficient_producers,sK2(A,B)),growth_rate(first_movers,sK2(A,B)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_9,plain,
( in_environment(A,sK3(A))
| ~ greater(growth_rate(efficient_producers,sK2(A,B)),growth_rate(first_movers,sK2(A,B)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_10,plain,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sK3(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sK2(A,B),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_11,plain,
( ~ greater(growth_rate(efficient_producers,sK3(A)),growth_rate(first_movers,sK3(A)))
| greater_or_equal(sK2(A,B),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_12,plain,
( in_environment(A,sK3(A))
| greater_or_equal(sK2(A,B),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_13,plain,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sK3(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sK2(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,sK3(A)),growth_rate(first_movers,sK3(A)))
| subpopulations(first_movers,efficient_producers,A,sK2(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_15,plain,
( in_environment(A,sK3(A))
| subpopulations(first_movers,efficient_producers,A,sK2(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_earliest_time_growth_rate_exceeds]) ).
cnf(c_16,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_4,c_5]) ).
cnf(c_17,negated_conjecture,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| greater_or_equal(sK2(sK0,A),A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_10]) ).
cnf(c_18,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| greater_or_equal(sK2(sK0,A),A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_11]) ).
cnf(c_19,negated_conjecture,
( in_environment(sK0,sK3(sK0))
| greater_or_equal(sK2(sK0,A),A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_12]) ).
cnf(c_20,negated_conjecture,
stable(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l12_neg]) ).
cnf(c_21,negated_conjecture,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| ~ in_environment(sK0,sK1(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_16,c_17]) ).
cnf(c_22,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| ~ in_environment(sK0,sK1(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_16,c_18]) ).
cnf(c_23,negated_conjecture,
( in_environment(sK0,sK3(sK0))
| ~ in_environment(sK0,sK1(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_16,c_19]) ).
cnf(c_24,negated_conjecture,
( in_environment(sK0,sK1(sK0))
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_25,negated_conjecture,
in_environment(sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_26,negated_conjecture,
( in_environment(sK0,sK3(sK0))
| ~ in_environment(sK0,sK1(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_27,negated_conjecture,
( in_environment(sK0,sK3(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_25,c_26]) ).
cnf(c_28,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| ~ in_environment(sK0,sK1(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_20,c_22]) ).
cnf(c_29,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_25,c_28]) ).
cnf(c_30,negated_conjecture,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| ~ in_environment(sK0,sK1(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_20,c_21]) ).
cnf(c_31,negated_conjecture,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_25,c_30]) ).
cnf(c_32,negated_conjecture,
( in_environment(sK0,sK3(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,A))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_15]) ).
cnf(c_33,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,A))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_14]) ).
cnf(c_34,negated_conjecture,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,A))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_13]) ).
cnf(c_35,negated_conjecture,
( in_environment(sK0,sK3(sK0))
| ~ greater(growth_rate(efficient_producers,sK2(sK0,A)),growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_9]) ).
cnf(c_36,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| ~ greater(growth_rate(efficient_producers,sK2(sK0,A)),growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_8]) ).
cnf(c_37,negated_conjecture,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| ~ greater(growth_rate(efficient_producers,sK2(sK0,A)),growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_38,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK4(A)),growth_rate(first_movers,sK4(A)))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_prove_l12_neg]) ).
cnf(c_39,negated_conjecture,
( greater(sK4(A),A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_prove_l12_neg]) ).
cnf(c_40,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK0,sK4(A))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_prove_l12_neg]) ).
cnf(c_42,plain,
( in_environment(sK0,sK3(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_32,c_25]) ).
cnf(c_43,plain,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_33,c_25]) ).
cnf(c_44,plain,
( in_environment(sK0,sK3(sK0))
| ~ greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_35,c_25]) ).
cnf(c_45,plain,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| ~ greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_36,c_25]) ).
cnf(c_158,negated_conjecture,
( in_environment(sK0,sK3(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| in_environment(sK0,sK3(sK0)) ),
inference(resolve,[status(thm)],[c_42,c_27]) ).
cnf(c_52,negated_conjecture,
( greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| in_environment(sK0,sK3(sK0)) ),
inference(copy,[status(thm)],[c_158]) ).
cnf(c_159,plain,
( in_environment(sK0,sK3(sK0))
| in_environment(sK0,sK3(sK0)) ),
inference(resolve,[status(thm)],[c_52,c_44]) ).
cnf(c_65,plain,
in_environment(sK0,sK3(sK0)),
inference(copy,[status(thm)],[c_159]) ).
cnf(c_66,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK4(sK3(sK0)))
| greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0))) ),
inference(resolve,[status(thm)],[c_65,c_40]) ).
cnf(c_67,plain,
( greater(sK4(sK3(sK0)),sK3(sK0))
| greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0))) ),
inference(resolve,[status(thm)],[c_65,c_39]) ).
cnf(c_68,plain,
( ~ greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0))) ),
inference(resolve,[status(thm)],[c_65,c_38]) ).
cnf(c_71,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| greater(sK4(sK3(sK0)),sK3(sK0)) ),
inference(resolve,[status(thm)],[c_67,c_43]) ).
cnf(c_77,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| subpopulations(first_movers,efficient_producers,sK0,sK4(sK3(sK0))) ),
inference(resolve,[status(thm)],[c_66,c_43]) ).
cnf(c_82,plain,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater(sK4(sK3(sK0)),sK3(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,A))
| ~ in_environment(sK0,A)
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_77,c_34]) ).
cnf(c_160,plain,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater(sK4(sK3(sK0)),sK3(sK0))
| ~ in_environment(sK0,sK1(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(factor,[status(thm)],[c_82]) ).
cnf(c_86,negated_conjecture,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater(sK4(sK3(sK0)),sK3(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_25,c_160]) ).
cnf(c_161,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_86,c_71]) ).
cnf(c_104,plain,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(copy,[status(thm)],[c_161]) ).
cnf(c_109,plain,
( greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_104,c_68]) ).
cnf(c_162,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_109,c_43]) ).
cnf(c_115,plain,
subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_122,negated_conjecture,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_115,c_31]) ).
cnf(c_123,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_115,c_29]) ).
cnf(c_124,plain,
( greater(sK4(sK3(sK0)),sK3(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_123,c_67]) ).
cnf(c_125,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK4(sK3(sK0)))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_123,c_66]) ).
cnf(c_126,plain,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| greater(sK4(sK3(sK0)),sK3(sK0)) ),
inference(resolve,[status(thm)],[c_124,c_45]) ).
cnf(c_163,plain,
( greater(sK4(sK3(sK0)),sK3(sK0))
| greater(sK4(sK3(sK0)),sK3(sK0)) ),
inference(resolve,[status(thm)],[c_126,c_67]) ).
cnf(c_127,plain,
greater(sK4(sK3(sK0)),sK3(sK0)),
inference(copy,[status(thm)],[c_163]) ).
cnf(c_142,plain,
( ~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0)))
| subpopulations(first_movers,efficient_producers,sK0,sK4(sK3(sK0))) ),
inference(resolve,[status(thm)],[c_125,c_45]) ).
cnf(c_164,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK4(sK3(sK0)))
| subpopulations(first_movers,efficient_producers,sK0,sK4(sK3(sK0))) ),
inference(resolve,[status(thm)],[c_142,c_66]) ).
cnf(c_145,plain,
subpopulations(first_movers,efficient_producers,sK0,sK4(sK3(sK0))),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_165,negated_conjecture,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater(sK4(sK3(sK0)),sK3(sK0))
| ~ greater(growth_rate(efficient_producers,sK2(sK0,A)),growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_145,c_37]) ).
cnf(c_146,negated_conjecture,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater(growth_rate(efficient_producers,sK2(sK0,A)),growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_127,c_165]) ).
cnf(c_149,plain,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_146,c_25]) ).
cnf(c_166,negated_conjecture,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater(sK4(sK3(sK0)),sK3(sK0))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_122,c_145]) ).
cnf(c_150,negated_conjecture,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_127,c_166]) ).
cnf(c_167,plain,
( greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0))))
| greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0)))) ),
inference(resolve,[status(thm)],[c_150,c_149]) ).
cnf(c_152,plain,
greater(growth_rate(efficient_producers,sK4(sK3(sK0))),growth_rate(first_movers,sK4(sK3(sK0)))),
inference(copy,[status(thm)],[c_167]) ).
cnf(c_154,plain,
greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0))),
inference(resolve,[status(thm)],[c_152,c_68]) ).
cnf(c_155,negated_conjecture,
greater(growth_rate(efficient_producers,sK2(sK0,sK1(sK0))),growth_rate(first_movers,sK2(sK0,sK1(sK0)))),
inference(resolve,[status(thm)],[c_154,c_123]) ).
cnf(c_168,negated_conjecture,
~ greater(growth_rate(efficient_producers,sK3(sK0)),growth_rate(first_movers,sK3(sK0))),
inference(resolve,[status(thm)],[c_155,c_45]) ).
cnf(c_157,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_154,c_168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/15.43 % Computer : n004.cluster.edu
% 0.15/15.43 % Model : x86_64 x86_64
% 0.15/15.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.43 % Memory : 8046.5625MB
% 0.15/15.43 % OS : Linux 6.8.0-71-generic
% 0.15/15.43 % CPULimit : 300
% 0.15/15.43 % WCLimit : 300
% 0.15/15.43 % DateTime : Sat Sep 26 00:05:23 UTC 2026
% 0.15/15.44 % CPUTime :
% 0.15/15.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/15.44 % Process 300495 was started by sandbox2 on n004,
% 0.15/15.44 % Sat Sep 26 00:05:23 2026
% 0.15/15.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/15.44
% 0.15/15.44 % From the command line: assign(max_seconds, 300).
% 0.15/15.46
% 0.15/15.46 % SZS status Theorem for theBenchmark
% 0.15/15.46
% 0.15/15.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/15.46 % Length of proof is 71.
% 0.15/15.46 % Level of proof is 24.
% 0.15/15.46 % Maximum clause weight is 57.000.
% 0.15/15.46 % Given clauses 61.
% 0.15/15.46
% 0.15/15.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------