%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT028+1 : 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 : n016.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 08:02:10 AM UTC 2026
% Result : Theorem 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 75 ( 10 unt; 0 def)
% Number of atoms : 332 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 416 ( 159 ~; 203 |; 45 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 44 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_first_movers_negative_growth,axiom,
! [E] :
( ( ? [T1] :
( ! [T] :
( ( greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& in_environment(E,T1) )
& stable(E)
& environment(E) )
=> ? [T2] :
( ! [T] :
( ( greater_or_equal(T,T2)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(T2,appear(efficient_producers,E)) ) ),
file('theBenchmark.p',mp_first_movers_negative_growth) ).
fof(l11,axiom,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) ) )
& in_environment(E,To) ) ),
file('theBenchmark.p',l11) ).
fof(prove_l10,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(To,appear(efficient_producers,E)) ) ),
file('theBenchmark.p',prove_l10) ).
fof(prove_l10_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(To,appear(efficient_producers,E)) ) ),
inference(assume_negation,[status(cth)],[prove_l10]) ).
fof(nnf_3,plain,
? [E] :
( ! [To] :
( ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ greater(To,appear(efficient_producers,E)) )
& stable(E)
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_l10_neg]) ).
fof(sk_prove_l10_neg_sk,plain,
( ! [To] :
( ( ~ greater(zero,growth_rate(first_movers,sK4(To)))
& greater_or_equal(sK4(To),To)
& subpopulations(first_movers,efficient_producers,sK0,sK4(To)) )
| ~ greater(To,appear(efficient_producers,sK0)) )
& 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_l10_neg,plain,
( ! [VAR_0] :
( ~ greater(zero,growth_rate(first_movers,sK4(VAR_0)))
| ~ greater(VAR_0,appear(efficient_producers,sK0)) )
& ! [VAR_0] :
( greater_or_equal(sK4(VAR_0),VAR_0)
| ~ greater(VAR_0,appear(efficient_producers,sK0)) )
& ! [VAR_0] :
( subpopulations(first_movers,efficient_producers,sK0,sK4(VAR_0))
| ~ greater(VAR_0,appear(efficient_producers,sK0)) )
& stable(sK0)
& environment(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_prove_l10_neg_sk]) ).
cnf(c_4,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l10_neg]) ).
fof(nnf_2,plain,
! [E] :
( ? [To] :
( ! [T] :
( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ~ 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)],[l11]) ).
fof(sk_l11_sk,plain,
! [E] :
( ( ! [T] :
( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ~ 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_l11,plain,
( ! [VAR_0,VAR_1] :
( greater(zero,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,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),zero)
| ~ 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_l11_sk]) ).
cnf(c_5,plain,
( greater(zero,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_l11]) ).
cnf(c_7,plain,
( in_environment(A,sK1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_l11]) ).
fof(nnf_1,plain,
! [E] :
( ? [T2] :
( ! [T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,T2)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(T2,appear(efficient_producers,E)) )
| ! [T1] :
( ? [X0] :
( ~ greater(zero,growth_rate(first_movers,X0))
& greater_or_equal(X0,T1)
& subpopulations(first_movers,efficient_producers,E,X0) )
| ~ in_environment(E,T1) )
| ~ stable(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[mp_first_movers_negative_growth]) ).
fof(sk_mp_first_movers_negative_growth_sk,plain,
! [E] :
( ( ! [T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,sK3(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(sK3(E),appear(efficient_producers,E)) )
| ! [T1] :
( ( ~ greater(zero,growth_rate(first_movers,sK2(E,T1)))
& greater_or_equal(sK2(E,T1),T1)
& subpopulations(first_movers,efficient_producers,E,sK2(E,T1)) )
| ~ in_environment(E,T1) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2(E,T1)),skolemize(T2,sK3(E))],[nnf_1]) ).
fof(sk_mp_first_movers_negative_growth,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( greater(zero,growth_rate(first_movers,VAR_2))
| ~ greater_or_equal(VAR_2,sK3(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| ~ greater(zero,growth_rate(first_movers,sK2(VAR_0,VAR_1)))
| ~ in_environment(VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( greater(sK3(VAR_0),appear(efficient_producers,VAR_0))
| ~ greater(zero,growth_rate(first_movers,sK2(VAR_0,VAR_1)))
| ~ in_environment(VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( greater(zero,growth_rate(first_movers,VAR_2))
| ~ greater_or_equal(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)
| ~ stable(VAR_0)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( greater(sK3(VAR_0),appear(efficient_producers,VAR_0))
| greater_or_equal(sK2(VAR_0,VAR_1),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( greater(zero,growth_rate(first_movers,VAR_2))
| ~ greater_or_equal(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)
| ~ stable(VAR_0)
| ~ environment(VAR_0) )
& ! [VAR_0,VAR_1] :
( greater(sK3(VAR_0),appear(efficient_producers,VAR_0))
| subpopulations(first_movers,efficient_producers,VAR_0,sK2(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mp_first_movers_negative_growth_sk]) ).
cnf(c_8,plain,
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sK3(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(zero,growth_rate(first_movers,sK2(A,B)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_first_movers_negative_growth]) ).
cnf(c_9,plain,
( greater(sK3(A),appear(efficient_producers,A))
| ~ greater(zero,growth_rate(first_movers,sK2(A,B)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_first_movers_negative_growth]) ).
cnf(c_10,plain,
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sK3(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sK2(A,B),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_first_movers_negative_growth]) ).
cnf(c_11,plain,
( greater(sK3(A),appear(efficient_producers,A))
| greater_or_equal(sK2(A,B),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_first_movers_negative_growth]) ).
cnf(c_12,plain,
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sK3(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sK2(A,B))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_first_movers_negative_growth]) ).
cnf(c_13,plain,
( greater(sK3(A),appear(efficient_producers,A))
| subpopulations(first_movers,efficient_producers,A,sK2(A,B))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_mp_first_movers_negative_growth]) ).
cnf(c_14,negated_conjecture,
stable(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l10_neg]) ).
cnf(c_15,negated_conjecture,
( greater(zero,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,
( in_environment(sK0,sK1(sK0))
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_18,negated_conjecture,
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| ~ greater(zero,growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A)
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_8]) ).
cnf(c_19,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| ~ greater(zero,growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A)
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_9]) ).
cnf(c_20,negated_conjecture,
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| greater_or_equal(sK2(sK0,A),A)
| ~ in_environment(sK0,A)
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_10]) ).
cnf(c_21,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| greater_or_equal(sK2(sK0,A),A)
| ~ in_environment(sK0,A)
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_11]) ).
cnf(c_22,negated_conjecture,
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,A))
| ~ in_environment(sK0,A)
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_12]) ).
cnf(c_23,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,A))
| ~ in_environment(sK0,A)
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_13]) ).
cnf(c_24,negated_conjecture,
in_environment(sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_14,c_17]) ).
cnf(c_25,negated_conjecture,
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,B)
| ~ greater(zero,growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_14,c_18]) ).
cnf(c_26,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| ~ greater(zero,growth_rate(first_movers,sK2(sK0,A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_14,c_19]) ).
cnf(c_27,negated_conjecture,
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(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_14,c_20]) ).
cnf(c_28,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| greater_or_equal(sK2(sK0,A),A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_14,c_21]) ).
cnf(c_29,negated_conjecture,
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(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_14,c_22]) ).
cnf(c_30,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,A))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_14,c_23]) ).
cnf(c_31,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_24,c_30]) ).
cnf(c_32,negated_conjecture,
( greater(zero,growth_rate(first_movers,A))
| ~ greater_or_equal(A,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0))) ),
inference(resolve,[status(thm)],[c_24,c_29]) ).
cnf(c_33,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| greater_or_equal(sK2(sK0,sK1(sK0)),sK1(sK0)) ),
inference(resolve,[status(thm)],[c_24,c_28]) ).
cnf(c_34,negated_conjecture,
( greater(zero,growth_rate(first_movers,A))
| ~ greater_or_equal(A,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| greater_or_equal(sK2(sK0,sK1(sK0)),sK1(sK0)) ),
inference(resolve,[status(thm)],[c_24,c_27]) ).
cnf(c_35,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| ~ greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_24,c_26]) ).
cnf(c_36,negated_conjecture,
( greater(zero,growth_rate(first_movers,A))
| ~ greater_or_equal(A,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| ~ greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_24,c_25]) ).
cnf(c_37,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sK4(A)))
| ~ greater(A,appear(efficient_producers,sK0)) ),
inference(split_conjunct,[status(thm)],[sk_prove_l10_neg]) ).
cnf(c_38,negated_conjecture,
( greater_or_equal(sK4(A),A)
| ~ greater(A,appear(efficient_producers,sK0)) ),
inference(split_conjunct,[status(thm)],[sk_prove_l10_neg]) ).
cnf(c_39,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK0,sK4(A))
| ~ greater(A,appear(efficient_producers,sK0)) ),
inference(split_conjunct,[status(thm)],[sk_prove_l10_neg]) ).
cnf(c_40,negated_conjecture,
( greater(zero,growth_rate(first_movers,A))
| ~ greater_or_equal(A,sK1(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_14,c_15]) ).
cnf(c_42,plain,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ greater_or_equal(sK2(sK0,sK1(sK0)),sK1(sK0)) ),
inference(resolve,[status(thm)],[c_40,c_31]) ).
cnf(c_67,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| greater(sK3(sK0),appear(efficient_producers,sK0))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_42,c_33]) ).
cnf(c_44,negated_conjecture,
( greater(sK3(sK0),appear(efficient_producers,sK0))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_45,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK4(sK3(sK0)))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_44,c_39]) ).
cnf(c_46,plain,
( greater_or_equal(sK4(sK3(sK0)),sK3(sK0))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_44,c_38]) ).
cnf(c_47,plain,
( ~ greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_44,c_37]) ).
cnf(c_50,plain,
( greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater_or_equal(sK4(sK3(sK0)),sK3(sK0))
| greater_or_equal(sK2(sK0,sK1(sK0)),sK1(sK0))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_45,c_34]) ).
cnf(c_51,plain,
( greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater_or_equal(sK4(sK3(sK0)),sK3(sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_45,c_32]) ).
cnf(c_68,plain,
( greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater_or_equal(sK2(sK0,sK1(sK0)),sK1(sK0))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_50,c_46]) ).
cnf(c_53,plain,
( greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater_or_equal(sK2(sK0,sK1(sK0)),sK1(sK0))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,plain,
( greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_51,c_46]) ).
cnf(c_54,plain,
( greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| subpopulations(first_movers,efficient_producers,sK0,sK2(sK0,sK1(sK0)))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_70,negated_conjecture,
( greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| ~ greater_or_equal(sK2(sK0,sK1(sK0)),sK1(sK0))
| greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_54,c_40]) ).
cnf(c_56,negated_conjecture,
( ~ greater_or_equal(sK2(sK0,sK1(sK0)),sK1(sK0))
| greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_71,plain,
( greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_56,c_53]) ).
cnf(c_72,plain,
( greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_57,plain,
( greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_73,plain,
( greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0))))
| greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))) ),
inference(resolve,[status(thm)],[c_57,c_47]) ).
cnf(c_58,plain,
greater(zero,growth_rate(first_movers,sK2(sK0,sK1(sK0)))),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_59,negated_conjecture,
( greater(zero,growth_rate(first_movers,A))
| ~ greater_or_equal(A,sK3(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_58,c_36]) ).
cnf(c_60,negated_conjecture,
greater(sK3(sK0),appear(efficient_producers,sK0)),
inference(resolve,[status(thm)],[c_58,c_35]) ).
cnf(c_61,plain,
subpopulations(first_movers,efficient_producers,sK0,sK4(sK3(sK0))),
inference(resolve,[status(thm)],[c_60,c_39]) ).
cnf(c_62,plain,
greater_or_equal(sK4(sK3(sK0)),sK3(sK0)),
inference(resolve,[status(thm)],[c_60,c_38]) ).
cnf(c_63,plain,
~ greater(zero,growth_rate(first_movers,sK4(sK3(sK0)))),
inference(resolve,[status(thm)],[c_60,c_37]) ).
cnf(c_74,negated_conjecture,
( greater(zero,growth_rate(first_movers,sK4(sK3(sK0))))
| ~ greater_or_equal(sK4(sK3(sK0)),sK3(sK0)) ),
inference(resolve,[status(thm)],[c_59,c_61]) ).
cnf(c_75,negated_conjecture,
greater(zero,growth_rate(first_movers,sK4(sK3(sK0)))),
inference(resolve,[status(thm)],[c_62,c_74]) ).
cnf(c_66,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n016.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Sat Sep 26 00:09:51 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.38 % Process 3627849 was started by sandbox on n016,
% 0.12/5.38 % Sat Sep 26 00:09:51 2026
% 0.12/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/5.39
% 0.12/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.40
% 0.14/5.40 % SZS status Theorem for theBenchmark
% 0.14/5.40
% 0.14/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.40 % Length of proof is 56.
% 0.14/5.40 % Level of proof is 15.
% 0.14/5.40 % Maximum clause weight is 29.000.
% 0.14/5.40 % Given clauses 31.
% 0.14/5.40
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------