%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT030-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 97 ( 13 unt; 0 def)
% Number of atoms : 338 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 401 ( 160 ~; 241 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 73 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l12_12,axiom,
environment(sk4),
file('theBenchmark.p',prove_l12_12) ).
cnf(c_1,plain,
environment(sk4),
inference(clausify,[status(thm)],[prove_l12_12]) ).
fof(l1_11,axiom,
! [VAR_0,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ greater_or_equal(VAR_1,sk3(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l1_11) ).
cnf(c_2,plain,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk3(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l1_11]) ).
fof(l1_10,axiom,
! [VAR_0] :
( in_environment(VAR_0,sk3(VAR_0))
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l1_10) ).
cnf(c_3,plain,
( in_environment(A,sk3(A))
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l1_10]) ).
fof(mp_earliest_time_growth_rate_exceeds_9,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(growth_rate(efficient_producers,VAR_2),growth_rate(first_movers,VAR_2))
| ~ greater(VAR_2,sk2(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| ~ greater(growth_rate(efficient_producers,sk1(VAR_1,VAR_0)),growth_rate(first_movers,sk1(VAR_1,VAR_0)))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds_9) ).
cnf(c_4,plain,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_growth_rate_exceeds_9]) ).
fof(mp_earliest_time_growth_rate_exceeds_8,axiom,
! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,sk2(VAR_0)),growth_rate(first_movers,sk2(VAR_0)))
| ~ greater(growth_rate(efficient_producers,sk1(VAR_1,VAR_0)),growth_rate(first_movers,sk1(VAR_1,VAR_0)))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds_8) ).
cnf(c_5,plain,
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_growth_rate_exceeds_8]) ).
fof(mp_earliest_time_growth_rate_exceeds_7,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,sk2(VAR_0))
| ~ greater(growth_rate(efficient_producers,sk1(VAR_1,VAR_0)),growth_rate(first_movers,sk1(VAR_1,VAR_0)))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds_7) ).
cnf(c_6,plain,
( in_environment(A,sk2(A))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_growth_rate_exceeds_7]) ).
fof(mp_earliest_time_growth_rate_exceeds_6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(growth_rate(efficient_producers,VAR_2),growth_rate(first_movers,VAR_2))
| ~ greater(VAR_2,sk2(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| greater_or_equal(sk1(VAR_1,VAR_0),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds_6) ).
cnf(c_7,plain,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_growth_rate_exceeds_6]) ).
fof(mp_earliest_time_growth_rate_exceeds_5,axiom,
! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,sk2(VAR_0)),growth_rate(first_movers,sk2(VAR_0)))
| greater_or_equal(sk1(VAR_1,VAR_0),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds_5) ).
cnf(c_8,plain,
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_growth_rate_exceeds_5]) ).
fof(mp_earliest_time_growth_rate_exceeds_4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(growth_rate(efficient_producers,VAR_2),growth_rate(first_movers,VAR_2))
| ~ greater(VAR_2,sk2(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
| subpopulations(first_movers,efficient_producers,VAR_0,sk1(VAR_1,VAR_0))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds_4) ).
cnf(c_9,plain,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_growth_rate_exceeds_4]) ).
fof(mp_earliest_time_growth_rate_exceeds_3,axiom,
! [VAR_0,VAR_1] :
( ~ greater(growth_rate(efficient_producers,sk2(VAR_0)),growth_rate(first_movers,sk2(VAR_0)))
| subpopulations(first_movers,efficient_producers,VAR_0,sk1(VAR_1,VAR_0))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds_3) ).
cnf(c_10,plain,
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_growth_rate_exceeds_3]) ).
fof(mp_earliest_time_growth_rate_exceeds_2,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,sk2(VAR_0))
| greater_or_equal(sk1(VAR_1,VAR_0),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds_2) ).
cnf(c_11,plain,
( in_environment(A,sk2(A))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_growth_rate_exceeds_2]) ).
fof(mp_earliest_time_growth_rate_exceeds_1,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,sk2(VAR_0))
| subpopulations(first_movers,efficient_producers,VAR_0,sk1(VAR_1,VAR_0))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_growth_rate_exceeds_1) ).
cnf(c_12,plain,
( in_environment(A,sk2(A))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_growth_rate_exceeds_1]) ).
cnf(c_13,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater_or_equal(A,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,A)
| ~ stable(sk4) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_14,plain,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,B)
| greater_or_equal(sk1(A,sk4),A)
| ~ in_environment(sk4,A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_15,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater_or_equal(sk1(A,sk4),A)
| ~ in_environment(sk4,A) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_16,plain,
( in_environment(sk4,sk2(sk4))
| greater_or_equal(sk1(A,sk4),A)
| ~ in_environment(sk4,A) ),
inference(resolve,[status(thm)],[c_1,c_11]) ).
fof(prove_l12_13,axiom,
stable(sk4),
file('theBenchmark.p',prove_l12_13) ).
cnf(c_17,plain,
stable(sk4),
inference(clausify,[status(thm)],[prove_l12_13]) ).
cnf(c_18,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,A)
| ~ in_environment(sk4,sk3(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ stable(sk4) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
cnf(c_19,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ in_environment(sk4,sk3(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ stable(sk4) ),
inference(resolve,[status(thm)],[c_13,c_15]) ).
cnf(c_20,plain,
( in_environment(sk4,sk2(sk4))
| ~ in_environment(sk4,sk3(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ stable(sk4) ),
inference(resolve,[status(thm)],[c_13,c_16]) ).
cnf(c_21,plain,
( in_environment(sk4,sk3(sk4))
| ~ stable(sk4) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_22,plain,
in_environment(sk4,sk3(sk4)),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_23,plain,
( in_environment(sk4,sk2(sk4))
| ~ in_environment(sk4,sk3(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolve,[status(thm)],[c_17,c_20]) ).
cnf(c_24,plain,
( in_environment(sk4,sk2(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolve,[status(thm)],[c_22,c_23]) ).
cnf(c_25,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ in_environment(sk4,sk3(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolve,[status(thm)],[c_17,c_19]) ).
cnf(c_26,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolve,[status(thm)],[c_22,c_25]) ).
cnf(c_27,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,A)
| ~ in_environment(sk4,sk3(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_28,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,A)
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolve,[status(thm)],[c_22,c_27]) ).
cnf(c_29,plain,
( in_environment(sk4,sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(A,sk4))
| ~ in_environment(sk4,A) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_30,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk1(A,sk4))
| ~ in_environment(sk4,A) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_31,plain,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,B)
| subpopulations(first_movers,efficient_producers,sk4,sk1(A,sk4))
| ~ in_environment(sk4,A) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_32,plain,
( in_environment(sk4,sk2(sk4))
| ~ greater(growth_rate(efficient_producers,sk1(A,sk4)),growth_rate(first_movers,sk1(A,sk4)))
| ~ in_environment(sk4,A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_33,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ greater(growth_rate(efficient_producers,sk1(A,sk4)),growth_rate(first_movers,sk1(A,sk4)))
| ~ in_environment(sk4,A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_34,plain,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,B)
| ~ greater(growth_rate(efficient_producers,sk1(A,sk4)),growth_rate(first_movers,sk1(A,sk4)))
| ~ in_environment(sk4,A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
fof(prove_l12_16,axiom,
! [VAR_0] :
( ~ greater(growth_rate(efficient_producers,sk5(VAR_0)),growth_rate(first_movers,sk5(VAR_0)))
| greater(growth_rate(efficient_producers,VAR_0),growth_rate(first_movers,VAR_0))
| ~ in_environment(sk4,VAR_0) ),
file('theBenchmark.p',prove_l12_16) ).
cnf(c_35,plain,
( ~ greater(growth_rate(efficient_producers,sk5(A)),growth_rate(first_movers,sk5(A)))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
inference(clausify,[status(thm)],[prove_l12_16]) ).
fof(prove_l12_15,axiom,
! [VAR_0] :
( greater(sk5(VAR_0),VAR_0)
| greater(growth_rate(efficient_producers,VAR_0),growth_rate(first_movers,VAR_0))
| ~ in_environment(sk4,VAR_0) ),
file('theBenchmark.p',prove_l12_15) ).
cnf(c_36,plain,
( greater(sk5(A),A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
inference(clausify,[status(thm)],[prove_l12_15]) ).
fof(prove_l12_14,axiom,
! [VAR_0] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(VAR_0))
| greater(growth_rate(efficient_producers,VAR_0),growth_rate(first_movers,VAR_0))
| ~ in_environment(sk4,VAR_0) ),
file('theBenchmark.p',prove_l12_14) ).
cnf(c_37,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(A))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
inference(clausify,[status(thm)],[prove_l12_14]) ).
cnf(c_39,plain,
( in_environment(sk4,sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolve,[status(thm)],[c_29,c_22]) ).
cnf(c_40,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolve,[status(thm)],[c_30,c_22]) ).
cnf(c_41,plain,
( in_environment(sk4,sk2(sk4))
| ~ greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_32,c_22]) ).
cnf(c_42,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_97,plain,
( in_environment(sk4,sk2(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| in_environment(sk4,sk2(sk4)) ),
inference(resolve,[status(thm)],[c_39,c_24]) ).
cnf(c_49,plain,
( greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| in_environment(sk4,sk2(sk4)) ),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_53,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_49,c_37]) ).
cnf(c_54,plain,
( greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_49,c_36]) ).
cnf(c_55,plain,
( ~ greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_49,c_35]) ).
cnf(c_59,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(A,sk4))
| ~ in_environment(sk4,A)
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_53,c_31]) ).
cnf(c_98,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_53,c_28]) ).
cnf(c_60,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_98]) ).
cnf(c_66,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_59,c_22]) ).
cnf(c_99,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_66,c_54]) ).
cnf(c_100,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_99]) ).
cnf(c_72,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_100]) ).
cnf(c_101,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_72,c_60]) ).
cnf(c_102,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_101]) ).
cnf(c_103,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_73,plain,
( ~ greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_103]) ).
cnf(c_104,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_73,c_54]) ).
cnf(c_105,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_104]) ).
cnf(c_78,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_106,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_78,c_55]) ).
cnf(c_107,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_79,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_107]) ).
cnf(c_81,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_79,c_40]) ).
cnf(c_108,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_81,c_26]) ).
cnf(c_88,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(copy,[status(thm)],[c_108]) ).
cnf(c_109,plain,
( greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_88,c_79]) ).
cnf(c_89,plain,
greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))),
inference(copy,[status(thm)],[c_109]) ).
cnf(c_91,plain,
~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))),
inference(resolve,[status(thm)],[c_89,c_42]) ).
cnf(c_92,plain,
in_environment(sk4,sk2(sk4)),
inference(resolve,[status(thm)],[c_89,c_41]) ).
cnf(c_110,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(resolve,[status(thm)],[c_92,c_37]) ).
cnf(c_93,plain,
subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
inference(resolve,[status(thm)],[c_91,c_110]) ).
cnf(c_111,plain,
( greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(resolve,[status(thm)],[c_92,c_36]) ).
cnf(c_94,plain,
greater(sk5(sk2(sk4)),sk2(sk4)),
inference(resolve,[status(thm)],[c_91,c_111]) ).
cnf(c_112,plain,
( ~ greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(resolve,[status(thm)],[c_92,c_35]) ).
cnf(c_95,plain,
~ greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4)))),
inference(resolve,[status(thm)],[c_91,c_112]) ).
cnf(c_113,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,A)
| ~ greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolve,[status(thm)],[c_34,c_22]) ).
cnf(c_114,plain,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(A,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,A) ),
inference(resolve,[status(thm)],[c_113,c_89]) ).
cnf(c_115,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(resolve,[status(thm)],[c_114,c_94]) ).
cnf(c_116,plain,
~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
inference(resolve,[status(thm)],[c_115,c_95]) ).
cnf(c_96,plain,
$false,
inference(resolve,[status(thm)],[c_93,c_116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT030-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 00:08:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2607604 was started by sandbox on n015,
% 0.09/0.37 % Sat Sep 26 00:08:44 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 61.
% 0.09/0.39 % Level of proof is 18.
% 0.09/0.39 % Maximum clause weight is 49.000.
% 0.09/0.39 % Given clauses 53.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------