%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT024-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Unsatisfiable 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of formulae : 102 ( 18 unt; 0 def)
% Number of atoms : 329 ( 65 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 360 ( 133 ~; 227 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l6_39,axiom,
environment(sk1),
file('theBenchmark.p',prove_l6_39) ).
cnf(c_1,plain,
environment(sk1),
inference(clausify,[status(thm)],[prove_l6_39]) ).
fof(l7_38,axiom,
! [VAR_0,VAR_1] :
( greater(zero,growth_rate(first_movers,VAR_1))
| greater(zero,growth_rate(efficient_producers,VAR_1))
| growth_rate(efficient_producers,VAR_1) = zero
| ~ constant(number_of_organizations(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l7_38) ).
cnf(c_2,plain,
( greater(zero,growth_rate(first_movers,B))
| greater(zero,growth_rate(efficient_producers,B))
| growth_rate(efficient_producers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7_38]) ).
fof(l7_37,axiom,
! [VAR_0,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),zero)
| greater(zero,growth_rate(efficient_producers,VAR_1))
| growth_rate(efficient_producers,VAR_1) = zero
| ~ constant(number_of_organizations(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l7_37) ).
cnf(c_3,plain,
( greater(growth_rate(efficient_producers,B),zero)
| greater(zero,growth_rate(efficient_producers,B))
| growth_rate(efficient_producers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7_37]) ).
fof(l7_36,axiom,
! [VAR_0,VAR_1] :
( greater(zero,growth_rate(first_movers,VAR_1))
| greater(growth_rate(first_movers,VAR_1),zero)
| growth_rate(efficient_producers,VAR_1) = zero
| ~ constant(number_of_organizations(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l7_36) ).
cnf(c_4,plain,
( greater(zero,growth_rate(first_movers,B))
| greater(growth_rate(first_movers,B),zero)
| growth_rate(efficient_producers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7_36]) ).
fof(l7_35,axiom,
! [VAR_0,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),zero)
| greater(growth_rate(first_movers,VAR_1),zero)
| growth_rate(efficient_producers,VAR_1) = zero
| ~ constant(number_of_organizations(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l7_35) ).
cnf(c_5,plain,
( greater(growth_rate(efficient_producers,B),zero)
| greater(growth_rate(first_movers,B),zero)
| growth_rate(efficient_producers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7_35]) ).
fof(l7_34,axiom,
! [VAR_0,VAR_1] :
( greater(zero,growth_rate(first_movers,VAR_1))
| greater(zero,growth_rate(efficient_producers,VAR_1))
| growth_rate(first_movers,VAR_1) = zero
| ~ constant(number_of_organizations(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l7_34) ).
cnf(c_6,plain,
( greater(zero,growth_rate(first_movers,B))
| greater(zero,growth_rate(efficient_producers,B))
| growth_rate(first_movers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7_34]) ).
fof(l7_33,axiom,
! [VAR_0,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),zero)
| greater(zero,growth_rate(efficient_producers,VAR_1))
| growth_rate(first_movers,VAR_1) = zero
| ~ constant(number_of_organizations(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l7_33) ).
cnf(c_7,plain,
( greater(growth_rate(efficient_producers,B),zero)
| greater(zero,growth_rate(efficient_producers,B))
| growth_rate(first_movers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7_33]) ).
fof(l7_32,axiom,
! [VAR_0,VAR_1] :
( greater(zero,growth_rate(first_movers,VAR_1))
| greater(growth_rate(first_movers,VAR_1),zero)
| growth_rate(first_movers,VAR_1) = zero
| ~ constant(number_of_organizations(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l7_32) ).
cnf(c_8,plain,
( greater(zero,growth_rate(first_movers,B))
| greater(growth_rate(first_movers,B),zero)
| growth_rate(first_movers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7_32]) ).
fof(l7_31,axiom,
! [VAR_0,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),zero)
| greater(growth_rate(first_movers,VAR_1),zero)
| growth_rate(first_movers,VAR_1) = zero
| ~ constant(number_of_organizations(VAR_0,VAR_1))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l7_31) ).
cnf(c_9,plain,
( greater(growth_rate(efficient_producers,B),zero)
| greater(growth_rate(first_movers,B),zero)
| growth_rate(first_movers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7_31]) ).
fof(a6_30,axiom,
! [VAR_0,VAR_1] :
( constant(number_of_organizations(VAR_0,VAR_1))
| ~ constant(resources(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a6_30) ).
cnf(c_10,plain,
( constant(number_of_organizations(A,B))
| ~ constant(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a6_30]) ).
fof(a3_28,axiom,
! [VAR_0,VAR_1] :
( constant(resources(VAR_0,VAR_1))
| greater(equilibrium(VAR_0),VAR_1)
| ~ greater(number_of_organizations(VAR_0,VAR_1),zero)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a3_28) ).
cnf(c_12,plain,
( constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a3_28]) ).
fof(mp_equilibrium_26,axiom,
! [VAR_0,VAR_1] :
( ~ greater(equilibrium(VAR_0),VAR_1)
| ~ greater_or_equal(VAR_1,equilibrium(VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_equilibrium_26) ).
cnf(c_14,plain,
( ~ greater(equilibrium(A),B)
| ~ greater_or_equal(B,equilibrium(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_equilibrium_26]) ).
fof(mp_positive_number_of_organizations_25,axiom,
! [VAR_0,VAR_1] :
( greater(number_of_organizations(VAR_0,VAR_1),zero)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_positive_number_of_organizations_25) ).
cnf(c_15,plain,
( greater(number_of_organizations(A,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_positive_number_of_organizations_25]) ).
fof(mp_time_point_occur_24,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,VAR_1)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_time_point_occur_24) ).
cnf(c_16,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_occur_24]) ).
cnf(c_17,plain,
( in_environment(sk1,A)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_18,plain,
( greater(number_of_organizations(sk1,A),zero)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_19,plain,
( ~ greater(equilibrium(sk1),A)
| ~ greater_or_equal(A,equilibrium(sk1)) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_21,plain,
( constant(resources(sk1,A))
| greater(equilibrium(sk1),A)
| ~ greater(number_of_organizations(sk1,A),zero)
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_12]) ).
cnf(c_23,plain,
( constant(number_of_organizations(sk1,A))
| ~ constant(resources(sk1,A))
| ~ in_environment(sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_24,plain,
( greater(growth_rate(efficient_producers,A),zero)
| greater(growth_rate(first_movers,A),zero)
| growth_rate(first_movers,A) = zero
| ~ constant(number_of_organizations(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_25,plain,
( greater(zero,growth_rate(first_movers,A))
| greater(growth_rate(first_movers,A),zero)
| growth_rate(first_movers,A) = zero
| ~ constant(number_of_organizations(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_26,plain,
( greater(growth_rate(efficient_producers,A),zero)
| greater(zero,growth_rate(efficient_producers,A))
| growth_rate(first_movers,A) = zero
| ~ constant(number_of_organizations(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_27,plain,
( greater(zero,growth_rate(first_movers,A))
| greater(zero,growth_rate(efficient_producers,A))
| growth_rate(first_movers,A) = zero
| ~ constant(number_of_organizations(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_28,plain,
( greater(growth_rate(efficient_producers,A),zero)
| greater(growth_rate(first_movers,A),zero)
| growth_rate(efficient_producers,A) = zero
| ~ constant(number_of_organizations(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_29,plain,
( greater(zero,growth_rate(first_movers,A))
| greater(growth_rate(first_movers,A),zero)
| growth_rate(efficient_producers,A) = zero
| ~ constant(number_of_organizations(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_30,plain,
( greater(growth_rate(efficient_producers,A),zero)
| greater(zero,growth_rate(efficient_producers,A))
| growth_rate(efficient_producers,A) = zero
| ~ constant(number_of_organizations(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_31,plain,
( greater(zero,growth_rate(first_movers,A))
| greater(zero,growth_rate(efficient_producers,A))
| growth_rate(efficient_producers,A) = zero
| ~ constant(number_of_organizations(sk1,A))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_l6_44,axiom,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
file('theBenchmark.p',prove_l6_44) ).
cnf(c_32,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(clausify,[status(thm)],[prove_l6_44]) ).
fof(prove_l6_43,axiom,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
file('theBenchmark.p',prove_l6_43) ).
cnf(c_33,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(clausify,[status(thm)],[prove_l6_43]) ).
fof(prove_l6_42,axiom,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
file('theBenchmark.p',prove_l6_42) ).
cnf(c_34,plain,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
inference(clausify,[status(thm)],[prove_l6_42]) ).
fof(prove_l6_41,axiom,
greater_or_equal(sk2,equilibrium(sk1)),
file('theBenchmark.p',prove_l6_41) ).
cnf(c_35,plain,
greater_or_equal(sk2,equilibrium(sk1)),
inference(clausify,[status(thm)],[prove_l6_41]) ).
fof(prove_l6_40,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('theBenchmark.p',prove_l6_40) ).
cnf(c_36,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(clausify,[status(thm)],[prove_l6_40]) ).
cnf(c_37,plain,
~ greater(equilibrium(sk1),sk2),
inference(resolve,[status(thm)],[c_35,c_19]) ).
cnf(c_38,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(efficient_producers,sk2) = zero
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_36,c_31]) ).
cnf(c_39,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(efficient_producers,sk2) = zero
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_36,c_30]) ).
cnf(c_40,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| growth_rate(efficient_producers,sk2) = zero
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_36,c_29]) ).
cnf(c_41,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero)
| growth_rate(efficient_producers,sk2) = zero
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_36,c_28]) ).
cnf(c_42,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(first_movers,sk2) = zero
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_36,c_27]) ).
cnf(c_43,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(first_movers,sk2) = zero
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_36,c_26]) ).
cnf(c_44,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| growth_rate(first_movers,sk2) = zero
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_36,c_25]) ).
cnf(c_45,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero)
| growth_rate(first_movers,sk2) = zero
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_36,c_24]) ).
cnf(c_46,plain,
greater(number_of_organizations(sk1,sk2),zero),
inference(resolve,[status(thm)],[c_36,c_18]) ).
cnf(c_47,plain,
in_environment(sk1,sk2),
inference(resolve,[status(thm)],[c_36,c_17]) ).
cnf(c_48,plain,
( constant(number_of_organizations(sk1,sk2))
| ~ constant(resources(sk1,sk2)) ),
inference(resolve,[status(thm)],[c_47,c_23]) ).
cnf(c_90,plain,
( constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero) ),
inference(resolve,[status(thm)],[c_47,c_21]) ).
cnf(c_91,plain,
( constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2) ),
inference(resolve,[status(thm)],[c_46,c_90]) ).
cnf(c_50,plain,
constant(resources(sk1,sk2)),
inference(resolve,[status(thm)],[c_37,c_91]) ).
cnf(c_51,plain,
constant(number_of_organizations(sk1,sk2)),
inference(resolve,[status(thm)],[c_50,c_48]) ).
cnf(c_52,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero)
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_51,c_45]) ).
cnf(c_53,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_51,c_44]) ).
cnf(c_54,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_51,c_43]) ).
cnf(c_55,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_51,c_42]) ).
cnf(c_56,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero)
| growth_rate(efficient_producers,sk2) = zero ),
inference(resolve,[status(thm)],[c_51,c_41]) ).
cnf(c_57,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| growth_rate(efficient_producers,sk2) = zero ),
inference(resolve,[status(thm)],[c_51,c_40]) ).
cnf(c_58,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(efficient_producers,sk2) = zero ),
inference(resolve,[status(thm)],[c_51,c_39]) ).
cnf(c_59,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(efficient_producers,sk2) = zero ),
inference(resolve,[status(thm)],[c_51,c_38]) ).
cnf(c_60,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero)
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_52,c_33]) ).
cnf(c_61,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_53,c_33]) ).
cnf(c_62,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_54,c_32]) ).
cnf(c_63,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero)
| growth_rate(efficient_producers,sk2) = zero ),
inference(resolve,[status(thm)],[c_56,c_33]) ).
cnf(c_64,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2))
| growth_rate(efficient_producers,sk2) = zero ),
inference(resolve,[status(thm)],[c_57,c_33]) ).
cnf(c_65,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(efficient_producers,sk2) = zero ),
inference(resolve,[status(thm)],[c_58,c_32]) ).
cnf(c_92,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(first_movers,sk2) = zero
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_62,c_55]) ).
cnf(c_93,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_67,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
( greater(zero,growth_rate(first_movers,sk2))
| growth_rate(first_movers,sk2) = zero
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_67,c_61]) ).
cnf(c_70,plain,
( greater(zero,growth_rate(first_movers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_95,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| growth_rate(first_movers,sk2) = zero
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_67,c_60]) ).
cnf(c_71,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| growth_rate(first_movers,sk2) = zero ),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_72,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_71,c_32]) ).
cnf(c_96,plain,
( growth_rate(first_movers,sk2) = zero
| growth_rate(first_movers,sk2) = zero ),
inference(resolve,[status(thm)],[c_72,c_70]) ).
cnf(c_73,plain,
growth_rate(first_movers,sk2) = zero,
inference(copy,[status(thm)],[c_96]) ).
cnf(c_74,plain,
growth_rate(efficient_producers,sk2) != zero,
inference(resolve,[status(thm)],[c_73,c_34]) ).
cnf(c_75,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_74,c_65]) ).
cnf(c_76,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(resolve,[status(thm)],[c_74,c_64]) ).
cnf(c_77,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) ),
inference(resolve,[status(thm)],[c_74,c_63]) ).
cnf(c_78,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_74,c_59]) ).
cnf(c_97,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(resolve,[status(thm)],[c_78,c_75]) ).
cnf(c_84,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_86,plain,
greater(growth_rate(efficient_producers,sk2),zero),
inference(resolve,[status(thm)],[c_84,c_77]) ).
cnf(c_87,plain,
greater(zero,growth_rate(first_movers,sk2)),
inference(resolve,[status(thm)],[c_84,c_76]) ).
cnf(c_98,plain,
~ greater(zero,growth_rate(first_movers,sk2)),
inference(resolve,[status(thm)],[c_86,c_32]) ).
cnf(c_89,plain,
$false,
inference(resolve,[status(thm)],[c_87,c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT024-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n009.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 00:04:29 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.45 % Process 2887916 was started by sandbox2 on n009,
% 0.16/0.45 % Sat Sep 26 00:04:29 2026
% 0.16/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 0.16/0.47
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.47 % Length of proof is 74.
% 0.16/0.47 % Level of proof is 15.
% 0.16/0.47 % Maximum clause weight is 34.000.
% 0.16/0.47 % Given clauses 53.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------