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Prover9---2026-6A.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : Prover9---2026-6A
% Problem  : MGT028-1 : 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 : 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 08:02:11 AM UTC 2026

% Result   : Unsatisfiable 0.10s 0.39s
% Output   : CNFRefutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   75 (  12 unt;   0 def)
%            Number of atoms       :  252 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  307 ( 130   ~; 177   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 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   :   66 (   0 sgn  21   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_l10_10,axiom,
    environment(sk4),
    file('theBenchmark.p',prove_l10_10) ).

cnf(c_1,plain,
    environment(sk4),
    inference(clausify,[status(thm)],[prove_l10_10]) ).

fof(l11_9,axiom,
    ! [VAR_0,VAR_1] :
      ( greater(zero,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',l11_9) ).

cnf(c_2,plain,
    ( greater(zero,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)],[l11_9]) ).

fof(l11_7,axiom,
    ! [VAR_0] :
      ( in_environment(VAR_0,sk3(VAR_0))
      | ~ stable(VAR_0)
      | ~ environment(VAR_0) ),
    file('theBenchmark.p',l11_7) ).

cnf(c_4,plain,
    ( in_environment(A,sk3(A))
    | ~ stable(A)
    | ~ environment(A) ),
    inference(clausify,[status(thm)],[l11_7]) ).

fof(mp_first_movers_negative_growth_6,axiom,
    ! [VAR_0,VAR_1,VAR_2] :
      ( greater(zero,growth_rate(first_movers,VAR_2))
      | ~ greater_or_equal(VAR_2,sk2(VAR_0))
      | ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_2)
      | ~ greater(zero,growth_rate(first_movers,sk1(VAR_1,VAR_0)))
      | ~ in_environment(VAR_0,VAR_1)
      | ~ stable(VAR_0)
      | ~ environment(VAR_0) ),
    file('theBenchmark.p',mp_first_movers_negative_growth_6) ).

cnf(c_5,plain,
    ( greater(zero,growth_rate(first_movers,C))
    | ~ greater_or_equal(C,sk2(A))
    | ~ subpopulations(first_movers,efficient_producers,A,C)
    | ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
    | ~ in_environment(A,B)
    | ~ stable(A)
    | ~ environment(A) ),
    inference(clausify,[status(thm)],[mp_first_movers_negative_growth_6]) ).

fof(mp_first_movers_negative_growth_5,axiom,
    ! [VAR_0,VAR_1] :
      ( greater(sk2(VAR_0),appear(efficient_producers,VAR_0))
      | ~ greater(zero,growth_rate(first_movers,sk1(VAR_1,VAR_0)))
      | ~ in_environment(VAR_0,VAR_1)
      | ~ stable(VAR_0)
      | ~ environment(VAR_0) ),
    file('theBenchmark.p',mp_first_movers_negative_growth_5) ).

cnf(c_6,plain,
    ( greater(sk2(A),appear(efficient_producers,A))
    | ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
    | ~ in_environment(A,B)
    | ~ stable(A)
    | ~ environment(A) ),
    inference(clausify,[status(thm)],[mp_first_movers_negative_growth_5]) ).

fof(mp_first_movers_negative_growth_4,axiom,
    ! [VAR_0,VAR_1,VAR_2] :
      ( greater(zero,growth_rate(first_movers,VAR_2))
      | ~ greater_or_equal(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)
      | ~ stable(VAR_0)
      | ~ environment(VAR_0) ),
    file('theBenchmark.p',mp_first_movers_negative_growth_4) ).

cnf(c_7,plain,
    ( greater(zero,growth_rate(first_movers,C))
    | ~ greater_or_equal(C,sk2(A))
    | ~ subpopulations(first_movers,efficient_producers,A,C)
    | greater_or_equal(sk1(B,A),B)
    | ~ in_environment(A,B)
    | ~ stable(A)
    | ~ environment(A) ),
    inference(clausify,[status(thm)],[mp_first_movers_negative_growth_4]) ).

fof(mp_first_movers_negative_growth_3,axiom,
    ! [VAR_0,VAR_1,VAR_2] :
      ( greater(zero,growth_rate(first_movers,VAR_2))
      | ~ greater_or_equal(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)
      | ~ stable(VAR_0)
      | ~ environment(VAR_0) ),
    file('theBenchmark.p',mp_first_movers_negative_growth_3) ).

cnf(c_8,plain,
    ( greater(zero,growth_rate(first_movers,C))
    | ~ greater_or_equal(C,sk2(A))
    | ~ subpopulations(first_movers,efficient_producers,A,C)
    | subpopulations(first_movers,efficient_producers,A,sk1(B,A))
    | ~ in_environment(A,B)
    | ~ stable(A)
    | ~ environment(A) ),
    inference(clausify,[status(thm)],[mp_first_movers_negative_growth_3]) ).

fof(mp_first_movers_negative_growth_2,axiom,
    ! [VAR_0,VAR_1] :
      ( greater(sk2(VAR_0),appear(efficient_producers,VAR_0))
      | greater_or_equal(sk1(VAR_1,VAR_0),VAR_1)
      | ~ in_environment(VAR_0,VAR_1)
      | ~ stable(VAR_0)
      | ~ environment(VAR_0) ),
    file('theBenchmark.p',mp_first_movers_negative_growth_2) ).

cnf(c_9,plain,
    ( greater(sk2(A),appear(efficient_producers,A))
    | greater_or_equal(sk1(B,A),B)
    | ~ in_environment(A,B)
    | ~ stable(A)
    | ~ environment(A) ),
    inference(clausify,[status(thm)],[mp_first_movers_negative_growth_2]) ).

fof(mp_first_movers_negative_growth_1,axiom,
    ! [VAR_0,VAR_1] :
      ( greater(sk2(VAR_0),appear(efficient_producers,VAR_0))
      | subpopulations(first_movers,efficient_producers,VAR_0,sk1(VAR_1,VAR_0))
      | ~ in_environment(VAR_0,VAR_1)
      | ~ stable(VAR_0)
      | ~ environment(VAR_0) ),
    file('theBenchmark.p',mp_first_movers_negative_growth_1) ).

cnf(c_10,plain,
    ( greater(sk2(A),appear(efficient_producers,A))
    | subpopulations(first_movers,efficient_producers,A,sk1(B,A))
    | ~ in_environment(A,B)
    | ~ stable(A)
    | ~ environment(A) ),
    inference(clausify,[status(thm)],[mp_first_movers_negative_growth_1]) ).

fof(prove_l10_11,axiom,
    stable(sk4),
    file('theBenchmark.p',prove_l10_11) ).

cnf(c_11,plain,
    stable(sk4),
    inference(clausify,[status(thm)],[prove_l10_11]) ).

cnf(c_12,plain,
    ( greater(zero,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,
    ( in_environment(sk4,sk3(sk4))
    | ~ stable(sk4) ),
    inference(resolve,[status(thm)],[c_1,c_4]) ).

cnf(c_15,plain,
    ( greater(zero,growth_rate(first_movers,B))
    | ~ greater_or_equal(B,sk2(sk4))
    | ~ subpopulations(first_movers,efficient_producers,sk4,B)
    | ~ greater(zero,growth_rate(first_movers,sk1(A,sk4)))
    | ~ in_environment(sk4,A)
    | ~ stable(sk4) ),
    inference(resolve,[status(thm)],[c_1,c_5]) ).

cnf(c_16,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | ~ greater(zero,growth_rate(first_movers,sk1(A,sk4)))
    | ~ in_environment(sk4,A)
    | ~ stable(sk4) ),
    inference(resolve,[status(thm)],[c_1,c_6]) ).

cnf(c_17,plain,
    ( greater(zero,growth_rate(first_movers,B))
    | ~ greater_or_equal(B,sk2(sk4))
    | ~ subpopulations(first_movers,efficient_producers,sk4,B)
    | greater_or_equal(sk1(A,sk4),A)
    | ~ in_environment(sk4,A)
    | ~ stable(sk4) ),
    inference(resolve,[status(thm)],[c_1,c_7]) ).

cnf(c_18,plain,
    ( greater(zero,growth_rate(first_movers,B))
    | ~ greater_or_equal(B,sk2(sk4))
    | ~ subpopulations(first_movers,efficient_producers,sk4,B)
    | subpopulations(first_movers,efficient_producers,sk4,sk1(A,sk4))
    | ~ in_environment(sk4,A)
    | ~ stable(sk4) ),
    inference(resolve,[status(thm)],[c_1,c_8]) ).

cnf(c_19,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | greater_or_equal(sk1(A,sk4),A)
    | ~ in_environment(sk4,A)
    | ~ stable(sk4) ),
    inference(resolve,[status(thm)],[c_1,c_9]) ).

cnf(c_20,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | subpopulations(first_movers,efficient_producers,sk4,sk1(A,sk4))
    | ~ in_environment(sk4,A)
    | ~ stable(sk4) ),
    inference(resolve,[status(thm)],[c_1,c_10]) ).

cnf(c_21,plain,
    in_environment(sk4,sk3(sk4)),
    inference(resolve,[status(thm)],[c_11,c_14]) ).

cnf(c_22,plain,
    ( greater(zero,growth_rate(first_movers,B))
    | ~ greater_or_equal(B,sk2(sk4))
    | ~ subpopulations(first_movers,efficient_producers,sk4,B)
    | ~ greater(zero,growth_rate(first_movers,sk1(A,sk4)))
    | ~ in_environment(sk4,A) ),
    inference(resolve,[status(thm)],[c_11,c_15]) ).

cnf(c_23,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | ~ greater(zero,growth_rate(first_movers,sk1(A,sk4)))
    | ~ in_environment(sk4,A) ),
    inference(resolve,[status(thm)],[c_11,c_16]) ).

cnf(c_24,plain,
    ( greater(zero,growth_rate(first_movers,B))
    | ~ greater_or_equal(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_11,c_17]) ).

cnf(c_25,plain,
    ( greater(zero,growth_rate(first_movers,B))
    | ~ greater_or_equal(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_11,c_18]) ).

cnf(c_26,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | greater_or_equal(sk1(A,sk4),A)
    | ~ in_environment(sk4,A) ),
    inference(resolve,[status(thm)],[c_11,c_19]) ).

cnf(c_27,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | subpopulations(first_movers,efficient_producers,sk4,sk1(A,sk4))
    | ~ in_environment(sk4,A) ),
    inference(resolve,[status(thm)],[c_11,c_20]) ).

cnf(c_28,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
    inference(resolve,[status(thm)],[c_21,c_27]) ).

cnf(c_29,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
    inference(resolve,[status(thm)],[c_21,c_26]) ).

cnf(c_30,plain,
    ( greater(zero,growth_rate(first_movers,A))
    | ~ greater_or_equal(A,sk2(sk4))
    | ~ subpopulations(first_movers,efficient_producers,sk4,A)
    | subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
    inference(resolve,[status(thm)],[c_21,c_25]) ).

cnf(c_31,plain,
    ( greater(zero,growth_rate(first_movers,A))
    | ~ greater_or_equal(A,sk2(sk4))
    | ~ subpopulations(first_movers,efficient_producers,sk4,A)
    | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
    inference(resolve,[status(thm)],[c_21,c_24]) ).

cnf(c_32,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_21,c_23]) ).

cnf(c_33,plain,
    ( greater(zero,growth_rate(first_movers,A))
    | ~ greater_or_equal(A,sk2(sk4))
    | ~ subpopulations(first_movers,efficient_producers,sk4,A)
    | ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_21,c_22]) ).

fof(prove_l10_14,axiom,
    ! [VAR_0] :
      ( ~ greater(zero,growth_rate(first_movers,sk5(VAR_0)))
      | ~ greater(VAR_0,appear(efficient_producers,sk4)) ),
    file('theBenchmark.p',prove_l10_14) ).

cnf(c_34,plain,
    ( ~ greater(zero,growth_rate(first_movers,sk5(A)))
    | ~ greater(A,appear(efficient_producers,sk4)) ),
    inference(clausify,[status(thm)],[prove_l10_14]) ).

fof(prove_l10_13,axiom,
    ! [VAR_0] :
      ( greater_or_equal(sk5(VAR_0),VAR_0)
      | ~ greater(VAR_0,appear(efficient_producers,sk4)) ),
    file('theBenchmark.p',prove_l10_13) ).

cnf(c_35,plain,
    ( greater_or_equal(sk5(A),A)
    | ~ greater(A,appear(efficient_producers,sk4)) ),
    inference(clausify,[status(thm)],[prove_l10_13]) ).

fof(prove_l10_12,axiom,
    ! [VAR_0] :
      ( subpopulations(first_movers,efficient_producers,sk4,sk5(VAR_0))
      | ~ greater(VAR_0,appear(efficient_producers,sk4)) ),
    file('theBenchmark.p',prove_l10_12) ).

cnf(c_36,plain,
    ( subpopulations(first_movers,efficient_producers,sk4,sk5(A))
    | ~ greater(A,appear(efficient_producers,sk4)) ),
    inference(clausify,[status(thm)],[prove_l10_12]) ).

cnf(c_37,plain,
    ( greater(zero,growth_rate(first_movers,A))
    | ~ greater_or_equal(A,sk3(sk4))
    | ~ subpopulations(first_movers,efficient_producers,sk4,A) ),
    inference(resolve,[status(thm)],[c_11,c_12]) ).

cnf(c_39,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
    inference(resolve,[status(thm)],[c_37,c_28]) ).

cnf(c_77,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | greater(sk2(sk4),appear(efficient_producers,sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_39,c_29]) ).

cnf(c_41,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(copy,[status(thm)],[c_77]) ).

cnf(c_42,plain,
    ( subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_41,c_36]) ).

cnf(c_43,plain,
    ( greater_or_equal(sk5(sk2(sk4)),sk2(sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_41,c_35]) ).

cnf(c_44,plain,
    ( ~ greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_41,c_34]) ).

cnf(c_47,plain,
    ( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | ~ greater_or_equal(sk5(sk2(sk4)),sk2(sk4))
    | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_42,c_31]) ).

cnf(c_48,plain,
    ( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | ~ greater_or_equal(sk5(sk2(sk4)),sk2(sk4))
    | subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_42,c_30]) ).

cnf(c_78,plain,
    ( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_47,c_43]) ).

cnf(c_59,plain,
    ( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(copy,[status(thm)],[c_78]) ).

cnf(c_79,plain,
    ( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_48,c_43]) ).

cnf(c_61,plain,
    ( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(copy,[status(thm)],[c_79]) ).

cnf(c_80,plain,
    ( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
    | greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_61,c_37]) ).

cnf(c_63,plain,
    ( ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
    | greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(copy,[status(thm)],[c_80]) ).

cnf(c_81,plain,
    ( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_63,c_59]) ).

cnf(c_82,plain,
    ( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(copy,[status(thm)],[c_81]) ).

cnf(c_64,plain,
    ( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(copy,[status(thm)],[c_82]) ).

cnf(c_83,plain,
    ( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolve,[status(thm)],[c_64,c_44]) ).

cnf(c_66,plain,
    greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))),
    inference(copy,[status(thm)],[c_83]) ).

cnf(c_68,plain,
    ( greater(zero,growth_rate(first_movers,A))
    | ~ greater_or_equal(A,sk2(sk4))
    | ~ subpopulations(first_movers,efficient_producers,sk4,A) ),
    inference(resolve,[status(thm)],[c_66,c_33]) ).

cnf(c_69,plain,
    greater(sk2(sk4),appear(efficient_producers,sk4)),
    inference(resolve,[status(thm)],[c_66,c_32]) ).

cnf(c_70,plain,
    subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
    inference(resolve,[status(thm)],[c_69,c_36]) ).

cnf(c_71,plain,
    greater_or_equal(sk5(sk2(sk4)),sk2(sk4)),
    inference(resolve,[status(thm)],[c_69,c_35]) ).

cnf(c_72,plain,
    ~ greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))),
    inference(resolve,[status(thm)],[c_69,c_34]) ).

cnf(c_84,plain,
    ( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | ~ greater_or_equal(sk5(sk2(sk4)),sk2(sk4)) ),
    inference(resolve,[status(thm)],[c_68,c_70]) ).

cnf(c_85,plain,
    greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))),
    inference(resolve,[status(thm)],[c_71,c_84]) ).

cnf(c_76,plain,
    $false,
    inference(resolve,[status(thm)],[c_72,c_85]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : MGT028-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36  % Computer : n016.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.10/0.36  % CPULimit : 300
% 0.10/0.36  % WCLimit  : 300
% 0.10/0.36  % DateTime : Sat Sep 26 00:09:46 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37  % Process 3627681 was started by sandbox2 on n016,
% 0.10/0.37  % Sat Sep 26 00:09:46 2026
% 0.10/0.37  % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37  
% 0.10/0.37  % From the command line: assign(max_seconds, 300).
% 0.10/0.39  
% 0.10/0.39  % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39  
% 0.10/0.39  % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39  % Length of proof is 53.
% 0.10/0.39  % Level of proof is 14.
% 0.10/0.39  % Maximum clause weight is 29.000.
% 0.10/0.39  % Given clauses 37.
% 0.10/0.39  
% 0.10/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------