TSTP Solution File: MGT027-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : MGT027-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 10:49:36 EDT 2023

% Result   : Unsatisfiable 4.15s 2.33s
% Output   : CNFRefutation 4.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  101 (  15 unt;  16 typ;   0 def)
%            Number of atoms       :  327 (  14 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  465 ( 223   ~; 242   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  12   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  104 (; 104   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > contracts_from > stable > environment > sk1 > growth_rate > cardinality_at_time > appear > #nlpp > sk2 > zero > sk3 > first_movers > efficient_producers

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(subpopulations,type,
    subpopulations: ( $i * $i * $i * $i ) > $o ).

tff(greater,type,
    greater: ( $i * $i ) > $o ).

tff(sk2,type,
    sk2: $i > $i ).

tff(in_environment,type,
    in_environment: ( $i * $i ) > $o ).

tff(appear,type,
    appear: ( $i * $i ) > $i ).

tff(efficient_producers,type,
    efficient_producers: $i ).

tff(contracts_from,type,
    contracts_from: ( $i * $i ) > $o ).

tff(cardinality_at_time,type,
    cardinality_at_time: ( $i * $i ) > $i ).

tff(growth_rate,type,
    growth_rate: ( $i * $i ) > $i ).

tff(environment,type,
    environment: $i > $o ).

tff(first_movers,type,
    first_movers: $i ).

tff(sk3,type,
    sk3: $i ).

tff(greater_or_equal,type,
    greater_or_equal: ( $i * $i ) > $o ).

tff(sk1,type,
    sk1: ( $i * $i ) > $i ).

tff(zero,type,
    zero: $i ).

tff(stable,type,
    stable: $i > $o ).

tff(f_159,axiom,
    environment(sk3),
    file(unknown,unknown) ).

tff(f_160,axiom,
    stable(sk3),
    file(unknown,unknown) ).

tff(f_100,axiom,
    ! [A] :
      ( ~ environment(A)
      | ~ stable(A)
      | in_environment(A,appear(efficient_producers,A)) ),
    file(unknown,unknown) ).

tff(f_144,axiom,
    ! [A] :
      ( ~ environment(A)
      | ~ stable(A)
      | greater(sk2(A),appear(efficient_producers,A)) ),
    file(unknown,unknown) ).

tff(f_92,axiom,
    ! [A,B,C] :
      ( ~ environment(A)
      | ~ stable(A)
      | ~ in_environment(A,B)
      | ~ greater(C,B)
      | in_environment(A,C) ),
    file(unknown,unknown) ).

tff(f_166,axiom,
    ! [A] :
      ( ~ greater(A,appear(efficient_producers,sk3))
      | ~ contracts_from(A,first_movers) ),
    file(unknown,unknown) ).

tff(f_50,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | ~ stable(A)
      | ~ in_environment(A,B)
      | greater_or_equal(sk1(B,A),B)
      | contracts_from(B,first_movers) ),
    file(unknown,unknown) ).

tff(f_115,axiom,
    ! [A,B] :
      ( ~ greater_or_equal(A,B)
      | greater(A,B)
      | ( A = B ) ),
    file(unknown,unknown) ).

tff(f_108,axiom,
    ! [A,B,C] :
      ( ~ greater(A,B)
      | ~ greater(B,C)
      | greater(A,C) ),
    file(unknown,unknown) ).

tff(f_120,axiom,
    ! [A,B] :
      ( ~ greater(A,B)
      | greater_or_equal(A,B) ),
    file(unknown,unknown) ).

tff(f_136,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | ~ in_environment(A,B)
      | ~ greater_or_equal(B,appear(efficient_producers,A))
      | greater(cardinality_at_time(efficient_producers,B),zero) ),
    file(unknown,unknown) ).

tff(f_37,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | ~ stable(A)
      | ~ in_environment(A,B)
      | greater(cardinality_at_time(first_movers,sk1(B,A)),zero)
      | contracts_from(B,first_movers) ),
    file(unknown,unknown) ).

tff(f_78,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | ~ in_environment(A,B)
      | ~ greater(cardinality_at_time(first_movers,B),zero)
      | ~ greater(cardinality_at_time(efficient_producers,B),zero)
      | subpopulations(first_movers,efficient_producers,A,B) ),
    file(unknown,unknown) ).

tff(f_158,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | ~ stable(A)
      | ~ subpopulations(first_movers,efficient_producers,A,B)
      | ~ greater_or_equal(B,sk2(A))
      | greater(zero,growth_rate(first_movers,B)) ),
    file(unknown,unknown) ).

tff(f_64,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | ~ stable(A)
      | ~ in_environment(A,B)
      | ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
      | contracts_from(B,first_movers) ),
    file(unknown,unknown) ).

tff(c_28,plain,
    environment(sk3),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_30,plain,
    stable(sk3),
    inference(cnfTransformation,[status(thm)],[f_160]) ).

tff(c_12,plain,
    ! [A_12] :
      ( in_environment(A_12,appear(efficient_producers,A_12))
      | ~ stable(A_12)
      | ~ environment(A_12) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_24,plain,
    ! [A_24] :
      ( greater(sk2(A_24),appear(efficient_producers,A_24))
      | ~ stable(A_24)
      | ~ environment(A_24) ),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_59,plain,
    ! [A_39,C_40,B_41] :
      ( in_environment(A_39,C_40)
      | ~ greater(C_40,B_41)
      | ~ in_environment(A_39,B_41)
      | ~ stable(A_39)
      | ~ environment(A_39) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_141,plain,
    ! [A_65,A_66] :
      ( in_environment(A_65,sk2(A_66))
      | ~ in_environment(A_65,appear(efficient_producers,A_66))
      | ~ stable(A_65)
      | ~ environment(A_65)
      | ~ stable(A_66)
      | ~ environment(A_66) ),
    inference(resolution,[status(thm)],[c_24,c_59]) ).

tff(c_145,plain,
    ! [A_12] :
      ( in_environment(A_12,sk2(A_12))
      | ~ stable(A_12)
      | ~ environment(A_12) ),
    inference(resolution,[status(thm)],[c_12,c_141]) ).

tff(c_48,plain,
    ! [A_38] :
      ( greater(sk2(A_38),appear(efficient_producers,A_38))
      | ~ stable(A_38)
      | ~ environment(A_38) ),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_32,plain,
    ! [A_27] :
      ( ~ contracts_from(A_27,first_movers)
      | ~ greater(A_27,appear(efficient_producers,sk3)) ),
    inference(cnfTransformation,[status(thm)],[f_166]) ).

tff(c_54,plain,
    ( ~ contracts_from(sk2(sk3),first_movers)
    | ~ stable(sk3)
    | ~ environment(sk3) ),
    inference(resolution,[status(thm)],[c_48,c_32]) ).

tff(c_58,plain,
    ~ contracts_from(sk2(sk3),first_movers),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_30,c_54]) ).

tff(c_78,plain,
    ! [B_45,A_46] :
      ( contracts_from(B_45,first_movers)
      | greater_or_equal(sk1(B_45,A_46),B_45)
      | ~ in_environment(A_46,B_45)
      | ~ stable(A_46)
      | ~ environment(A_46) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_16,plain,
    ! [B_17,A_16] :
      ( ( B_17 = A_16 )
      | greater(A_16,B_17)
      | ~ greater_or_equal(A_16,B_17) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_82,plain,
    ! [B_45,A_46] :
      ( ( sk1(B_45,A_46) = B_45 )
      | greater(sk1(B_45,A_46),B_45)
      | contracts_from(B_45,first_movers)
      | ~ in_environment(A_46,B_45)
      | ~ stable(A_46)
      | ~ environment(A_46) ),
    inference(resolution,[status(thm)],[c_78,c_16]) ).

tff(c_14,plain,
    ! [A_13,C_15,B_14] :
      ( greater(A_13,C_15)
      | ~ greater(B_14,C_15)
      | ~ greater(A_13,B_14) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_63,plain,
    ! [A_42,A_43] :
      ( greater(A_42,appear(efficient_producers,A_43))
      | ~ greater(A_42,sk2(A_43))
      | ~ stable(A_43)
      | ~ environment(A_43) ),
    inference(resolution,[status(thm)],[c_48,c_14]) ).

tff(c_10,plain,
    ! [A_9,C_11,B_10] :
      ( in_environment(A_9,C_11)
      | ~ greater(C_11,B_10)
      | ~ in_environment(A_9,B_10)
      | ~ stable(A_9)
      | ~ environment(A_9) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_235,plain,
    ! [A_87,A_88,A_89] :
      ( in_environment(A_87,A_88)
      | ~ in_environment(A_87,appear(efficient_producers,A_89))
      | ~ stable(A_87)
      | ~ environment(A_87)
      | ~ greater(A_88,sk2(A_89))
      | ~ stable(A_89)
      | ~ environment(A_89) ),
    inference(resolution,[status(thm)],[c_63,c_10]) ).

tff(c_239,plain,
    ! [A_90,A_91] :
      ( in_environment(A_90,A_91)
      | ~ greater(A_91,sk2(A_90))
      | ~ stable(A_90)
      | ~ environment(A_90) ),
    inference(resolution,[status(thm)],[c_12,c_235]) ).

tff(c_244,plain,
    ! [A_90,A_46] :
      ( in_environment(A_90,sk1(sk2(A_90),A_46))
      | ~ stable(A_90)
      | ~ environment(A_90)
      | ( sk1(sk2(A_90),A_46) = sk2(A_90) )
      | contracts_from(sk2(A_90),first_movers)
      | ~ in_environment(A_46,sk2(A_90))
      | ~ stable(A_46)
      | ~ environment(A_46) ),
    inference(resolution,[status(thm)],[c_82,c_239]) ).

tff(c_185,plain,
    ! [B_82,A_83] :
      ( ( sk1(B_82,A_83) = B_82 )
      | greater(sk1(B_82,A_83),B_82)
      | contracts_from(B_82,first_movers)
      | ~ in_environment(A_83,B_82)
      | ~ stable(A_83)
      | ~ environment(A_83) ),
    inference(resolution,[status(thm)],[c_78,c_16]) ).

tff(c_55,plain,
    ! [A_13,A_38] :
      ( greater(A_13,appear(efficient_producers,A_38))
      | ~ greater(A_13,sk2(A_38))
      | ~ stable(A_38)
      | ~ environment(A_38) ),
    inference(resolution,[status(thm)],[c_48,c_14]) ).

tff(c_18,plain,
    ! [A_18,B_19] :
      ( greater_or_equal(A_18,B_19)
      | ~ greater(A_18,B_19) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_83,plain,
    ! [B_47,A_48] :
      ( greater(cardinality_at_time(efficient_producers,B_47),zero)
      | ~ greater_or_equal(B_47,appear(efficient_producers,A_48))
      | ~ in_environment(A_48,B_47)
      | ~ environment(A_48) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_119,plain,
    ! [A_57,A_58] :
      ( greater(cardinality_at_time(efficient_producers,A_57),zero)
      | ~ in_environment(A_58,A_57)
      | ~ environment(A_58)
      | ~ greater(A_57,appear(efficient_producers,A_58)) ),
    inference(resolution,[status(thm)],[c_18,c_83]) ).

tff(c_124,plain,
    ! [A_13,A_38] :
      ( greater(cardinality_at_time(efficient_producers,A_13),zero)
      | ~ in_environment(A_38,A_13)
      | ~ greater(A_13,sk2(A_38))
      | ~ stable(A_38)
      | ~ environment(A_38) ),
    inference(resolution,[status(thm)],[c_55,c_119]) ).

tff(c_391,plain,
    ! [A_155,A_156] :
      ( greater(cardinality_at_time(efficient_producers,sk1(sk2(A_155),A_156)),zero)
      | ~ in_environment(A_155,sk1(sk2(A_155),A_156))
      | ~ stable(A_155)
      | ~ environment(A_155)
      | ( sk1(sk2(A_155),A_156) = sk2(A_155) )
      | contracts_from(sk2(A_155),first_movers)
      | ~ in_environment(A_156,sk2(A_155))
      | ~ stable(A_156)
      | ~ environment(A_156) ),
    inference(resolution,[status(thm)],[c_185,c_124]) ).

tff(c_420,plain,
    ! [A_167,A_168] :
      ( greater(cardinality_at_time(efficient_producers,sk1(sk2(A_167),A_168)),zero)
      | ~ stable(A_167)
      | ~ environment(A_167)
      | ( sk1(sk2(A_167),A_168) = sk2(A_167) )
      | contracts_from(sk2(A_167),first_movers)
      | ~ in_environment(A_168,sk2(A_167))
      | ~ stable(A_168)
      | ~ environment(A_168) ),
    inference(resolution,[status(thm)],[c_244,c_391]) ).

tff(c_2,plain,
    ! [B_2,A_1] :
      ( contracts_from(B_2,first_movers)
      | greater(cardinality_at_time(first_movers,sk1(B_2,A_1)),zero)
      | ~ in_environment(A_1,B_2)
      | ~ stable(A_1)
      | ~ environment(A_1) ),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_177,plain,
    ! [A_73,B_74] :
      ( subpopulations(first_movers,efficient_producers,A_73,B_74)
      | ~ greater(cardinality_at_time(efficient_producers,B_74),zero)
      | ~ greater(cardinality_at_time(first_movers,B_74),zero)
      | ~ in_environment(A_73,B_74)
      | ~ environment(A_73) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_180,plain,
    ! [A_73,B_2,A_1] :
      ( subpopulations(first_movers,efficient_producers,A_73,sk1(B_2,A_1))
      | ~ greater(cardinality_at_time(efficient_producers,sk1(B_2,A_1)),zero)
      | ~ in_environment(A_73,sk1(B_2,A_1))
      | ~ environment(A_73)
      | contracts_from(B_2,first_movers)
      | ~ in_environment(A_1,B_2)
      | ~ stable(A_1)
      | ~ environment(A_1) ),
    inference(resolution,[status(thm)],[c_2,c_177]) ).

tff(c_456,plain,
    ! [A_180,A_181,A_182] :
      ( subpopulations(first_movers,efficient_producers,A_180,sk1(sk2(A_181),A_182))
      | ~ in_environment(A_180,sk1(sk2(A_181),A_182))
      | ~ environment(A_180)
      | ~ stable(A_181)
      | ~ environment(A_181)
      | ( sk1(sk2(A_181),A_182) = sk2(A_181) )
      | contracts_from(sk2(A_181),first_movers)
      | ~ in_environment(A_182,sk2(A_181))
      | ~ stable(A_182)
      | ~ environment(A_182) ),
    inference(resolution,[status(thm)],[c_420,c_180]) ).

tff(c_4,plain,
    ! [B_4,A_3] :
      ( contracts_from(B_4,first_movers)
      | greater_or_equal(sk1(B_4,A_3),B_4)
      | ~ in_environment(A_3,B_4)
      | ~ stable(A_3)
      | ~ environment(A_3) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_146,plain,
    ! [B_67,A_68] :
      ( greater(zero,growth_rate(first_movers,B_67))
      | ~ greater_or_equal(B_67,sk2(A_68))
      | ~ subpopulations(first_movers,efficient_producers,A_68,B_67)
      | ~ stable(A_68)
      | ~ environment(A_68) ),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_159,plain,
    ! [A_68,A_3] :
      ( greater(zero,growth_rate(first_movers,sk1(sk2(A_68),A_3)))
      | ~ subpopulations(first_movers,efficient_producers,A_68,sk1(sk2(A_68),A_3))
      | ~ stable(A_68)
      | ~ environment(A_68)
      | contracts_from(sk2(A_68),first_movers)
      | ~ in_environment(A_3,sk2(A_68))
      | ~ stable(A_3)
      | ~ environment(A_3) ),
    inference(resolution,[status(thm)],[c_4,c_146]) ).

tff(c_461,plain,
    ! [A_183,A_184] :
      ( greater(zero,growth_rate(first_movers,sk1(sk2(A_183),A_184)))
      | ~ in_environment(A_183,sk1(sk2(A_183),A_184))
      | ~ stable(A_183)
      | ~ environment(A_183)
      | ( sk1(sk2(A_183),A_184) = sk2(A_183) )
      | contracts_from(sk2(A_183),first_movers)
      | ~ in_environment(A_184,sk2(A_183))
      | ~ stable(A_184)
      | ~ environment(A_184) ),
    inference(resolution,[status(thm)],[c_456,c_159]) ).

tff(c_473,plain,
    ! [A_185,A_186] :
      ( greater(zero,growth_rate(first_movers,sk1(sk2(A_185),A_186)))
      | ~ stable(A_185)
      | ~ environment(A_185)
      | ( sk1(sk2(A_185),A_186) = sk2(A_185) )
      | contracts_from(sk2(A_185),first_movers)
      | ~ in_environment(A_186,sk2(A_185))
      | ~ stable(A_186)
      | ~ environment(A_186) ),
    inference(resolution,[status(thm)],[c_244,c_461]) ).

tff(c_6,plain,
    ! [B_6,A_5] :
      ( contracts_from(B_6,first_movers)
      | ~ greater(zero,growth_rate(first_movers,sk1(B_6,A_5)))
      | ~ in_environment(A_5,B_6)
      | ~ stable(A_5)
      | ~ environment(A_5) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_487,plain,
    ! [A_187,A_188] :
      ( ~ stable(A_187)
      | ~ environment(A_187)
      | ( sk1(sk2(A_187),A_188) = sk2(A_187) )
      | contracts_from(sk2(A_187),first_movers)
      | ~ in_environment(A_188,sk2(A_187))
      | ~ stable(A_188)
      | ~ environment(A_188) ),
    inference(resolution,[status(thm)],[c_473,c_6]) ).

tff(c_492,plain,
    ! [A_189] :
      ( ( sk1(sk2(A_189),A_189) = sk2(A_189) )
      | contracts_from(sk2(A_189),first_movers)
      | ~ stable(A_189)
      | ~ environment(A_189) ),
    inference(resolution,[status(thm)],[c_145,c_487]) ).

tff(c_538,plain,
    ( ( sk1(sk2(sk3),sk3) = sk2(sk3) )
    | ~ stable(sk3)
    | ~ environment(sk3) ),
    inference(resolution,[status(thm)],[c_492,c_58]) ).

tff(c_546,plain,
    sk1(sk2(sk3),sk3) = sk2(sk3),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_30,c_538]) ).

tff(c_600,plain,
    ( contracts_from(sk2(sk3),first_movers)
    | ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
    | ~ in_environment(sk3,sk2(sk3))
    | ~ stable(sk3)
    | ~ environment(sk3) ),
    inference(superposition,[status(thm),theory(equality)],[c_546,c_6]) ).

tff(c_649,plain,
    ( contracts_from(sk2(sk3),first_movers)
    | ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
    | ~ in_environment(sk3,sk2(sk3)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_30,c_600]) ).

tff(c_650,plain,
    ( ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
    | ~ in_environment(sk3,sk2(sk3)) ),
    inference(negUnitSimplification,[status(thm)],[c_58,c_649]) ).

tff(c_658,plain,
    ~ in_environment(sk3,sk2(sk3)),
    inference(splitLeft,[status(thm)],[c_650]) ).

tff(c_661,plain,
    ( ~ stable(sk3)
    | ~ environment(sk3) ),
    inference(resolution,[status(thm)],[c_145,c_658]) ).

tff(c_665,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_30,c_661]) ).

tff(c_667,plain,
    in_environment(sk3,sk2(sk3)),
    inference(splitRight,[status(thm)],[c_650]) ).

tff(c_162,plain,
    ! [A_69] :
      ( in_environment(A_69,sk2(A_69))
      | ~ stable(A_69)
      | ~ environment(A_69) ),
    inference(resolution,[status(thm)],[c_12,c_141]) ).

tff(c_125,plain,
    ! [A_24] :
      ( greater(cardinality_at_time(efficient_producers,sk2(A_24)),zero)
      | ~ in_environment(A_24,sk2(A_24))
      | ~ stable(A_24)
      | ~ environment(A_24) ),
    inference(resolution,[status(thm)],[c_24,c_119]) ).

tff(c_165,plain,
    ! [A_69] :
      ( greater(cardinality_at_time(efficient_producers,sk2(A_69)),zero)
      | ~ stable(A_69)
      | ~ environment(A_69) ),
    inference(resolution,[status(thm)],[c_162,c_125]) ).

tff(c_603,plain,
    ( contracts_from(sk2(sk3),first_movers)
    | greater(cardinality_at_time(first_movers,sk2(sk3)),zero)
    | ~ in_environment(sk3,sk2(sk3))
    | ~ stable(sk3)
    | ~ environment(sk3) ),
    inference(superposition,[status(thm),theory(equality)],[c_546,c_2]) ).

tff(c_652,plain,
    ( contracts_from(sk2(sk3),first_movers)
    | greater(cardinality_at_time(first_movers,sk2(sk3)),zero)
    | ~ in_environment(sk3,sk2(sk3)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_30,c_603]) ).

tff(c_653,plain,
    ( greater(cardinality_at_time(first_movers,sk2(sk3)),zero)
    | ~ in_environment(sk3,sk2(sk3)) ),
    inference(negUnitSimplification,[status(thm)],[c_58,c_652]) ).

tff(c_677,plain,
    greater(cardinality_at_time(first_movers,sk2(sk3)),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_667,c_653]) ).

tff(c_8,plain,
    ! [A_7,B_8] :
      ( subpopulations(first_movers,efficient_producers,A_7,B_8)
      | ~ greater(cardinality_at_time(efficient_producers,B_8),zero)
      | ~ greater(cardinality_at_time(first_movers,B_8),zero)
      | ~ in_environment(A_7,B_8)
      | ~ environment(A_7) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_686,plain,
    ! [A_7] :
      ( subpopulations(first_movers,efficient_producers,A_7,sk2(sk3))
      | ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
      | ~ in_environment(A_7,sk2(sk3))
      | ~ environment(A_7) ),
    inference(resolution,[status(thm)],[c_677,c_8]) ).

tff(c_708,plain,
    ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero),
    inference(splitLeft,[status(thm)],[c_686]) ).

tff(c_711,plain,
    ( ~ stable(sk3)
    | ~ environment(sk3) ),
    inference(resolution,[status(thm)],[c_165,c_708]) ).

tff(c_715,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_30,c_711]) ).

tff(c_733,plain,
    ! [A_199] :
      ( subpopulations(first_movers,efficient_producers,A_199,sk2(sk3))
      | ~ in_environment(A_199,sk2(sk3))
      | ~ environment(A_199) ),
    inference(splitRight,[status(thm)],[c_686]) ).

tff(c_666,plain,
    ~ greater(zero,growth_rate(first_movers,sk2(sk3))),
    inference(splitRight,[status(thm)],[c_650]) ).

tff(c_574,plain,
    ( greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
    | ~ subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
    | ~ stable(sk3)
    | ~ environment(sk3)
    | contracts_from(sk2(sk3),first_movers)
    | ~ in_environment(sk3,sk2(sk3))
    | ~ stable(sk3)
    | ~ environment(sk3) ),
    inference(superposition,[status(thm),theory(equality)],[c_546,c_159]) ).

tff(c_623,plain,
    ( greater(zero,growth_rate(first_movers,sk2(sk3)))
    | ~ subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
    | contracts_from(sk2(sk3),first_movers)
    | ~ in_environment(sk3,sk2(sk3)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_30,c_28,c_30,c_546,c_574]) ).

tff(c_624,plain,
    ( greater(zero,growth_rate(first_movers,sk2(sk3)))
    | ~ subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
    | ~ in_environment(sk3,sk2(sk3)) ),
    inference(negUnitSimplification,[status(thm)],[c_58,c_623]) ).

tff(c_704,plain,
    ( greater(zero,growth_rate(first_movers,sk2(sk3)))
    | ~ subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_667,c_624]) ).

tff(c_705,plain,
    ~ subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)),
    inference(negUnitSimplification,[status(thm)],[c_666,c_704]) ).

tff(c_736,plain,
    ( ~ in_environment(sk3,sk2(sk3))
    | ~ environment(sk3) ),
    inference(resolution,[status(thm)],[c_733,c_705]) ).

tff(c_743,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_667,c_736]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem  : MGT027-1 : TPTP v8.1.2. Released v2.4.0.
% 0.15/0.16  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.17/0.36  % Computer : n003.cluster.edu
% 0.17/0.36  % Model    : x86_64 x86_64
% 0.17/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36  % Memory   : 8042.1875MB
% 0.17/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36  % CPULimit : 300
% 0.17/0.36  % WCLimit  : 300
% 0.17/0.36  % DateTime : Thu Aug  3 20:34:53 EDT 2023
% 0.17/0.36  % CPUTime  : 
% 4.15/2.33  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.57/2.34  
% 4.57/2.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.57/2.38  
% 4.57/2.38  Inference rules
% 4.57/2.38  ----------------------
% 4.57/2.38  #Ref     : 0
% 4.57/2.38  #Sup     : 155
% 4.57/2.38  #Fact    : 0
% 4.57/2.38  #Define  : 0
% 4.57/2.38  #Split   : 6
% 4.57/2.38  #Chain   : 0
% 4.57/2.38  #Close   : 0
% 4.57/2.38  
% 4.57/2.38  Ordering : KBO
% 4.57/2.38  
% 4.57/2.38  Simplification rules
% 4.57/2.38  ----------------------
% 4.57/2.38  #Subsume      : 54
% 4.57/2.38  #Demod        : 78
% 4.57/2.38  #Tautology    : 12
% 4.57/2.38  #SimpNegUnit  : 18
% 4.57/2.38  #BackRed      : 0
% 4.57/2.38  
% 4.57/2.38  #Partial instantiations: 0
% 4.57/2.38  #Strategies tried      : 1
% 4.57/2.38  
% 4.57/2.38  Timing (in seconds)
% 4.57/2.38  ----------------------
% 4.57/2.38  Preprocessing        : 0.49
% 4.57/2.38  Parsing              : 0.26
% 4.57/2.38  CNF conversion       : 0.02
% 4.57/2.38  Main loop            : 0.60
% 4.57/2.38  Inferencing          : 0.25
% 4.57/2.38  Reduction            : 0.14
% 4.57/2.38  Demodulation         : 0.09
% 4.57/2.38  BG Simplification    : 0.02
% 4.57/2.39  Subsumption          : 0.15
% 4.57/2.39  Abstraction          : 0.02
% 4.57/2.39  MUC search           : 0.00
% 4.57/2.39  Cooper               : 0.00
% 4.57/2.39  Total                : 1.15
% 4.57/2.39  Index Insertion      : 0.00
% 4.57/2.39  Index Deletion       : 0.00
% 4.57/2.39  Index Matching       : 0.00
% 4.57/2.39  BG Taut test         : 0.00
%------------------------------------------------------------------------------