TSTP Solution File: MGT036-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : MGT036-2 : 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 : n024.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 10:49:39 EDT 2023

% Result   : Unsatisfiable 3.21s 1.79s
% Output   : CNFRefutation 3.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   64 (  21 unt;  13 typ;   0 def)
%            Number of atoms       :  106 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  116 (  61   ~;  55   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   8   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   95 (;  95   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subpopulations > outcompetes > in_environment > greater_or_equal > greater > environment > growth_rate > #nlpp > resilience > zero > sk2 > sk1 > 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(in_environment,type,
    in_environment: ( $i * $i ) > $o ).

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

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

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

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

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

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

tff(f_119,axiom,
    outcompetes(first_movers,efficient_producers,sk2),
    file(unknown,unknown) ).

tff(f_118,axiom,
    subpopulations(first_movers,efficient_producers,sk1,sk2),
    file(unknown,unknown) ).

tff(f_117,axiom,
    environment(sk1),
    file(unknown,unknown) ).

tff(f_31,axiom,
    ! [A,B,C,D] :
      ( ~ environment(A)
      | ~ subpopulations(B,C,A,D)
      | subpopulations(C,B,A,D) ),
    file(unknown,unknown) ).

tff(f_44,axiom,
    ! [A,B,C] :
      ( environment(A)
      | ~ greater(zero,growth_rate(B,C)) ),
    file(unknown,unknown) ).

tff(f_101,axiom,
    ! [A,B,C,D] :
      ( ~ environment(A)
      | ~ subpopulations(B,C,A,D)
      | ~ outcompetes(C,B,D)
      | greater(zero,growth_rate(B,D)) ),
    file(unknown,unknown) ).

tff(f_90,axiom,
    ! [A,B,C,D] :
      ( ~ environment(A)
      | ~ subpopulations(B,C,A,D)
      | ~ outcompetes(C,B,D)
      | greater_or_equal(growth_rate(C,D),zero) ),
    file(unknown,unknown) ).

tff(f_55,axiom,
    ! [A,B] :
      ( ~ greater_or_equal(growth_rate(A,B),zero)
      | ~ greater(zero,growth_rate(A,B)) ),
    file(unknown,unknown) ).

tff(f_102,axiom,
    greater(resilience(efficient_producers),resilience(first_movers)),
    file(unknown,unknown) ).

tff(f_49,axiom,
    ! [A,B,C,D] :
      ( subpopulations(A,B,C,D)
      | ~ greater(zero,growth_rate(A,D)) ),
    file(unknown,unknown) ).

tff(f_39,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | ~ subpopulations(first_movers,efficient_producers,A,B)
      | in_environment(A,B) ),
    file(unknown,unknown) ).

tff(f_116,axiom,
    ! [A,B,C,D] :
      ( ~ environment(A)
      | ~ in_environment(A,B)
      | greater(zero,growth_rate(C,B))
      | ~ greater(resilience(D),resilience(C))
      | ~ greater(zero,growth_rate(D,B)) ),
    file(unknown,unknown) ).

tff(c_28,plain,
    outcompetes(first_movers,efficient_producers,sk2),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_26,plain,
    subpopulations(first_movers,efficient_producers,sk1,sk2),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_24,plain,
    environment(sk1),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_38,plain,
    ! [C_40,B_41,A_42,D_43] :
      ( subpopulations(C_40,B_41,A_42,D_43)
      | ~ subpopulations(B_41,C_40,A_42,D_43)
      | ~ environment(A_42) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_40,plain,
    ( subpopulations(efficient_producers,first_movers,sk1,sk2)
    | ~ environment(sk1) ),
    inference(resolution,[status(thm)],[c_26,c_38]) ).

tff(c_43,plain,
    subpopulations(efficient_producers,first_movers,sk1,sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_40]) ).

tff(c_6,plain,
    ! [B_8,C_9,A_7] :
      ( ~ greater(zero,growth_rate(B_8,C_9))
      | environment(A_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_29,plain,
    ! [B_8,C_9] : ~ greater(zero,growth_rate(B_8,C_9)),
    inference(splitLeft,[status(thm)],[c_6]) ).

tff(c_18,plain,
    ! [B_29,D_31,C_30,A_28] :
      ( greater(zero,growth_rate(B_29,D_31))
      | ~ outcompetes(C_30,B_29,D_31)
      | ~ subpopulations(B_29,C_30,A_28,D_31)
      | ~ environment(A_28) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_62,plain,
    ! [C_48,B_49,D_50,A_51] :
      ( ~ outcompetes(C_48,B_49,D_50)
      | ~ subpopulations(B_49,C_48,A_51,D_50)
      | ~ environment(A_51) ),
    inference(negUnitSimplification,[status(thm)],[c_29,c_18]) ).

tff(c_65,plain,
    ( ~ outcompetes(first_movers,efficient_producers,sk2)
    | ~ environment(sk1) ),
    inference(resolution,[status(thm)],[c_43,c_62]) ).

tff(c_72,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_28,c_65]) ).

tff(c_73,plain,
    ! [A_7] : environment(A_7),
    inference(splitRight,[status(thm)],[c_6]) ).

tff(c_2,plain,
    ! [C_3,B_2,A_1,D_4] :
      ( subpopulations(C_3,B_2,A_1,D_4)
      | ~ subpopulations(B_2,C_3,A_1,D_4)
      | ~ environment(A_1) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_87,plain,
    ! [C_61,B_62,A_63,D_64] :
      ( subpopulations(C_61,B_62,A_63,D_64)
      | ~ subpopulations(B_62,C_61,A_63,D_64) ),
    inference(demodulation,[status(thm),theory(equality)],[c_73,c_2]) ).

tff(c_90,plain,
    subpopulations(efficient_producers,first_movers,sk1,sk2),
    inference(resolution,[status(thm)],[c_26,c_87]) ).

tff(c_16,plain,
    ! [C_26,D_27,B_25,A_24] :
      ( greater_or_equal(growth_rate(C_26,D_27),zero)
      | ~ outcompetes(C_26,B_25,D_27)
      | ~ subpopulations(B_25,C_26,A_24,D_27)
      | ~ environment(A_24) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_97,plain,
    ! [C_65,D_66,B_67,A_68] :
      ( greater_or_equal(growth_rate(C_65,D_66),zero)
      | ~ outcompetes(C_65,B_67,D_66)
      | ~ subpopulations(B_67,C_65,A_68,D_66) ),
    inference(demodulation,[status(thm),theory(equality)],[c_73,c_16]) ).

tff(c_99,plain,
    ( greater_or_equal(growth_rate(first_movers,sk2),zero)
    | ~ outcompetes(first_movers,efficient_producers,sk2) ),
    inference(resolution,[status(thm)],[c_90,c_97]) ).

tff(c_104,plain,
    greater_or_equal(growth_rate(first_movers,sk2),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_99]) ).

tff(c_10,plain,
    ! [A_14,B_15] :
      ( ~ greater(zero,growth_rate(A_14,B_15))
      | ~ greater_or_equal(growth_rate(A_14,B_15),zero) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_109,plain,
    ~ greater(zero,growth_rate(first_movers,sk2)),
    inference(resolution,[status(thm)],[c_104,c_10]) ).

tff(c_20,plain,
    greater(resilience(efficient_producers),resilience(first_movers)),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_112,plain,
    ! [B_69,D_70,C_71,A_72] :
      ( greater(zero,growth_rate(B_69,D_70))
      | ~ outcompetes(C_71,B_69,D_70)
      | ~ subpopulations(B_69,C_71,A_72,D_70) ),
    inference(demodulation,[status(thm),theory(equality)],[c_73,c_18]) ).

tff(c_114,plain,
    ( greater(zero,growth_rate(efficient_producers,sk2))
    | ~ outcompetes(first_movers,efficient_producers,sk2) ),
    inference(resolution,[status(thm)],[c_90,c_112]) ).

tff(c_119,plain,
    greater(zero,growth_rate(efficient_producers,sk2)),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_114]) ).

tff(c_8,plain,
    ! [A_10,D_13,B_11,C_12] :
      ( ~ greater(zero,growth_rate(A_10,D_13))
      | subpopulations(A_10,B_11,C_12,D_13) ),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_125,plain,
    ! [B_73,C_74] : subpopulations(efficient_producers,B_73,C_74,sk2),
    inference(resolution,[status(thm)],[c_119,c_8]) ).

tff(c_86,plain,
    ! [C_3,B_2,A_1,D_4] :
      ( subpopulations(C_3,B_2,A_1,D_4)
      | ~ subpopulations(B_2,C_3,A_1,D_4) ),
    inference(demodulation,[status(thm),theory(equality)],[c_73,c_2]) ).

tff(c_149,plain,
    ! [B_79,C_80] : subpopulations(B_79,efficient_producers,C_80,sk2),
    inference(resolution,[status(thm)],[c_125,c_86]) ).

tff(c_4,plain,
    ! [A_5,B_6] :
      ( in_environment(A_5,B_6)
      | ~ subpopulations(first_movers,efficient_producers,A_5,B_6)
      | ~ environment(A_5) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_79,plain,
    ! [A_5,B_6] :
      ( in_environment(A_5,B_6)
      | ~ subpopulations(first_movers,efficient_producers,A_5,B_6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_73,c_4]) ).

tff(c_167,plain,
    ! [C_80] : in_environment(C_80,sk2),
    inference(resolution,[status(thm)],[c_149,c_79]) ).

tff(c_22,plain,
    ! [D_35,B_33,C_34,A_32] :
      ( ~ greater(zero,growth_rate(D_35,B_33))
      | ~ greater(resilience(D_35),resilience(C_34))
      | greater(zero,growth_rate(C_34,B_33))
      | ~ in_environment(A_32,B_33)
      | ~ environment(A_32) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_174,plain,
    ! [D_82,B_83,C_84,A_85] :
      ( ~ greater(zero,growth_rate(D_82,B_83))
      | ~ greater(resilience(D_82),resilience(C_84))
      | greater(zero,growth_rate(C_84,B_83))
      | ~ in_environment(A_85,B_83) ),
    inference(demodulation,[status(thm),theory(equality)],[c_73,c_22]) ).

tff(c_176,plain,
    ! [C_84,A_85] :
      ( ~ greater(resilience(efficient_producers),resilience(C_84))
      | greater(zero,growth_rate(C_84,sk2))
      | ~ in_environment(A_85,sk2) ),
    inference(resolution,[status(thm)],[c_119,c_174]) ).

tff(c_226,plain,
    ! [C_95] :
      ( ~ greater(resilience(efficient_producers),resilience(C_95))
      | greater(zero,growth_rate(C_95,sk2)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_167,c_176]) ).

tff(c_229,plain,
    greater(zero,growth_rate(first_movers,sk2)),
    inference(resolution,[status(thm)],[c_20,c_226]) ).

tff(c_233,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_109,c_229]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : MGT036-2 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14  % 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
% 0.15/0.36  % Computer : n024.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 20:31:15 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 3.21/1.79  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.31/1.80  
% 3.31/1.80  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/1.83  
% 3.39/1.83  Inference rules
% 3.39/1.83  ----------------------
% 3.39/1.83  #Ref     : 0
% 3.39/1.83  #Sup     : 37
% 3.39/1.83  #Fact    : 0
% 3.39/1.83  #Define  : 0
% 3.39/1.83  #Split   : 4
% 3.39/1.83  #Chain   : 0
% 3.39/1.83  #Close   : 0
% 3.39/1.83  
% 3.39/1.83  Ordering : KBO
% 3.39/1.83  
% 3.39/1.83  Simplification rules
% 3.39/1.83  ----------------------
% 3.39/1.83  #Subsume      : 9
% 3.39/1.83  #Demod        : 31
% 3.39/1.83  #Tautology    : 12
% 3.39/1.83  #SimpNegUnit  : 4
% 3.39/1.83  #BackRed      : 0
% 3.39/1.83  
% 3.39/1.83  #Partial instantiations: 0
% 3.39/1.83  #Strategies tried      : 1
% 3.39/1.83  
% 3.39/1.83  Timing (in seconds)
% 3.39/1.83  ----------------------
% 3.39/1.84  Preprocessing        : 0.45
% 3.39/1.84  Parsing              : 0.25
% 3.39/1.84  CNF conversion       : 0.03
% 3.39/1.84  Main loop            : 0.31
% 3.39/1.84  Inferencing          : 0.12
% 3.39/1.84  Reduction            : 0.08
% 3.39/1.84  Demodulation         : 0.06
% 3.39/1.84  BG Simplification    : 0.02
% 3.39/1.84  Subsumption          : 0.06
% 3.39/1.84  Abstraction          : 0.01
% 3.39/1.84  MUC search           : 0.00
% 3.39/1.84  Cooper               : 0.00
% 3.39/1.84  Total                : 0.82
% 3.39/1.84  Index Insertion      : 0.00
% 3.39/1.84  Index Deletion       : 0.00
% 3.39/1.84  Index Matching       : 0.00
% 3.39/1.84  BG Taut test         : 0.00
%------------------------------------------------------------------------------