TSTP Solution File: MGT036-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : MGT036-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n008.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 3.06s 1.77s
% Output   : CNFRefutation 3.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   61 (  21 unt;  13 typ;   0 def)
%            Number of atoms       :  100 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  111 (  59   ~;  52   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 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   :   71 (;  71   !;   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] :
      ( ~ environment(A)
      | ~ subpopulations(first_movers,efficient_producers,A,B)
      | subpopulations(efficient_producers,first_movers,A,B) ),
    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_116,axiom,
    greater(resilience(efficient_producers),resilience(first_movers)),
    file(unknown,unknown) ).

tff(f_115,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(f_39,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | ~ subpopulations(first_movers,efficient_producers,A,B)
      | in_environment(A,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,
    ! [A_38,B_39] :
      ( subpopulations(efficient_producers,first_movers,A_38,B_39)
      | ~ subpopulations(first_movers,efficient_producers,A_38,B_39)
      | ~ environment(A_38) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_41,plain,
    ( subpopulations(efficient_producers,first_movers,sk1,sk2)
    | ~ environment(sk1) ),
    inference(resolution,[status(thm)],[c_26,c_38]) ).

tff(c_44,plain,
    subpopulations(efficient_producers,first_movers,sk1,sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_41]) ).

tff(c_6,plain,
    ! [B_6,C_7,A_5] :
      ( ~ greater(zero,growth_rate(B_6,C_7))
      | environment(A_5) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_29,plain,
    ! [B_6,C_7] : ~ greater(zero,growth_rate(B_6,C_7)),
    inference(splitLeft,[status(thm)],[c_6]) ).

tff(c_18,plain,
    ! [B_27,D_29,C_28,A_26] :
      ( greater(zero,growth_rate(B_27,D_29))
      | ~ outcompetes(C_28,B_27,D_29)
      | ~ subpopulations(B_27,C_28,A_26,D_29)
      | ~ environment(A_26) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_58,plain,
    ! [C_44,B_45,D_46,A_47] :
      ( ~ outcompetes(C_44,B_45,D_46)
      | ~ subpopulations(B_45,C_44,A_47,D_46)
      | ~ environment(A_47) ),
    inference(negUnitSimplification,[status(thm)],[c_29,c_18]) ).

tff(c_61,plain,
    ( ~ outcompetes(first_movers,efficient_producers,sk2)
    | ~ environment(sk1) ),
    inference(resolution,[status(thm)],[c_44,c_58]) ).

tff(c_68,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_28,c_61]) ).

tff(c_69,plain,
    ! [A_5] : environment(A_5),
    inference(splitRight,[status(thm)],[c_6]) ).

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

tff(c_83,plain,
    ! [A_57,B_58] :
      ( subpopulations(efficient_producers,first_movers,A_57,B_58)
      | ~ subpopulations(first_movers,efficient_producers,A_57,B_58) ),
    inference(demodulation,[status(thm),theory(equality)],[c_69,c_2]) ).

tff(c_87,plain,
    subpopulations(efficient_producers,first_movers,sk1,sk2),
    inference(resolution,[status(thm)],[c_26,c_83]) ).

tff(c_16,plain,
    ! [C_24,D_25,B_23,A_22] :
      ( greater_or_equal(growth_rate(C_24,D_25),zero)
      | ~ outcompetes(C_24,B_23,D_25)
      | ~ subpopulations(B_23,C_24,A_22,D_25)
      | ~ environment(A_22) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_90,plain,
    ! [C_59,D_60,B_61,A_62] :
      ( greater_or_equal(growth_rate(C_59,D_60),zero)
      | ~ outcompetes(C_59,B_61,D_60)
      | ~ subpopulations(B_61,C_59,A_62,D_60) ),
    inference(demodulation,[status(thm),theory(equality)],[c_69,c_16]) ).

tff(c_92,plain,
    ( greater_or_equal(growth_rate(first_movers,sk2),zero)
    | ~ outcompetes(first_movers,efficient_producers,sk2) ),
    inference(resolution,[status(thm)],[c_87,c_90]) ).

tff(c_97,plain,
    greater_or_equal(growth_rate(first_movers,sk2),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_92]) ).

tff(c_10,plain,
    ! [A_12,B_13] :
      ( ~ greater(zero,growth_rate(A_12,B_13))
      | ~ greater_or_equal(growth_rate(A_12,B_13),zero) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_102,plain,
    ~ greater(zero,growth_rate(first_movers,sk2)),
    inference(resolution,[status(thm)],[c_97,c_10]) ).

tff(c_22,plain,
    greater(resilience(efficient_producers),resilience(first_movers)),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_105,plain,
    ! [B_63,D_64,C_65,A_66] :
      ( greater(zero,growth_rate(B_63,D_64))
      | ~ outcompetes(C_65,B_63,D_64)
      | ~ subpopulations(B_63,C_65,A_66,D_64) ),
    inference(demodulation,[status(thm),theory(equality)],[c_69,c_18]) ).

tff(c_107,plain,
    ( greater(zero,growth_rate(efficient_producers,sk2))
    | ~ outcompetes(first_movers,efficient_producers,sk2) ),
    inference(resolution,[status(thm)],[c_87,c_105]) ).

tff(c_112,plain,
    greater(zero,growth_rate(efficient_producers,sk2)),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_107]) ).

tff(c_20,plain,
    ! [D_33,B_31,C_32,A_30] :
      ( ~ greater(zero,growth_rate(D_33,B_31))
      | ~ greater(resilience(D_33),resilience(C_32))
      | greater(zero,growth_rate(C_32,B_31))
      | ~ in_environment(A_30,B_31)
      | ~ environment(A_30) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_151,plain,
    ! [D_75,B_76,C_77,A_78] :
      ( ~ greater(zero,growth_rate(D_75,B_76))
      | ~ greater(resilience(D_75),resilience(C_77))
      | greater(zero,growth_rate(C_77,B_76))
      | ~ in_environment(A_78,B_76) ),
    inference(demodulation,[status(thm),theory(equality)],[c_69,c_20]) ).

tff(c_154,plain,
    ! [C_77,A_78] :
      ( ~ greater(resilience(efficient_producers),resilience(C_77))
      | greater(zero,growth_rate(C_77,sk2))
      | ~ in_environment(A_78,sk2) ),
    inference(resolution,[status(thm)],[c_112,c_151]) ).

tff(c_155,plain,
    ! [A_78] : ~ in_environment(A_78,sk2),
    inference(splitLeft,[status(thm)],[c_154]) ).

tff(c_4,plain,
    ! [A_3,B_4] :
      ( in_environment(A_3,B_4)
      | ~ subpopulations(first_movers,efficient_producers,A_3,B_4)
      | ~ environment(A_3) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_76,plain,
    ! [A_55,B_56] :
      ( in_environment(A_55,B_56)
      | ~ subpopulations(first_movers,efficient_producers,A_55,B_56) ),
    inference(demodulation,[status(thm),theory(equality)],[c_69,c_4]) ).

tff(c_80,plain,
    in_environment(sk1,sk2),
    inference(resolution,[status(thm)],[c_26,c_76]) ).

tff(c_157,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_155,c_80]) ).

tff(c_159,plain,
    ! [C_79] :
      ( ~ greater(resilience(efficient_producers),resilience(C_79))
      | greater(zero,growth_rate(C_79,sk2)) ),
    inference(splitRight,[status(thm)],[c_154]) ).

tff(c_162,plain,
    greater(zero,growth_rate(first_movers,sk2)),
    inference(resolution,[status(thm)],[c_22,c_159]) ).

tff(c_166,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_102,c_162]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : MGT036-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 20:34:48 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 3.06/1.77  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.23/1.79  
% 3.23/1.79  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.23/1.82  
% 3.23/1.82  Inference rules
% 3.23/1.82  ----------------------
% 3.23/1.82  #Ref     : 0
% 3.23/1.82  #Sup     : 22
% 3.23/1.82  #Fact    : 0
% 3.23/1.82  #Define  : 0
% 3.23/1.82  #Split   : 3
% 3.23/1.82  #Chain   : 0
% 3.23/1.82  #Close   : 0
% 3.23/1.82  
% 3.23/1.82  Ordering : KBO
% 3.23/1.82  
% 3.23/1.82  Simplification rules
% 3.23/1.82  ----------------------
% 3.23/1.82  #Subsume      : 4
% 3.23/1.82  #Demod        : 20
% 3.23/1.82  #Tautology    : 5
% 3.23/1.82  #SimpNegUnit  : 5
% 3.23/1.82  #BackRed      : 1
% 3.23/1.82  
% 3.23/1.82  #Partial instantiations: 0
% 3.23/1.82  #Strategies tried      : 1
% 3.23/1.82  
% 3.23/1.82  Timing (in seconds)
% 3.23/1.82  ----------------------
% 3.23/1.83  Preprocessing        : 0.45
% 3.23/1.83  Parsing              : 0.25
% 3.23/1.83  CNF conversion       : 0.03
% 3.23/1.83  Main loop            : 0.29
% 3.23/1.83  Inferencing          : 0.12
% 3.23/1.83  Reduction            : 0.08
% 3.23/1.83  Demodulation         : 0.06
% 3.23/1.83  BG Simplification    : 0.02
% 3.23/1.83  Subsumption          : 0.05
% 3.23/1.83  Abstraction          : 0.01
% 3.23/1.83  MUC search           : 0.00
% 3.23/1.83  Cooper               : 0.00
% 3.23/1.83  Total                : 0.81
% 3.23/1.83  Index Insertion      : 0.00
% 3.23/1.83  Index Deletion       : 0.00
% 3.23/1.83  Index Matching       : 0.00
% 3.23/1.83  BG Taut test         : 0.00
%------------------------------------------------------------------------------