TSTP Solution File: MGT020+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : MGT020+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : 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 10:49:33 EDT 2023

% Result   : Theorem 4.67s 2.26s
% Output   : CNFRefutation 4.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   62 (  11 unt;  14 typ;   0 def)
%            Number of atoms       :  143 (   5 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  171 (  76   ~;  72   |;  11   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  10   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   59 (;  59   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater_or_equal > greater > environment > decreases > disbanding_rate > difference > #nlpp > start_time > initial_FM_EP > first_movers > efficient_producers > #skF_2 > #skF_1

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

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

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

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

tff('#skF_2',type,
    '#skF_2': $i ).

tff('#skF_1',type,
    '#skF_1': $i ).

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

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

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

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

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

tff(f_142,negated_conjecture,
    ~ ! [E,T] :
        ( ( environment(E)
          & subpopulations(first_movers,efficient_producers,E,T) )
       => greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2) ).

tff(f_51,axiom,
    ! [E,T] :
      ( environment(E)
     => ( ( in_environment(E,initial_FM_EP(E))
         => subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) )
        & ( subpopulations(first_movers,efficient_producers,E,T)
         => greater_or_equal(T,initial_FM_EP(E)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_point) ).

tff(f_112,axiom,
    ! [X,Y] :
      ( greater_or_equal(X,Y)
     => ( greater(X,Y)
        | ( X = Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).

tff(f_85,axiom,
    ! [E] :
      ( environment(E)
     => greater_or_equal(initial_FM_EP(E),start_time(E)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_initial_time) ).

tff(f_79,axiom,
    ! [E,T] :
      ( ( environment(E)
        & subpopulations(first_movers,efficient_producers,E,T) )
     => in_environment(E,T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occurs) ).

tff(f_98,axiom,
    ! [E,T1,T2] :
      ( ( environment(E)
        & greater_or_equal(T1,start_time(E))
        & greater(T2,T1)
        & in_environment(E,T2) )
     => in_environment(E,T1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_order) ).

tff(f_118,hypothesis,
    ! [E] :
      ( environment(E)
     => greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a8) ).

tff(f_70,axiom,
    ! [E,T,T1,T2] :
      ( ( environment(E)
        & greater_or_equal(T,T1)
        & greater_or_equal(T2,T)
        & subpopulations(first_movers,efficient_producers,E,T2)
        & greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1)) )
     => ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
       => greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_function_difference) ).

tff(f_39,axiom,
    ! [E,T] :
      ( ( environment(E)
        & subpopulations(first_movers,efficient_producers,E,T) )
     => ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).

tff(c_28,plain,
    environment('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_142]) ).

tff(c_26,plain,
    subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_142]) ).

tff(c_4,plain,
    ! [T_4,E_3] :
      ( greater_or_equal(T_4,initial_FM_EP(E_3))
      | ~ subpopulations(first_movers,efficient_producers,E_3,T_4)
      | ~ environment(E_3) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_24,plain,
    ~ greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2')),
    inference(cnfTransformation,[status(thm)],[f_142]) ).

tff(c_43,plain,
    ! [T_33,E_34] :
      ( greater_or_equal(T_33,initial_FM_EP(E_34))
      | ~ subpopulations(first_movers,efficient_producers,E_34,T_33)
      | ~ environment(E_34) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_18,plain,
    ! [Y_19,X_18] :
      ( ( Y_19 = X_18 )
      | greater(X_18,Y_19)
      | ~ greater_or_equal(X_18,Y_19) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_47,plain,
    ! [E_34,T_33] :
      ( ( initial_FM_EP(E_34) = T_33 )
      | greater(T_33,initial_FM_EP(E_34))
      | ~ subpopulations(first_movers,efficient_producers,E_34,T_33)
      | ~ environment(E_34) ),
    inference(resolution,[status(thm)],[c_43,c_18]) ).

tff(c_12,plain,
    ! [E_11] :
      ( greater_or_equal(initial_FM_EP(E_11),start_time(E_11))
      | ~ environment(E_11) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_36,plain,
    ! [E_31,T_32] :
      ( in_environment(E_31,T_32)
      | ~ subpopulations(first_movers,efficient_producers,E_31,T_32)
      | ~ environment(E_31) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_39,plain,
    ( in_environment('#skF_1','#skF_2')
    | ~ environment('#skF_1') ),
    inference(resolution,[status(thm)],[c_26,c_36]) ).

tff(c_42,plain,
    in_environment('#skF_1','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_39]) ).

tff(c_70,plain,
    ! [E_44,T1_45,T2_46] :
      ( in_environment(E_44,T1_45)
      | ~ in_environment(E_44,T2_46)
      | ~ greater(T2_46,T1_45)
      | ~ greater_or_equal(T1_45,start_time(E_44))
      | ~ environment(E_44) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_72,plain,
    ! [T1_45] :
      ( in_environment('#skF_1',T1_45)
      | ~ greater('#skF_2',T1_45)
      | ~ greater_or_equal(T1_45,start_time('#skF_1'))
      | ~ environment('#skF_1') ),
    inference(resolution,[status(thm)],[c_42,c_70]) ).

tff(c_76,plain,
    ! [T1_47] :
      ( in_environment('#skF_1',T1_47)
      | ~ greater('#skF_2',T1_47)
      | ~ greater_or_equal(T1_47,start_time('#skF_1')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_72]) ).

tff(c_80,plain,
    ( in_environment('#skF_1',initial_FM_EP('#skF_1'))
    | ~ greater('#skF_2',initial_FM_EP('#skF_1'))
    | ~ environment('#skF_1') ),
    inference(resolution,[status(thm)],[c_12,c_76]) ).

tff(c_83,plain,
    ( in_environment('#skF_1',initial_FM_EP('#skF_1'))
    | ~ greater('#skF_2',initial_FM_EP('#skF_1')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_80]) ).

tff(c_84,plain,
    ~ greater('#skF_2',initial_FM_EP('#skF_1')),
    inference(splitLeft,[status(thm)],[c_83]) ).

tff(c_87,plain,
    ( ( initial_FM_EP('#skF_1') = '#skF_2' )
    | ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
    | ~ environment('#skF_1') ),
    inference(resolution,[status(thm)],[c_47,c_84]) ).

tff(c_90,plain,
    initial_FM_EP('#skF_1') = '#skF_2',
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_87]) ).

tff(c_20,plain,
    ! [E_20] :
      ( greater(disbanding_rate(first_movers,initial_FM_EP(E_20)),disbanding_rate(efficient_producers,initial_FM_EP(E_20)))
      | ~ environment(E_20) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_107,plain,
    ( greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,initial_FM_EP('#skF_1')))
    | ~ environment('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_90,c_20]) ).

tff(c_128,plain,
    greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_90,c_107]) ).

tff(c_130,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24,c_128]) ).

tff(c_131,plain,
    in_environment('#skF_1',initial_FM_EP('#skF_1')),
    inference(splitRight,[status(thm)],[c_83]) ).

tff(c_6,plain,
    ! [E_3] :
      ( subpopulations(first_movers,efficient_producers,E_3,initial_FM_EP(E_3))
      | ~ in_environment(E_3,initial_FM_EP(E_3))
      | ~ environment(E_3) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_325,plain,
    ! [T2_81,T_82,T1_83,E_84] :
      ( greater(disbanding_rate(first_movers,T2_81),disbanding_rate(efficient_producers,T2_81))
      | decreases(difference(disbanding_rate(first_movers,T_82),disbanding_rate(efficient_producers,T_82)))
      | ~ greater(disbanding_rate(first_movers,T1_83),disbanding_rate(efficient_producers,T1_83))
      | ~ subpopulations(first_movers,efficient_producers,E_84,T2_81)
      | ~ greater_or_equal(T2_81,T_82)
      | ~ greater_or_equal(T_82,T1_83)
      | ~ environment(E_84) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_955,plain,
    ! [T2_191,T_192,E_193,E_194] :
      ( greater(disbanding_rate(first_movers,T2_191),disbanding_rate(efficient_producers,T2_191))
      | decreases(difference(disbanding_rate(first_movers,T_192),disbanding_rate(efficient_producers,T_192)))
      | ~ subpopulations(first_movers,efficient_producers,E_193,T2_191)
      | ~ greater_or_equal(T2_191,T_192)
      | ~ greater_or_equal(T_192,initial_FM_EP(E_194))
      | ~ environment(E_193)
      | ~ environment(E_194) ),
    inference(resolution,[status(thm)],[c_20,c_325]) ).

tff(c_959,plain,
    ! [T_192,E_194] :
      ( greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))
      | decreases(difference(disbanding_rate(first_movers,T_192),disbanding_rate(efficient_producers,T_192)))
      | ~ greater_or_equal('#skF_2',T_192)
      | ~ greater_or_equal(T_192,initial_FM_EP(E_194))
      | ~ environment('#skF_1')
      | ~ environment(E_194) ),
    inference(resolution,[status(thm)],[c_26,c_955]) ).

tff(c_963,plain,
    ! [T_192,E_194] :
      ( greater(disbanding_rate(first_movers,'#skF_2'),disbanding_rate(efficient_producers,'#skF_2'))
      | decreases(difference(disbanding_rate(first_movers,T_192),disbanding_rate(efficient_producers,T_192)))
      | ~ greater_or_equal('#skF_2',T_192)
      | ~ greater_or_equal(T_192,initial_FM_EP(E_194))
      | ~ environment(E_194) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_959]) ).

tff(c_965,plain,
    ! [T_195,E_196] :
      ( decreases(difference(disbanding_rate(first_movers,T_195),disbanding_rate(efficient_producers,T_195)))
      | ~ greater_or_equal('#skF_2',T_195)
      | ~ greater_or_equal(T_195,initial_FM_EP(E_196))
      | ~ environment(E_196) ),
    inference(negUnitSimplification,[status(thm)],[c_24,c_963]) ).

tff(c_969,plain,
    ! [T_197,E_198] :
      ( decreases(difference(disbanding_rate(first_movers,T_197),disbanding_rate(efficient_producers,T_197)))
      | ~ greater_or_equal('#skF_2',T_197)
      | ~ subpopulations(first_movers,efficient_producers,E_198,T_197)
      | ~ environment(E_198) ),
    inference(resolution,[status(thm)],[c_4,c_965]) ).

tff(c_979,plain,
    ! [E_199] :
      ( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(E_199)),disbanding_rate(efficient_producers,initial_FM_EP(E_199))))
      | ~ greater_or_equal('#skF_2',initial_FM_EP(E_199))
      | ~ in_environment(E_199,initial_FM_EP(E_199))
      | ~ environment(E_199) ),
    inference(resolution,[status(thm)],[c_6,c_969]) ).

tff(c_2,plain,
    ! [T_2,E_1] :
      ( ~ decreases(difference(disbanding_rate(first_movers,T_2),disbanding_rate(efficient_producers,T_2)))
      | ~ subpopulations(first_movers,efficient_producers,E_1,T_2)
      | ~ environment(E_1) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_983,plain,
    ! [E_200,E_201] :
      ( ~ subpopulations(first_movers,efficient_producers,E_200,initial_FM_EP(E_201))
      | ~ environment(E_200)
      | ~ greater_or_equal('#skF_2',initial_FM_EP(E_201))
      | ~ in_environment(E_201,initial_FM_EP(E_201))
      | ~ environment(E_201) ),
    inference(resolution,[status(thm)],[c_979,c_2]) ).

tff(c_987,plain,
    ! [E_202] :
      ( ~ greater_or_equal('#skF_2',initial_FM_EP(E_202))
      | ~ in_environment(E_202,initial_FM_EP(E_202))
      | ~ environment(E_202) ),
    inference(resolution,[status(thm)],[c_6,c_983]) ).

tff(c_990,plain,
    ( ~ greater_or_equal('#skF_2',initial_FM_EP('#skF_1'))
    | ~ environment('#skF_1') ),
    inference(resolution,[status(thm)],[c_131,c_987]) ).

tff(c_993,plain,
    ~ greater_or_equal('#skF_2',initial_FM_EP('#skF_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_990]) ).

tff(c_996,plain,
    ( ~ subpopulations(first_movers,efficient_producers,'#skF_1','#skF_2')
    | ~ environment('#skF_1') ),
    inference(resolution,[status(thm)],[c_4,c_993]) ).

tff(c_1000,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_996]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : MGT020+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13  % 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
% 0.17/0.34  % Computer : n008.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Thu Aug  3 20:35:34 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 4.67/2.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.67/2.27  
% 4.67/2.27  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.67/2.30  
% 4.67/2.30  Inference rules
% 4.67/2.30  ----------------------
% 4.67/2.30  #Ref     : 0
% 4.67/2.30  #Sup     : 199
% 4.67/2.30  #Fact    : 0
% 4.67/2.30  #Define  : 0
% 4.67/2.30  #Split   : 6
% 4.67/2.30  #Chain   : 0
% 4.67/2.30  #Close   : 0
% 4.67/2.30  
% 4.67/2.30  Ordering : KBO
% 4.67/2.30  
% 4.67/2.30  Simplification rules
% 4.67/2.30  ----------------------
% 4.67/2.30  #Subsume      : 51
% 4.67/2.30  #Demod        : 176
% 4.67/2.30  #Tautology    : 33
% 4.67/2.30  #SimpNegUnit  : 14
% 4.67/2.30  #BackRed      : 4
% 4.67/2.30  
% 4.67/2.30  #Partial instantiations: 0
% 4.67/2.30  #Strategies tried      : 1
% 4.67/2.30  
% 4.67/2.30  Timing (in seconds)
% 4.67/2.30  ----------------------
% 4.67/2.30  Preprocessing        : 0.51
% 4.67/2.30  Parsing              : 0.29
% 4.67/2.30  CNF conversion       : 0.03
% 4.67/2.30  Main loop            : 0.69
% 4.67/2.30  Inferencing          : 0.29
% 4.67/2.30  Reduction            : 0.17
% 4.67/2.30  Demodulation         : 0.11
% 4.67/2.30  BG Simplification    : 0.03
% 4.67/2.30  Subsumption          : 0.16
% 4.67/2.30  Abstraction          : 0.03
% 4.67/2.30  MUC search           : 0.00
% 4.67/2.30  Cooper               : 0.00
% 4.67/2.30  Total                : 1.26
% 4.67/2.30  Index Insertion      : 0.00
% 4.67/2.30  Index Deletion       : 0.00
% 4.67/2.30  Index Matching       : 0.00
% 4.67/2.30  BG Taut test         : 0.00
%------------------------------------------------------------------------------