TSTP Solution File: MGT023+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : MGT023+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/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 : n026.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 10:49:34 EDT 2023

% Result   : Theorem 2.98s 1.87s
% Output   : CNFRefutation 3.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   36 (   6 unt;  12 typ;   0 def)
%            Number of atoms       :   91 (  13 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  117 (  50   ~;  53   |;   9   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   9   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   28 (;  27   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater > stable > environment > growth_rate > #nlpp > critical_point > first_movers > efficient_producers > #skF_2 > #skF_3 > #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('#skF_2',type,
    '#skF_2': $i > $i ).

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

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

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

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

tff('#skF_3',type,
    '#skF_3': $i ).

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

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

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

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

tff(f_74,negated_conjecture,
    ~ ! [E] :
        ( ( environment(E)
          & stable(E) )
       => in_environment(E,critical_point(E)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).

tff(f_66,hypothesis,
    ! [E] :
      ( ( environment(E)
        & stable(E) )
     => ? [To] :
          ( in_environment(E,To)
          & ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
          & ! [T] :
              ( ( subpopulations(first_movers,efficient_producers,E,T)
                & greater(T,To) )
             => greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).

tff(f_47,hypothesis,
    ! [E,To] :
      ( ( environment(E)
        & ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
        & in_environment(E,To)
        & ! [T] :
            ( ( subpopulations(first_movers,efficient_producers,E,T)
              & greater(T,To) )
           => greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) )
     => ( To = critical_point(E) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).

tff(c_18,plain,
    environment('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_16,plain,
    stable('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_12,plain,
    ! [E_4] :
      ( in_environment(E_4,'#skF_2'(E_4))
      | ~ stable(E_4)
      | ~ environment(E_4) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_35,plain,
    ! [E_18,To_19] :
      ( subpopulations(first_movers,efficient_producers,E_18,'#skF_1'(E_18,To_19))
      | ( critical_point(E_18) = To_19 )
      | ~ in_environment(E_18,To_19)
      | greater(growth_rate(efficient_producers,To_19),growth_rate(first_movers,To_19))
      | ~ environment(E_18) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_10,plain,
    ! [E_4] :
      ( ~ greater(growth_rate(efficient_producers,'#skF_2'(E_4)),growth_rate(first_movers,'#skF_2'(E_4)))
      | ~ stable(E_4)
      | ~ environment(E_4) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_39,plain,
    ! [E_4,E_18] :
      ( ~ stable(E_4)
      | ~ environment(E_4)
      | subpopulations(first_movers,efficient_producers,E_18,'#skF_1'(E_18,'#skF_2'(E_4)))
      | ( critical_point(E_18) = '#skF_2'(E_4) )
      | ~ in_environment(E_18,'#skF_2'(E_4))
      | ~ environment(E_18) ),
    inference(resolution,[status(thm)],[c_35,c_10]) ).

tff(c_21,plain,
    ! [E_12,To_13] :
      ( greater('#skF_1'(E_12,To_13),To_13)
      | ( critical_point(E_12) = To_13 )
      | ~ in_environment(E_12,To_13)
      | greater(growth_rate(efficient_producers,To_13),growth_rate(first_movers,To_13))
      | ~ environment(E_12) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_31,plain,
    ! [E_16,E_17] :
      ( ~ stable(E_16)
      | ~ environment(E_16)
      | greater('#skF_1'(E_17,'#skF_2'(E_16)),'#skF_2'(E_16))
      | ( critical_point(E_17) = '#skF_2'(E_16) )
      | ~ in_environment(E_17,'#skF_2'(E_16))
      | ~ environment(E_17) ),
    inference(resolution,[status(thm)],[c_21,c_10]) ).

tff(c_8,plain,
    ! [T_9,E_4] :
      ( greater(growth_rate(efficient_producers,T_9),growth_rate(first_movers,T_9))
      | ~ greater(T_9,'#skF_2'(E_4))
      | ~ subpopulations(first_movers,efficient_producers,E_4,T_9)
      | ~ stable(E_4)
      | ~ environment(E_4) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_50,plain,
    ! [E_24,E_25] :
      ( greater(growth_rate(efficient_producers,'#skF_1'(E_24,'#skF_2'(E_25))),growth_rate(first_movers,'#skF_1'(E_24,'#skF_2'(E_25))))
      | ~ subpopulations(first_movers,efficient_producers,E_25,'#skF_1'(E_24,'#skF_2'(E_25)))
      | ~ stable(E_25)
      | ~ environment(E_25)
      | ( critical_point(E_24) = '#skF_2'(E_25) )
      | ~ in_environment(E_24,'#skF_2'(E_25))
      | ~ environment(E_24) ),
    inference(resolution,[status(thm)],[c_31,c_8]) ).

tff(c_2,plain,
    ! [E_1,To_2] :
      ( ~ greater(growth_rate(efficient_producers,'#skF_1'(E_1,To_2)),growth_rate(first_movers,'#skF_1'(E_1,To_2)))
      | ( critical_point(E_1) = To_2 )
      | ~ in_environment(E_1,To_2)
      | greater(growth_rate(efficient_producers,To_2),growth_rate(first_movers,To_2))
      | ~ environment(E_1) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_55,plain,
    ! [E_26,E_27] :
      ( greater(growth_rate(efficient_producers,'#skF_2'(E_26)),growth_rate(first_movers,'#skF_2'(E_26)))
      | ~ subpopulations(first_movers,efficient_producers,E_26,'#skF_1'(E_27,'#skF_2'(E_26)))
      | ~ stable(E_26)
      | ~ environment(E_26)
      | ( critical_point(E_27) = '#skF_2'(E_26) )
      | ~ in_environment(E_27,'#skF_2'(E_26))
      | ~ environment(E_27) ),
    inference(resolution,[status(thm)],[c_50,c_2]) ).

tff(c_64,plain,
    ! [E_28] :
      ( greater(growth_rate(efficient_producers,'#skF_2'(E_28)),growth_rate(first_movers,'#skF_2'(E_28)))
      | ~ stable(E_28)
      | ( critical_point(E_28) = '#skF_2'(E_28) )
      | ~ in_environment(E_28,'#skF_2'(E_28))
      | ~ environment(E_28) ),
    inference(resolution,[status(thm)],[c_39,c_55]) ).

tff(c_69,plain,
    ! [E_29] :
      ( ~ stable(E_29)
      | ( critical_point(E_29) = '#skF_2'(E_29) )
      | ~ in_environment(E_29,'#skF_2'(E_29))
      | ~ environment(E_29) ),
    inference(resolution,[status(thm)],[c_64,c_10]) ).

tff(c_83,plain,
    ! [E_33] :
      ( ( critical_point(E_33) = '#skF_2'(E_33) )
      | ~ stable(E_33)
      | ~ environment(E_33) ),
    inference(resolution,[status(thm)],[c_12,c_69]) ).

tff(c_86,plain,
    ( ( critical_point('#skF_3') = '#skF_2'('#skF_3') )
    | ~ environment('#skF_3') ),
    inference(resolution,[status(thm)],[c_16,c_83]) ).

tff(c_89,plain,
    critical_point('#skF_3') = '#skF_2'('#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_18,c_86]) ).

tff(c_14,plain,
    ~ in_environment('#skF_3',critical_point('#skF_3')),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_90,plain,
    ~ in_environment('#skF_3','#skF_2'('#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_89,c_14]) ).

tff(c_97,plain,
    ( ~ stable('#skF_3')
    | ~ environment('#skF_3') ),
    inference(resolution,[status(thm)],[c_12,c_90]) ).

tff(c_101,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_18,c_16,c_97]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : MGT023+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/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
% 0.17/0.34  % Computer : n026.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 20:49:01 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 2.98/1.87  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.21/1.88  
% 3.21/1.88  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.23/1.91  
% 3.23/1.91  Inference rules
% 3.23/1.91  ----------------------
% 3.23/1.91  #Ref     : 0
% 3.23/1.91  #Sup     : 17
% 3.23/1.91  #Fact    : 0
% 3.23/1.91  #Define  : 0
% 3.23/1.91  #Split   : 0
% 3.23/1.91  #Chain   : 0
% 3.23/1.91  #Close   : 0
% 3.23/1.91  
% 3.23/1.91  Ordering : KBO
% 3.23/1.91  
% 3.23/1.91  Simplification rules
% 3.23/1.91  ----------------------
% 3.23/1.91  #Subsume      : 2
% 3.23/1.91  #Demod        : 4
% 3.23/1.91  #Tautology    : 2
% 3.23/1.91  #SimpNegUnit  : 0
% 3.23/1.91  #BackRed      : 1
% 3.23/1.91  
% 3.23/1.91  #Partial instantiations: 0
% 3.23/1.91  #Strategies tried      : 1
% 3.23/1.91  
% 3.23/1.91  Timing (in seconds)
% 3.23/1.91  ----------------------
% 3.23/1.91  Preprocessing        : 0.45
% 3.23/1.91  Parsing              : 0.26
% 3.23/1.91  CNF conversion       : 0.03
% 3.23/1.91  Main loop            : 0.28
% 3.23/1.91  Inferencing          : 0.13
% 3.23/1.91  Reduction            : 0.05
% 3.23/1.91  Demodulation         : 0.04
% 3.23/1.91  BG Simplification    : 0.01
% 3.23/1.91  Subsumption          : 0.06
% 3.23/1.91  Abstraction          : 0.01
% 3.23/1.91  MUC search           : 0.00
% 3.23/1.91  Cooper               : 0.00
% 3.23/1.91  Total                : 0.78
% 3.23/1.91  Index Insertion      : 0.00
% 3.23/1.91  Index Deletion       : 0.00
% 3.23/1.91  Index Matching       : 0.00
% 3.23/1.91  BG Taut test         : 0.00
%------------------------------------------------------------------------------