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 v2.4.0.
% 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 : n010.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   : Unsatisfiable 3.06s 1.85s
% Output   : CNFRefutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   42 (   9 unt;  12 typ;   0 def)
%            Number of atoms       :  104 (  15 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  137 (  63   ~;  74   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 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   :   31 (;  31   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subpopulations > in_environment > greater > stable > environment > sk1 > growth_rate > #nlpp > sk2 > critical_point > 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(efficient_producers,type,
    efficient_producers: $i ).

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

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

tff(f_95,axiom,
    ~ in_environment(sk3,critical_point(sk3)),
    file(unknown,unknown) ).

tff(f_92,axiom,
    environment(sk3),
    file(unknown,unknown) ).

tff(f_93,axiom,
    stable(sk3),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ! [A] :
      ( ~ environment(A)
      | ~ stable(A)
      | in_environment(A,sk2(A)) ),
    file(unknown,unknown) ).

tff(f_35,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
      | ~ in_environment(A,B)
      | subpopulations(first_movers,efficient_producers,A,sk1(B,A))
      | ( B = critical_point(A) ) ),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ! [A] :
      ( ~ environment(A)
      | ~ stable(A)
      | ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A))) ),
    file(unknown,unknown) ).

tff(f_47,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
      | ~ in_environment(A,B)
      | greater(sk1(B,A),B)
      | ( B = critical_point(A) ) ),
    file(unknown,unknown) ).

tff(f_91,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | ~ stable(A)
      | ~ subpopulations(first_movers,efficient_producers,A,B)
      | ~ greater(B,sk2(A))
      | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) ),
    file(unknown,unknown) ).

tff(f_60,axiom,
    ! [A,B] :
      ( ~ environment(A)
      | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
      | ~ in_environment(A,B)
      | ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
      | ( B = critical_point(A) ) ),
    file(unknown,unknown) ).

tff(c_18,plain,
    ~ in_environment(sk3,critical_point(sk3)),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_14,plain,
    environment(sk3),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_16,plain,
    stable(sk3),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_8,plain,
    ! [A_7] :
      ( in_environment(A_7,sk2(A_7))
      | ~ stable(A_7)
      | ~ environment(A_7) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_35,plain,
    ! [A_19,B_20] :
      ( ( critical_point(A_19) = B_20 )
      | subpopulations(first_movers,efficient_producers,A_19,sk1(B_20,A_19))
      | ~ in_environment(A_19,B_20)
      | greater(growth_rate(efficient_producers,B_20),growth_rate(first_movers,B_20))
      | ~ environment(A_19) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_10,plain,
    ! [A_8] :
      ( ~ greater(growth_rate(efficient_producers,sk2(A_8)),growth_rate(first_movers,sk2(A_8)))
      | ~ stable(A_8)
      | ~ environment(A_8) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_39,plain,
    ! [A_8,A_19] :
      ( ~ stable(A_8)
      | ~ environment(A_8)
      | ( sk2(A_8) = critical_point(A_19) )
      | subpopulations(first_movers,efficient_producers,A_19,sk1(sk2(A_8),A_19))
      | ~ in_environment(A_19,sk2(A_8))
      | ~ environment(A_19) ),
    inference(resolution,[status(thm)],[c_35,c_10]) ).

tff(c_21,plain,
    ! [A_13,B_14] :
      ( ( critical_point(A_13) = B_14 )
      | greater(sk1(B_14,A_13),B_14)
      | ~ in_environment(A_13,B_14)
      | greater(growth_rate(efficient_producers,B_14),growth_rate(first_movers,B_14))
      | ~ environment(A_13) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_31,plain,
    ! [A_17,A_18] :
      ( ~ stable(A_17)
      | ~ environment(A_17)
      | ( sk2(A_17) = critical_point(A_18) )
      | greater(sk1(sk2(A_17),A_18),sk2(A_17))
      | ~ in_environment(A_18,sk2(A_17))
      | ~ environment(A_18) ),
    inference(resolution,[status(thm)],[c_21,c_10]) ).

tff(c_12,plain,
    ! [B_10,A_9] :
      ( greater(growth_rate(efficient_producers,B_10),growth_rate(first_movers,B_10))
      | ~ greater(B_10,sk2(A_9))
      | ~ subpopulations(first_movers,efficient_producers,A_9,B_10)
      | ~ stable(A_9)
      | ~ environment(A_9) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_50,plain,
    ! [A_25,A_26] :
      ( greater(growth_rate(efficient_producers,sk1(sk2(A_25),A_26)),growth_rate(first_movers,sk1(sk2(A_25),A_26)))
      | ~ subpopulations(first_movers,efficient_producers,A_25,sk1(sk2(A_25),A_26))
      | ~ stable(A_25)
      | ~ environment(A_25)
      | ( sk2(A_25) = critical_point(A_26) )
      | ~ in_environment(A_26,sk2(A_25))
      | ~ environment(A_26) ),
    inference(resolution,[status(thm)],[c_31,c_12]) ).

tff(c_6,plain,
    ! [A_5,B_6] :
      ( ( critical_point(A_5) = B_6 )
      | ~ greater(growth_rate(efficient_producers,sk1(B_6,A_5)),growth_rate(first_movers,sk1(B_6,A_5)))
      | ~ in_environment(A_5,B_6)
      | greater(growth_rate(efficient_producers,B_6),growth_rate(first_movers,B_6))
      | ~ environment(A_5) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_55,plain,
    ! [A_27,A_28] :
      ( greater(growth_rate(efficient_producers,sk2(A_27)),growth_rate(first_movers,sk2(A_27)))
      | ~ subpopulations(first_movers,efficient_producers,A_27,sk1(sk2(A_27),A_28))
      | ~ stable(A_27)
      | ~ environment(A_27)
      | ( sk2(A_27) = critical_point(A_28) )
      | ~ in_environment(A_28,sk2(A_27))
      | ~ environment(A_28) ),
    inference(resolution,[status(thm)],[c_50,c_6]) ).

tff(c_64,plain,
    ! [A_29] :
      ( greater(growth_rate(efficient_producers,sk2(A_29)),growth_rate(first_movers,sk2(A_29)))
      | ~ stable(A_29)
      | ( sk2(A_29) = critical_point(A_29) )
      | ~ in_environment(A_29,sk2(A_29))
      | ~ environment(A_29) ),
    inference(resolution,[status(thm)],[c_39,c_55]) ).

tff(c_69,plain,
    ! [A_30] :
      ( ~ stable(A_30)
      | ( sk2(A_30) = critical_point(A_30) )
      | ~ in_environment(A_30,sk2(A_30))
      | ~ environment(A_30) ),
    inference(resolution,[status(thm)],[c_64,c_10]) ).

tff(c_83,plain,
    ! [A_34] :
      ( ( sk2(A_34) = critical_point(A_34) )
      | ~ stable(A_34)
      | ~ environment(A_34) ),
    inference(resolution,[status(thm)],[c_8,c_69]) ).

tff(c_86,plain,
    ( ( sk2(sk3) = critical_point(sk3) )
    | ~ environment(sk3) ),
    inference(resolution,[status(thm)],[c_16,c_83]) ).

tff(c_89,plain,
    sk2(sk3) = critical_point(sk3),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_86]) ).

tff(c_118,plain,
    ( in_environment(sk3,critical_point(sk3))
    | ~ stable(sk3)
    | ~ environment(sk3) ),
    inference(superposition,[status(thm),theory(equality)],[c_89,c_8]) ).

tff(c_140,plain,
    in_environment(sk3,critical_point(sk3)),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_16,c_118]) ).

tff(c_142,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_140]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : MGT023-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 20:21:59 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.06/1.85  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.06/1.85  
% 3.06/1.85  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.33/1.88  
% 3.33/1.88  Inference rules
% 3.33/1.88  ----------------------
% 3.33/1.88  #Ref     : 0
% 3.33/1.88  #Sup     : 26
% 3.33/1.88  #Fact    : 0
% 3.33/1.88  #Define  : 0
% 3.33/1.88  #Split   : 0
% 3.33/1.88  #Chain   : 0
% 3.33/1.88  #Close   : 0
% 3.33/1.88  
% 3.33/1.88  Ordering : KBO
% 3.33/1.88  
% 3.33/1.88  Simplification rules
% 3.33/1.88  ----------------------
% 3.33/1.88  #Subsume      : 2
% 3.33/1.88  #Demod        : 43
% 3.33/1.88  #Tautology    : 1
% 3.33/1.88  #SimpNegUnit  : 1
% 3.33/1.88  #BackRed      : 0
% 3.33/1.88  
% 3.33/1.88  #Partial instantiations: 0
% 3.33/1.88  #Strategies tried      : 1
% 3.33/1.88  
% 3.33/1.88  Timing (in seconds)
% 3.33/1.88  ----------------------
% 3.33/1.89  Preprocessing        : 0.45
% 3.33/1.89  Parsing              : 0.25
% 3.33/1.89  CNF conversion       : 0.02
% 3.33/1.89  Main loop            : 0.32
% 3.33/1.89  Inferencing          : 0.15
% 3.33/1.89  Reduction            : 0.07
% 3.33/1.89  Demodulation         : 0.05
% 3.33/1.89  BG Simplification    : 0.02
% 3.33/1.89  Subsumption          : 0.07
% 3.33/1.89  Abstraction          : 0.01
% 3.33/1.89  MUC search           : 0.00
% 3.33/1.89  Cooper               : 0.00
% 3.33/1.89  Total                : 0.83
% 3.33/1.89  Index Insertion      : 0.00
% 3.33/1.89  Index Deletion       : 0.00
% 3.33/1.89  Index Matching       : 0.00
% 3.33/1.89  BG Taut test         : 0.00
%------------------------------------------------------------------------------