TSTP Solution File: SET921+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : 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 10:57:20 EDT 2023

% Result   : Theorem 3.34s 1.87s
% Output   : CNFRefutation 3.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   81 (  40 unt;  16 typ;   0 def)
%            Number of atoms       :   99 (  25 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   72 (  38   ~;  27   |;   2   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   8   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   8 con; 0-3 aty)
%            Number of variables   :   31 (;  31   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > set_difference > #nlpp > singleton > #skF_11 > #skF_4 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1 > #skF_12

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(set_difference,type,
    set_difference: ( $i * $i ) > $i ).

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

tff('#skF_11',type,
    '#skF_11': $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

tff('#skF_7',type,
    '#skF_7': $i ).

tff('#skF_10',type,
    '#skF_10': $i ).

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

tff('#skF_5',type,
    '#skF_5': $i ).

tff('#skF_6',type,
    '#skF_6': $i ).

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

tff('#skF_9',type,
    '#skF_9': $i ).

tff('#skF_8',type,
    '#skF_8': $i ).

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

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

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

tff('#skF_12',type,
    '#skF_12': $i ).

tff(f_38,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

tff(f_61,negated_conjecture,
    ~ ! [A,B,C] :
        ( in(A,set_difference(B,singleton(C)))
      <=> ( in(A,B)
          & ( A != C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).

tff(f_48,axiom,
    ! [A,B,C] :
      ( ( C = set_difference(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & ~ in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).

tff(c_6,plain,
    ! [C_7] : in(C_7,singleton(C_7)),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_40,plain,
    ( ( '#skF_7' != '#skF_9' )
    | ( '#skF_10' = '#skF_12' )
    | ~ in('#skF_10','#skF_11') ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_60,plain,
    ~ in('#skF_10','#skF_11'),
    inference(splitLeft,[status(thm)],[c_40]) ).

tff(c_46,plain,
    ( ( '#skF_7' != '#skF_9' )
    | in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_62,plain,
    '#skF_7' != '#skF_9',
    inference(splitLeft,[status(thm)],[c_46]) ).

tff(c_48,plain,
    ( in('#skF_7','#skF_8')
    | in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_65,plain,
    in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))),
    inference(splitLeft,[status(thm)],[c_48]) ).

tff(c_20,plain,
    ! [D_13,A_8,B_9] :
      ( in(D_13,A_8)
      | ~ in(D_13,set_difference(A_8,B_9)) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_68,plain,
    in('#skF_10','#skF_11'),
    inference(resolution,[status(thm)],[c_65,c_20]) ).

tff(c_77,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_60,c_68]) ).

tff(c_78,plain,
    in('#skF_7','#skF_8'),
    inference(splitRight,[status(thm)],[c_48]) ).

tff(c_16,plain,
    ! [D_13,A_8,B_9] :
      ( in(D_13,set_difference(A_8,B_9))
      | in(D_13,B_9)
      | ~ in(D_13,A_8) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_79,plain,
    ~ in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))),
    inference(splitRight,[status(thm)],[c_48]) ).

tff(c_44,plain,
    ( ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9')))
    | in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_116,plain,
    ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9'))),
    inference(negUnitSimplification,[status(thm)],[c_79,c_44]) ).

tff(c_119,plain,
    ( in('#skF_7',singleton('#skF_9'))
    | ~ in('#skF_7','#skF_8') ),
    inference(resolution,[status(thm)],[c_16,c_116]) ).

tff(c_122,plain,
    in('#skF_7',singleton('#skF_9')),
    inference(demodulation,[status(thm),theory(equality)],[c_78,c_119]) ).

tff(c_4,plain,
    ! [C_7,A_3] :
      ( ( C_7 = A_3 )
      | ~ in(C_7,singleton(A_3)) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_127,plain,
    '#skF_7' = '#skF_9',
    inference(resolution,[status(thm)],[c_122,c_4]) ).

tff(c_132,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_62,c_127]) ).

tff(c_133,plain,
    in('#skF_10',set_difference('#skF_11',singleton('#skF_12'))),
    inference(splitRight,[status(thm)],[c_46]) ).

tff(c_149,plain,
    ! [D_37,A_38,B_39] :
      ( in(D_37,A_38)
      | ~ in(D_37,set_difference(A_38,B_39)) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_152,plain,
    in('#skF_10','#skF_11'),
    inference(resolution,[status(thm)],[c_133,c_149]) ).

tff(c_156,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_60,c_152]) ).

tff(c_157,plain,
    ( ( '#skF_7' != '#skF_9' )
    | ( '#skF_10' = '#skF_12' ) ),
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_162,plain,
    '#skF_7' != '#skF_9',
    inference(splitLeft,[status(thm)],[c_157]) ).

tff(c_158,plain,
    in('#skF_10','#skF_11'),
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_42,plain,
    ( in('#skF_7','#skF_8')
    | ( '#skF_10' = '#skF_12' )
    | ~ in('#skF_10','#skF_11') ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_165,plain,
    ( in('#skF_7','#skF_8')
    | ( '#skF_10' = '#skF_12' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_158,c_42]) ).

tff(c_166,plain,
    '#skF_10' = '#skF_12',
    inference(splitLeft,[status(thm)],[c_165]) ).

tff(c_179,plain,
    ( in('#skF_7','#skF_8')
    | in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_166,c_48]) ).

tff(c_180,plain,
    in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))),
    inference(splitLeft,[status(thm)],[c_179]) ).

tff(c_18,plain,
    ! [D_13,B_9,A_8] :
      ( ~ in(D_13,B_9)
      | ~ in(D_13,set_difference(A_8,B_9)) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_186,plain,
    ~ in('#skF_12',singleton('#skF_12')),
    inference(resolution,[status(thm)],[c_180,c_18]) ).

tff(c_194,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_186]) ).

tff(c_195,plain,
    in('#skF_7','#skF_8'),
    inference(splitRight,[status(thm)],[c_179]) ).

tff(c_196,plain,
    ~ in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))),
    inference(splitRight,[status(thm)],[c_179]) ).

tff(c_243,plain,
    ( ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9')))
    | in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_166,c_44]) ).

tff(c_244,plain,
    ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9'))),
    inference(negUnitSimplification,[status(thm)],[c_196,c_243]) ).

tff(c_247,plain,
    ( in('#skF_7',singleton('#skF_9'))
    | ~ in('#skF_7','#skF_8') ),
    inference(resolution,[status(thm)],[c_16,c_244]) ).

tff(c_250,plain,
    in('#skF_7',singleton('#skF_9')),
    inference(demodulation,[status(thm),theory(equality)],[c_195,c_247]) ).

tff(c_255,plain,
    '#skF_7' = '#skF_9',
    inference(resolution,[status(thm)],[c_250,c_4]) ).

tff(c_260,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_162,c_255]) ).

tff(c_261,plain,
    in('#skF_7','#skF_8'),
    inference(splitRight,[status(thm)],[c_165]) ).

tff(c_273,plain,
    ! [D_65,A_66,B_67] :
      ( in(D_65,set_difference(A_66,B_67))
      | in(D_65,B_67)
      | ~ in(D_65,A_66) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_262,plain,
    '#skF_10' != '#skF_12',
    inference(splitRight,[status(thm)],[c_165]) ).

tff(c_38,plain,
    ( ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9')))
    | ( '#skF_10' = '#skF_12' )
    | ~ in('#skF_10','#skF_11') ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_270,plain,
    ( ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9')))
    | ( '#skF_10' = '#skF_12' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_158,c_38]) ).

tff(c_271,plain,
    ~ in('#skF_7',set_difference('#skF_8',singleton('#skF_9'))),
    inference(negUnitSimplification,[status(thm)],[c_262,c_270]) ).

tff(c_276,plain,
    ( in('#skF_7',singleton('#skF_9'))
    | ~ in('#skF_7','#skF_8') ),
    inference(resolution,[status(thm)],[c_273,c_271]) ).

tff(c_291,plain,
    in('#skF_7',singleton('#skF_9')),
    inference(demodulation,[status(thm),theory(equality)],[c_261,c_276]) ).

tff(c_300,plain,
    '#skF_7' = '#skF_9',
    inference(resolution,[status(thm)],[c_291,c_4]) ).

tff(c_305,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_162,c_300]) ).

tff(c_307,plain,
    '#skF_7' = '#skF_9',
    inference(splitRight,[status(thm)],[c_157]) ).

tff(c_306,plain,
    '#skF_10' = '#skF_12',
    inference(splitRight,[status(thm)],[c_157]) ).

tff(c_314,plain,
    ( ( '#skF_7' != '#skF_9' )
    | in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_306,c_46]) ).

tff(c_315,plain,
    '#skF_7' != '#skF_9',
    inference(splitLeft,[status(thm)],[c_314]) ).

tff(c_321,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_307,c_315]) ).

tff(c_322,plain,
    in('#skF_12',set_difference('#skF_11',singleton('#skF_12'))),
    inference(splitRight,[status(thm)],[c_314]) ).

tff(c_338,plain,
    ! [D_69,B_70,A_71] :
      ( ~ in(D_69,B_70)
      | ~ in(D_69,set_difference(A_71,B_70)) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_341,plain,
    ~ in('#skF_12',singleton('#skF_12')),
    inference(resolution,[status(thm)],[c_322,c_338]) ).

tff(c_345,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_341]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15  % 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
% 0.15/0.36  % 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 16:45:00 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 3.34/1.87  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.34/1.88  
% 3.34/1.88  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.34/1.91  
% 3.34/1.91  Inference rules
% 3.34/1.91  ----------------------
% 3.34/1.91  #Ref     : 0
% 3.34/1.91  #Sup     : 57
% 3.34/1.91  #Fact    : 0
% 3.34/1.91  #Define  : 0
% 3.34/1.91  #Split   : 7
% 3.34/1.91  #Chain   : 0
% 3.34/1.91  #Close   : 0
% 3.34/1.91  
% 3.34/1.91  Ordering : KBO
% 3.34/1.91  
% 3.34/1.91  Simplification rules
% 3.34/1.91  ----------------------
% 3.34/1.91  #Subsume      : 8
% 3.34/1.91  #Demod        : 31
% 3.34/1.91  #Tautology    : 24
% 3.34/1.91  #SimpNegUnit  : 8
% 3.34/1.91  #BackRed      : 4
% 3.34/1.91  
% 3.34/1.91  #Partial instantiations: 0
% 3.34/1.91  #Strategies tried      : 1
% 3.34/1.91  
% 3.34/1.91  Timing (in seconds)
% 3.34/1.91  ----------------------
% 3.34/1.92  Preprocessing        : 0.50
% 3.34/1.92  Parsing              : 0.24
% 3.34/1.92  CNF conversion       : 0.04
% 3.34/1.92  Main loop            : 0.35
% 3.34/1.92  Inferencing          : 0.12
% 3.34/1.92  Reduction            : 0.10
% 3.34/1.92  Demodulation         : 0.06
% 3.34/1.92  BG Simplification    : 0.02
% 3.34/1.92  Subsumption          : 0.09
% 3.34/1.92  Abstraction          : 0.01
% 3.34/1.92  MUC search           : 0.00
% 3.34/1.92  Cooper               : 0.00
% 3.34/1.92  Total                : 0.91
% 3.34/1.92  Index Insertion      : 0.00
% 3.34/1.92  Index Deletion       : 0.00
% 3.34/1.92  Index Matching       : 0.00
% 3.34/1.92  BG Taut test         : 0.00
%------------------------------------------------------------------------------