TSTP Solution File: SET893+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET893+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/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 : n001.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 10:57:17 EDT 2023

% Result   : Theorem 3.78s 2.04s
% Output   : CNFRefutation 4.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   73 (  32 unt;  18 typ;   0 def)
%            Number of atoms       :   87 (  31 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   67 (  35   ~;  26   |;   2   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   8   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;  10 con; 0-2 aty)
%            Number of variables   :   34 (;  34   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_11 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_2 > #skF_1 > #skF_12

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

tff(cartesian_product2,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

tff(f_40,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

tff(f_51,axiom,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).

tff(f_63,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))
      <=> ( ( A = C )
          & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).

tff(c_8,plain,
    ! [C_9] : in(C_9,singleton(C_9)),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_22,plain,
    ! [A_14,B_15,C_16,D_17] :
      ( in(ordered_pair(A_14,B_15),cartesian_product2(C_16,D_17))
      | ~ in(B_15,D_17)
      | ~ in(A_14,C_16) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_486,plain,
    ! [A_69,B_70,C_71,D_72] :
      ( in(ordered_pair(A_69,B_70),cartesian_product2(C_71,D_72))
      | ~ in(B_70,D_72)
      | ~ in(A_69,C_71) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_34,plain,
    ( ( '#skF_6' = '#skF_8' )
    | ( '#skF_10' != '#skF_12' )
    | ( '#skF_11' != '#skF_9' ) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_45,plain,
    '#skF_11' != '#skF_9',
    inference(splitLeft,[status(thm)],[c_34]) ).

tff(c_42,plain,
    ( ( '#skF_7' = '#skF_5' )
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_56,plain,
    in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))),
    inference(splitLeft,[status(thm)],[c_42]) ).

tff(c_154,plain,
    ! [A_32,C_33,B_34,D_35] :
      ( in(A_32,C_33)
      | ~ in(ordered_pair(A_32,B_34),cartesian_product2(C_33,D_35)) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_158,plain,
    in('#skF_9',singleton('#skF_11')),
    inference(resolution,[status(thm)],[c_56,c_154]) ).

tff(c_6,plain,
    ! [C_9,A_5] :
      ( ( C_9 = A_5 )
      | ~ in(C_9,singleton(A_5)) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_163,plain,
    '#skF_11' = '#skF_9',
    inference(resolution,[status(thm)],[c_158,c_6]) ).

tff(c_168,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_45,c_163]) ).

tff(c_170,plain,
    ~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))),
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_40,plain,
    ( ( '#skF_6' = '#skF_8' )
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_176,plain,
    in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))),
    inference(splitLeft,[status(thm)],[c_40]) ).

tff(c_243,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_170,c_176]) ).

tff(c_245,plain,
    ~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))),
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_244,plain,
    '#skF_6' = '#skF_8',
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_169,plain,
    '#skF_7' = '#skF_5',
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_38,plain,
    ( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_7'),singleton('#skF_8')))
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_458,plain,
    ( ~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8')))
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),singleton('#skF_12'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_244,c_169,c_38]) ).

tff(c_459,plain,
    ~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8'))),
    inference(negUnitSimplification,[status(thm)],[c_245,c_458]) ).

tff(c_492,plain,
    ( ~ in('#skF_8',singleton('#skF_8'))
    | ~ in('#skF_5',singleton('#skF_5')) ),
    inference(resolution,[status(thm)],[c_486,c_459]) ).

tff(c_505,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_492]) ).

tff(c_507,plain,
    '#skF_11' = '#skF_9',
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_980,plain,
    ! [A_122,B_123,C_124,D_125] :
      ( in(ordered_pair(A_122,B_123),cartesian_product2(C_124,D_125))
      | ~ in(B_123,D_125)
      | ~ in(A_122,C_124) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_506,plain,
    ( ( '#skF_10' != '#skF_12' )
    | ( '#skF_6' = '#skF_8' ) ),
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_512,plain,
    '#skF_10' != '#skF_12',
    inference(splitLeft,[status(thm)],[c_506]) ).

tff(c_559,plain,
    ( ( '#skF_7' = '#skF_5' )
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_507,c_42]) ).

tff(c_560,plain,
    in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))),
    inference(splitLeft,[status(thm)],[c_559]) ).

tff(c_746,plain,
    ! [B_92,D_93,A_94,C_95] :
      ( in(B_92,D_93)
      | ~ in(ordered_pair(A_94,B_92),cartesian_product2(C_95,D_93)) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_750,plain,
    in('#skF_10',singleton('#skF_12')),
    inference(resolution,[status(thm)],[c_560,c_746]) ).

tff(c_755,plain,
    '#skF_10' = '#skF_12',
    inference(resolution,[status(thm)],[c_750,c_6]) ).

tff(c_760,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_512,c_755]) ).

tff(c_762,plain,
    ~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))),
    inference(splitRight,[status(thm)],[c_559]) ).

tff(c_800,plain,
    ( ( '#skF_6' = '#skF_8' )
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_507,c_40]) ).

tff(c_801,plain,
    in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))),
    inference(splitLeft,[status(thm)],[c_800]) ).

tff(c_802,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_762,c_801]) ).

tff(c_803,plain,
    '#skF_6' = '#skF_8',
    inference(splitRight,[status(thm)],[c_800]) ).

tff(c_761,plain,
    '#skF_7' = '#skF_5',
    inference(splitRight,[status(thm)],[c_559]) ).

tff(c_956,plain,
    ( ~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8')))
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),singleton('#skF_12'))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_507,c_803,c_761,c_38]) ).

tff(c_957,plain,
    ~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8'))),
    inference(negUnitSimplification,[status(thm)],[c_762,c_956]) ).

tff(c_983,plain,
    ( ~ in('#skF_8',singleton('#skF_8'))
    | ~ in('#skF_5',singleton('#skF_5')) ),
    inference(resolution,[status(thm)],[c_980,c_957]) ).

tff(c_998,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_983]) ).

tff(c_1000,plain,
    '#skF_10' = '#skF_12',
    inference(splitRight,[status(thm)],[c_506]) ).

tff(c_36,plain,
    ( ( '#skF_7' = '#skF_5' )
    | ( '#skF_10' != '#skF_12' )
    | ( '#skF_11' != '#skF_9' ) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_1010,plain,
    '#skF_7' = '#skF_5',
    inference(demodulation,[status(thm),theory(equality)],[c_507,c_1000,c_36]) ).

tff(c_999,plain,
    '#skF_6' = '#skF_8',
    inference(splitRight,[status(thm)],[c_506]) ).

tff(c_32,plain,
    ( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_7'),singleton('#skF_8')))
    | ( '#skF_10' != '#skF_12' )
    | ( '#skF_11' != '#skF_9' ) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_1265,plain,
    ~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2(singleton('#skF_5'),singleton('#skF_8'))),
    inference(demodulation,[status(thm),theory(equality)],[c_507,c_1000,c_1010,c_999,c_32]) ).

tff(c_1268,plain,
    ( ~ in('#skF_8',singleton('#skF_8'))
    | ~ in('#skF_5',singleton('#skF_5')) ),
    inference(resolution,[status(thm)],[c_22,c_1265]) ).

tff(c_1272,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_1268]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET893+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14  % 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 : n001.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 17:26:25 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.78/2.04  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.78/2.04  
% 3.78/2.04  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.20/2.07  
% 4.20/2.07  Inference rules
% 4.20/2.07  ----------------------
% 4.20/2.07  #Ref     : 0
% 4.20/2.07  #Sup     : 315
% 4.20/2.07  #Fact    : 0
% 4.20/2.07  #Define  : 0
% 4.20/2.07  #Split   : 6
% 4.20/2.07  #Chain   : 0
% 4.20/2.07  #Close   : 0
% 4.20/2.07  
% 4.20/2.07  Ordering : KBO
% 4.20/2.07  
% 4.20/2.07  Simplification rules
% 4.20/2.07  ----------------------
% 4.20/2.07  #Subsume      : 6
% 4.20/2.07  #Demod        : 84
% 4.20/2.07  #Tautology    : 170
% 4.20/2.07  #SimpNegUnit  : 6
% 4.20/2.07  #BackRed      : 0
% 4.20/2.07  
% 4.20/2.07  #Partial instantiations: 0
% 4.20/2.07  #Strategies tried      : 1
% 4.20/2.07  
% 4.20/2.07  Timing (in seconds)
% 4.20/2.07  ----------------------
% 4.20/2.07  Preprocessing        : 0.49
% 4.20/2.08  Parsing              : 0.26
% 4.20/2.08  CNF conversion       : 0.03
% 4.20/2.08  Main loop            : 0.50
% 4.20/2.08  Inferencing          : 0.19
% 4.20/2.08  Reduction            : 0.15
% 4.20/2.08  Demodulation         : 0.12
% 4.20/2.08  BG Simplification    : 0.03
% 4.20/2.08  Subsumption          : 0.09
% 4.20/2.08  Abstraction          : 0.02
% 4.20/2.08  MUC search           : 0.00
% 4.20/2.08  Cooper               : 0.00
% 4.20/2.08  Total                : 1.05
% 4.20/2.08  Index Insertion      : 0.00
% 4.20/2.08  Index Deletion       : 0.00
% 4.20/2.08  Index Matching       : 0.00
% 4.20/2.08  BG Taut test         : 0.00
%------------------------------------------------------------------------------