TSTP Solution File: SET962+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : n012.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 10:57:25 EDT 2023

% Result   : Theorem 3.66s 1.94s
% Output   : CNFRefutation 3.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   63 (  22 unt;  12 typ;   0 def)
%            Number of atoms       :   96 (  19 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   89 (  44   ~;  40   |;   1   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   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    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :   59 (;  59   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4 > #skF_5

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_6',type,
    '#skF_6': ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

tff(f_55,negated_conjecture,
    ~ ! [A,B] :
        ( ( cartesian_product2(A,A) = cartesian_product2(B,B) )
       => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).

tff(f_62,axiom,
    ! [A,B] :
      ( ! [C] :
          ( in(C,A)
        <=> in(C,B) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

tff(f_45,axiom,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).

tff(c_20,plain,
    '#skF_3' != '#skF_4',
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_30,plain,
    ! [A_13,B_14] :
      ( in('#skF_5'(A_13,B_14),B_14)
      | in('#skF_6'(A_13,B_14),A_13)
      | ( B_14 = A_13 ) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_286,plain,
    ! [A_52,B_53,C_54,D_55] :
      ( in(ordered_pair(A_52,B_53),cartesian_product2(C_54,D_55))
      | ~ in(B_53,D_55)
      | ~ in(A_52,C_54) ),
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_22,plain,
    cartesian_product2('#skF_3','#skF_3') = cartesian_product2('#skF_4','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_195,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_45]) ).

tff(c_198,plain,
    ! [A_32,B_34] :
      ( in(A_32,'#skF_3')
      | ~ in(ordered_pair(A_32,B_34),cartesian_product2('#skF_4','#skF_4')) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_195]) ).

tff(c_306,plain,
    ! [A_52,B_53] :
      ( in(A_52,'#skF_3')
      | ~ in(B_53,'#skF_4')
      | ~ in(A_52,'#skF_4') ),
    inference(resolution,[status(thm)],[c_286,c_198]) ).

tff(c_312,plain,
    ! [B_56] : ~ in(B_56,'#skF_4'),
    inference(splitLeft,[status(thm)],[c_306]) ).

tff(c_323,plain,
    ! [B_14] :
      ( in('#skF_5'('#skF_4',B_14),B_14)
      | ( B_14 = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_30,c_312]) ).

tff(c_311,plain,
    ! [B_53] : ~ in(B_53,'#skF_4'),
    inference(splitLeft,[status(thm)],[c_306]) ).

tff(c_348,plain,
    ! [A_63,B_64] :
      ( in(ordered_pair(A_63,B_64),cartesian_product2('#skF_4','#skF_4'))
      | ~ in(B_64,'#skF_3')
      | ~ in(A_63,'#skF_3') ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_286]) ).

tff(c_14,plain,
    ! [A_9,C_11,B_10,D_12] :
      ( in(A_9,C_11)
      | ~ in(ordered_pair(A_9,B_10),cartesian_product2(C_11,D_12)) ),
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_357,plain,
    ! [A_63,B_64] :
      ( in(A_63,'#skF_4')
      | ~ in(B_64,'#skF_3')
      | ~ in(A_63,'#skF_3') ),
    inference(resolution,[status(thm)],[c_348,c_14]) ).

tff(c_367,plain,
    ! [B_64,A_63] :
      ( ~ in(B_64,'#skF_3')
      | ~ in(A_63,'#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_311,c_357]) ).

tff(c_376,plain,
    ! [A_67] : ~ in(A_67,'#skF_3'),
    inference(splitLeft,[status(thm)],[c_367]) ).

tff(c_380,plain,
    '#skF_3' = '#skF_4',
    inference(resolution,[status(thm)],[c_323,c_376]) ).

tff(c_394,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_380]) ).

tff(c_398,plain,
    ! [B_68] : ~ in(B_68,'#skF_3'),
    inference(splitRight,[status(thm)],[c_367]) ).

tff(c_402,plain,
    '#skF_3' = '#skF_4',
    inference(resolution,[status(thm)],[c_323,c_398]) ).

tff(c_416,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_402]) ).

tff(c_417,plain,
    ! [A_52] :
      ( in(A_52,'#skF_3')
      | ~ in(A_52,'#skF_4') ),
    inference(splitRight,[status(thm)],[c_306]) ).

tff(c_28,plain,
    ! [A_13,B_14] :
      ( ~ in('#skF_5'(A_13,B_14),A_13)
      | in('#skF_6'(A_13,B_14),A_13)
      | ( B_14 = A_13 ) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_446,plain,
    ! [A_76,B_77] :
      ( in(ordered_pair(A_76,B_77),cartesian_product2('#skF_4','#skF_4'))
      | ~ in(B_77,'#skF_3')
      | ~ in(A_76,'#skF_3') ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_286]) ).

tff(c_463,plain,
    ! [A_76,B_77] :
      ( in(A_76,'#skF_4')
      | ~ in(B_77,'#skF_3')
      | ~ in(A_76,'#skF_3') ),
    inference(resolution,[status(thm)],[c_446,c_14]) ).

tff(c_470,plain,
    ! [B_78] : ~ in(B_78,'#skF_3'),
    inference(splitLeft,[status(thm)],[c_463]) ).

tff(c_506,plain,
    ! [B_86] :
      ( in('#skF_5'('#skF_3',B_86),B_86)
      | ( B_86 = '#skF_3' ) ),
    inference(resolution,[status(thm)],[c_30,c_470]) ).

tff(c_466,plain,
    ! [B_77] : ~ in(B_77,'#skF_3'),
    inference(splitLeft,[status(thm)],[c_463]) ).

tff(c_467,plain,
    ! [A_52] : ~ in(A_52,'#skF_4'),
    inference(negUnitSimplification,[status(thm)],[c_466,c_417]) ).

tff(c_510,plain,
    '#skF_3' = '#skF_4',
    inference(resolution,[status(thm)],[c_506,c_467]) ).

tff(c_527,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_510]) ).

tff(c_529,plain,
    ! [A_87] :
      ( in(A_87,'#skF_4')
      | ~ in(A_87,'#skF_3') ),
    inference(splitRight,[status(thm)],[c_463]) ).

tff(c_565,plain,
    ! [B_91] :
      ( in('#skF_6'('#skF_3',B_91),'#skF_4')
      | ~ in('#skF_5'('#skF_3',B_91),'#skF_3')
      | ( B_91 = '#skF_3' ) ),
    inference(resolution,[status(thm)],[c_28,c_529]) ).

tff(c_418,plain,
    ! [A_69] :
      ( in(A_69,'#skF_3')
      | ~ in(A_69,'#skF_4') ),
    inference(splitRight,[status(thm)],[c_306]) ).

tff(c_24,plain,
    ! [A_13,B_14] :
      ( ~ in('#skF_5'(A_13,B_14),A_13)
      | ~ in('#skF_6'(A_13,B_14),B_14)
      | ( B_14 = A_13 ) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_434,plain,
    ! [B_14] :
      ( ~ in('#skF_6'('#skF_3',B_14),B_14)
      | ( B_14 = '#skF_3' )
      | ~ in('#skF_5'('#skF_3',B_14),'#skF_4') ),
    inference(resolution,[status(thm)],[c_418,c_24]) ).

tff(c_569,plain,
    ( ~ in('#skF_5'('#skF_3','#skF_4'),'#skF_4')
    | ~ in('#skF_5'('#skF_3','#skF_4'),'#skF_3')
    | ( '#skF_3' = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_565,c_434]) ).

tff(c_578,plain,
    ( ~ in('#skF_5'('#skF_3','#skF_4'),'#skF_4')
    | ~ in('#skF_5'('#skF_3','#skF_4'),'#skF_3') ),
    inference(negUnitSimplification,[status(thm)],[c_20,c_20,c_569]) ).

tff(c_582,plain,
    ~ in('#skF_5'('#skF_3','#skF_4'),'#skF_3'),
    inference(splitLeft,[status(thm)],[c_578]) ).

tff(c_586,plain,
    ~ in('#skF_5'('#skF_3','#skF_4'),'#skF_4'),
    inference(resolution,[status(thm)],[c_417,c_582]) ).

tff(c_592,plain,
    ! [B_96] :
      ( in('#skF_6'('#skF_3',B_96),'#skF_4')
      | in('#skF_5'('#skF_3',B_96),B_96)
      | ( B_96 = '#skF_3' ) ),
    inference(resolution,[status(thm)],[c_30,c_529]) ).

tff(c_26,plain,
    ! [A_13,B_14] :
      ( in('#skF_5'(A_13,B_14),B_14)
      | ~ in('#skF_6'(A_13,B_14),B_14)
      | ( B_14 = A_13 ) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_600,plain,
    ( in('#skF_5'('#skF_3','#skF_4'),'#skF_4')
    | ( '#skF_3' = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_592,c_26]) ).

tff(c_618,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_586,c_20,c_586,c_600]) ).

tff(c_619,plain,
    ~ in('#skF_5'('#skF_3','#skF_4'),'#skF_4'),
    inference(splitRight,[status(thm)],[c_578]) ).

tff(c_620,plain,
    in('#skF_5'('#skF_3','#skF_4'),'#skF_3'),
    inference(splitRight,[status(thm)],[c_578]) ).

tff(c_528,plain,
    ! [A_76] :
      ( in(A_76,'#skF_4')
      | ~ in(A_76,'#skF_3') ),
    inference(splitRight,[status(thm)],[c_463]) ).

tff(c_624,plain,
    in('#skF_5'('#skF_3','#skF_4'),'#skF_4'),
    inference(resolution,[status(thm)],[c_620,c_528]) ).

tff(c_635,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_619,c_624]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n012.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 16:02:22 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 3.66/1.94  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.66/1.94  
% 3.66/1.94  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.66/1.98  
% 3.66/1.98  Inference rules
% 3.66/1.98  ----------------------
% 3.66/1.98  #Ref     : 0
% 3.66/1.98  #Sup     : 128
% 3.66/1.98  #Fact    : 0
% 3.66/1.98  #Define  : 0
% 3.66/1.98  #Split   : 4
% 3.66/1.98  #Chain   : 0
% 3.66/1.98  #Close   : 0
% 3.66/1.98  
% 3.66/1.98  Ordering : KBO
% 3.66/1.98  
% 3.66/1.98  Simplification rules
% 3.66/1.98  ----------------------
% 3.66/1.98  #Subsume      : 21
% 3.66/1.98  #Demod        : 13
% 3.66/1.98  #Tautology    : 48
% 3.66/1.98  #SimpNegUnit  : 17
% 3.66/1.98  #BackRed      : 7
% 3.66/1.98  
% 3.66/1.98  #Partial instantiations: 0
% 3.66/1.98  #Strategies tried      : 1
% 3.66/1.98  
% 3.66/1.98  Timing (in seconds)
% 3.66/1.98  ----------------------
% 3.66/1.98  Preprocessing        : 0.47
% 3.66/1.98  Parsing              : 0.24
% 3.66/1.98  CNF conversion       : 0.03
% 3.66/1.98  Main loop            : 0.44
% 3.66/1.98  Inferencing          : 0.18
% 3.66/1.98  Reduction            : 0.11
% 3.66/1.98  Demodulation         : 0.08
% 3.66/1.98  BG Simplification    : 0.02
% 3.66/1.98  Subsumption          : 0.10
% 3.66/1.98  Abstraction          : 0.02
% 3.66/1.98  MUC search           : 0.00
% 3.66/1.98  Cooper               : 0.00
% 3.66/1.98  Total                : 0.96
% 3.66/1.98  Index Insertion      : 0.00
% 3.66/1.98  Index Deletion       : 0.00
% 3.66/1.98  Index Matching       : 0.00
% 3.66/1.98  BG Taut test         : 0.00
%------------------------------------------------------------------------------