TSTP Solution File: SET902+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET902+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 : n025.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 10:57:18 EDT 2023

% Result   : Theorem 3.20s 1.85s
% Output   : CNFRefutation 3.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   55 (  31 unt;  10 typ;   0 def)
%            Number of atoms       :   71 (  53 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   51 (  25   ~;  19   |;   6   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   37 (;  37   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > empty > set_union2 > #nlpp > singleton > empty_set > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

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

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

tff(subset,type,
    subset: ( $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(empty_set,type,
    empty_set: $i ).

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

tff(set_union2,type,
    set_union2: ( $i * $i ) > $i ).

tff(f_80,negated_conjecture,
    ~ ! [A,B,C] :
        ~ ( ( singleton(A) = set_union2(B,C) )
          & ~ ( ( B = singleton(A) )
              & ( C = singleton(A) ) )
          & ~ ( ( B = empty_set )
              & ( C = singleton(A) ) )
          & ~ ( ( B = singleton(A) )
              & ( C = empty_set ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).

tff(f_82,axiom,
    ! [A,B] : subset(A,set_union2(A,B)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).

tff(f_54,axiom,
    ! [A,B] :
      ( subset(A,singleton(B))
    <=> ( ( A = empty_set )
        | ( A = singleton(B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).

tff(f_30,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(f_48,axiom,
    ! [A] : ( singleton(A) != empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).

tff(f_45,axiom,
    ! [A,B] : ( set_union2(A,A) = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).

tff(c_28,plain,
    ( ( singleton('#skF_3') != '#skF_5' )
    | ( empty_set != '#skF_4' ) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_52,plain,
    empty_set != '#skF_4',
    inference(splitLeft,[status(thm)],[c_28]) ).

tff(c_26,plain,
    ( ( empty_set != '#skF_5' )
    | ( singleton('#skF_3') != '#skF_4' ) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_53,plain,
    singleton('#skF_3') != '#skF_4',
    inference(splitLeft,[status(thm)],[c_26]) ).

tff(c_32,plain,
    set_union2('#skF_4','#skF_5') = singleton('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_54,plain,
    ! [A_20,B_21] : subset(A_20,set_union2(A_20,B_21)),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_57,plain,
    subset('#skF_4',singleton('#skF_3')),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_54]) ).

tff(c_145,plain,
    ! [B_30,A_31] :
      ( ( singleton(B_30) = A_31 )
      | ( empty_set = A_31 )
      | ~ subset(A_31,singleton(B_30)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_151,plain,
    ( ( singleton('#skF_3') = '#skF_4' )
    | ( empty_set = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_57,c_145]) ).

tff(c_163,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_53,c_151]) ).

tff(c_164,plain,
    empty_set != '#skF_5',
    inference(splitRight,[status(thm)],[c_26]) ).

tff(c_165,plain,
    singleton('#skF_3') = '#skF_4',
    inference(splitRight,[status(thm)],[c_26]) ).

tff(c_30,plain,
    ( ( singleton('#skF_3') != '#skF_5' )
    | ( singleton('#skF_3') != '#skF_4' ) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_176,plain,
    '#skF_5' != '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_165,c_165,c_30]) ).

tff(c_166,plain,
    set_union2('#skF_4','#skF_5') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_165,c_32]) ).

tff(c_197,plain,
    ! [B_36,A_37] : ( set_union2(B_36,A_37) = set_union2(A_37,B_36) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_34,plain,
    ! [A_14,B_15] : subset(A_14,set_union2(A_14,B_15)),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_242,plain,
    ! [A_38,B_39] : subset(A_38,set_union2(B_39,A_38)),
    inference(superposition,[status(thm),theory(equality)],[c_197,c_34]) ).

tff(c_251,plain,
    subset('#skF_5','#skF_4'),
    inference(superposition,[status(thm),theory(equality)],[c_166,c_242]) ).

tff(c_272,plain,
    ! [B_42,A_43] :
      ( ( singleton(B_42) = A_43 )
      | ( empty_set = A_43 )
      | ~ subset(A_43,singleton(B_42)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_275,plain,
    ! [A_43] :
      ( ( singleton('#skF_3') = A_43 )
      | ( empty_set = A_43 )
      | ~ subset(A_43,'#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_165,c_272]) ).

tff(c_293,plain,
    ! [A_44] :
      ( ( A_44 = '#skF_4' )
      | ( empty_set = A_44 )
      | ~ subset(A_44,'#skF_4') ),
    inference(demodulation,[status(thm),theory(equality)],[c_165,c_275]) ).

tff(c_296,plain,
    ( ( '#skF_5' = '#skF_4' )
    | ( empty_set = '#skF_5' ) ),
    inference(resolution,[status(thm)],[c_251,c_293]) ).

tff(c_307,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_164,c_176,c_296]) ).

tff(c_309,plain,
    empty_set = '#skF_4',
    inference(splitRight,[status(thm)],[c_28]) ).

tff(c_12,plain,
    ! [A_9] : ( singleton(A_9) != empty_set ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_311,plain,
    ! [A_9] : ( singleton(A_9) != '#skF_4' ),
    inference(demodulation,[status(thm),theory(equality)],[c_309,c_12]) ).

tff(c_10,plain,
    ! [A_7] : ( set_union2(A_7,A_7) = A_7 ),
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_308,plain,
    singleton('#skF_3') != '#skF_5',
    inference(splitRight,[status(thm)],[c_28]) ).

tff(c_337,plain,
    ! [B_51,A_52] : ( set_union2(B_51,A_52) = set_union2(A_52,B_51) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_396,plain,
    ! [A_55,B_56] : subset(A_55,set_union2(B_56,A_55)),
    inference(superposition,[status(thm),theory(equality)],[c_337,c_34]) ).

tff(c_405,plain,
    subset('#skF_5',singleton('#skF_3')),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_396]) ).

tff(c_14,plain,
    ! [B_11,A_10] :
      ( ( singleton(B_11) = A_10 )
      | ( empty_set = A_10 )
      | ~ subset(A_10,singleton(B_11)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_414,plain,
    ! [B_57,A_58] :
      ( ( singleton(B_57) = A_58 )
      | ( A_58 = '#skF_4' )
      | ~ subset(A_58,singleton(B_57)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_309,c_14]) ).

tff(c_417,plain,
    ( ( singleton('#skF_3') = '#skF_5' )
    | ( '#skF_5' = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_405,c_414]) ).

tff(c_427,plain,
    '#skF_5' = '#skF_4',
    inference(negUnitSimplification,[status(thm)],[c_308,c_417]) ).

tff(c_438,plain,
    set_union2('#skF_4','#skF_4') = singleton('#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_427,c_32]) ).

tff(c_440,plain,
    singleton('#skF_3') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_438]) ).

tff(c_442,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_311,c_440]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET902+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n025.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
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Aug  3 16:31:49 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 3.20/1.85  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.20/1.86  
% 3.20/1.86  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.44/1.89  
% 3.44/1.89  Inference rules
% 3.44/1.89  ----------------------
% 3.44/1.89  #Ref     : 0
% 3.44/1.89  #Sup     : 97
% 3.44/1.89  #Fact    : 0
% 3.44/1.89  #Define  : 0
% 3.44/1.89  #Split   : 5
% 3.44/1.89  #Chain   : 0
% 3.44/1.89  #Close   : 0
% 3.44/1.89  
% 3.44/1.89  Ordering : KBO
% 3.44/1.89  
% 3.44/1.89  Simplification rules
% 3.44/1.89  ----------------------
% 3.44/1.89  #Subsume      : 19
% 3.44/1.89  #Demod        : 33
% 3.44/1.89  #Tautology    : 64
% 3.44/1.89  #SimpNegUnit  : 8
% 3.44/1.89  #BackRed      : 7
% 3.44/1.89  
% 3.44/1.89  #Partial instantiations: 0
% 3.44/1.89  #Strategies tried      : 1
% 3.44/1.89  
% 3.44/1.89  Timing (in seconds)
% 3.44/1.89  ----------------------
% 3.44/1.89  Preprocessing        : 0.48
% 3.44/1.89  Parsing              : 0.25
% 3.44/1.89  CNF conversion       : 0.03
% 3.44/1.89  Main loop            : 0.34
% 3.44/1.89  Inferencing          : 0.12
% 3.44/1.89  Reduction            : 0.11
% 3.44/1.89  Demodulation         : 0.08
% 3.44/1.89  BG Simplification    : 0.02
% 3.44/1.89  Subsumption          : 0.08
% 3.44/1.89  Abstraction          : 0.01
% 3.44/1.89  MUC search           : 0.00
% 3.44/1.89  Cooper               : 0.00
% 3.44/1.89  Total                : 0.88
% 3.44/1.89  Index Insertion      : 0.00
% 3.44/1.89  Index Deletion       : 0.00
% 3.44/1.89  Index Matching       : 0.00
% 3.44/1.89  BG Taut test         : 0.00
%------------------------------------------------------------------------------