TSTP Solution File: SET592+3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n011.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 10:56:38 EDT 2023

% Result   : Theorem 3.68s 1.87s
% Output   : CNFRefutation 3.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   32 (   9 unt;  12 typ;   0 def)
%            Number of atoms       :   42 (  10 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   38 (  16   ~;  13   |;   4   &)
%                                         (   2 <=>;   3  =>;   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  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   24 (;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > empty > intersection > #nlpp > empty_set > #skF_2 > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_2',type,
    '#skF_2': $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

tff(f_97,negated_conjecture,
    ~ ! [B,C,D] :
        ( ( subset(B,C)
          & subset(B,D)
          & ( intersection(C,D) = empty_set ) )
       => ( B = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th51) ).

tff(f_59,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

tff(f_44,axiom,
    ! [B] : ~ member(B,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

tff(f_40,axiom,
    ! [B,C,D] :
      ( ( subset(B,C)
        & subset(B,D) )
     => subset(B,intersection(C,D)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subsets) ).

tff(f_66,axiom,
    ! [B,C] :
      ( ( B = C )
    <=> ( subset(B,C)
        & subset(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

tff(c_46,plain,
    empty_set != '#skF_5',
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_52,plain,
    subset('#skF_5','#skF_6'),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_50,plain,
    subset('#skF_5','#skF_7'),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_158,plain,
    ! [B_46,C_47] :
      ( member('#skF_1'(B_46,C_47),B_46)
      | subset(B_46,C_47) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_6,plain,
    ! [B_5] : ~ member(B_5,empty_set),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_183,plain,
    ! [C_47] : subset(empty_set,C_47),
    inference(resolution,[status(thm)],[c_158,c_6]) ).

tff(c_48,plain,
    intersection('#skF_6','#skF_7') = empty_set,
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_329,plain,
    ! [B_66,C_67,D_68] :
      ( subset(B_66,intersection(C_67,D_68))
      | ~ subset(B_66,D_68)
      | ~ subset(B_66,C_67) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_394,plain,
    ! [B_72] :
      ( subset(B_72,empty_set)
      | ~ subset(B_72,'#skF_7')
      | ~ subset(B_72,'#skF_6') ),
    inference(superposition,[status(thm),theory(equality)],[c_48,c_329]) ).

tff(c_20,plain,
    ! [C_15,B_14] :
      ( ( C_15 = B_14 )
      | ~ subset(C_15,B_14)
      | ~ subset(B_14,C_15) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_405,plain,
    ! [B_72] :
      ( ( empty_set = B_72 )
      | ~ subset(empty_set,B_72)
      | ~ subset(B_72,'#skF_7')
      | ~ subset(B_72,'#skF_6') ),
    inference(resolution,[status(thm)],[c_394,c_20]) ).

tff(c_420,plain,
    ! [B_73] :
      ( ( empty_set = B_73 )
      | ~ subset(B_73,'#skF_7')
      | ~ subset(B_73,'#skF_6') ),
    inference(demodulation,[status(thm),theory(equality)],[c_183,c_405]) ).

tff(c_435,plain,
    ( ( empty_set = '#skF_5' )
    | ~ subset('#skF_5','#skF_6') ),
    inference(resolution,[status(thm)],[c_50,c_420]) ).

tff(c_444,plain,
    empty_set = '#skF_5',
    inference(demodulation,[status(thm),theory(equality)],[c_52,c_435]) ).

tff(c_446,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_46,c_444]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET592+3 : TPTP v8.1.2. Released v2.2.0.
% 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
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 16:31:05 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.68/1.87  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.68/1.87  
% 3.68/1.87  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.71/1.89  
% 3.71/1.89  Inference rules
% 3.71/1.89  ----------------------
% 3.71/1.89  #Ref     : 0
% 3.71/1.89  #Sup     : 85
% 3.71/1.89  #Fact    : 0
% 3.71/1.89  #Define  : 0
% 3.71/1.90  #Split   : 2
% 3.71/1.90  #Chain   : 0
% 3.71/1.90  #Close   : 0
% 3.71/1.90  
% 3.71/1.90  Ordering : KBO
% 3.71/1.90  
% 3.71/1.90  Simplification rules
% 3.71/1.90  ----------------------
% 3.71/1.90  #Subsume      : 20
% 3.71/1.90  #Demod        : 12
% 3.71/1.90  #Tautology    : 30
% 3.71/1.90  #SimpNegUnit  : 4
% 3.71/1.90  #BackRed      : 0
% 3.71/1.90  
% 3.71/1.90  #Partial instantiations: 0
% 3.71/1.90  #Strategies tried      : 1
% 3.71/1.90  
% 3.71/1.90  Timing (in seconds)
% 3.71/1.90  ----------------------
% 3.71/1.90  Preprocessing        : 0.51
% 3.71/1.90  Parsing              : 0.25
% 3.71/1.90  CNF conversion       : 0.04
% 3.71/1.90  Main loop            : 0.34
% 3.71/1.90  Inferencing          : 0.12
% 3.71/1.90  Reduction            : 0.09
% 3.71/1.90  Demodulation         : 0.07
% 3.71/1.90  BG Simplification    : 0.02
% 3.71/1.90  Subsumption          : 0.08
% 3.71/1.90  Abstraction          : 0.02
% 3.71/1.90  MUC search           : 0.00
% 3.71/1.90  Cooper               : 0.00
% 3.71/1.90  Total                : 0.89
% 3.71/1.90  Index Insertion      : 0.00
% 3.71/1.90  Index Deletion       : 0.00
% 3.71/1.90  Index Matching       : 0.00
% 3.71/1.90  BG Taut test         : 0.00
%------------------------------------------------------------------------------