TSTP Solution File: SET923+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET923+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 : n007.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 2.86s 1.74s
% Output   : CNFRefutation 2.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   20 (   4 unt;   9 typ;   0 def)
%            Number of atoms       :   22 (  17 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   20 (   9   ~;   7   |;   2   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   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    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   12 (;  12   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

tff(singleton,type,
    singleton: $i > $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(f_54,negated_conjecture,
    ~ ! [A,B] :
        ~ ( ( set_difference(A,singleton(B)) = empty_set )
          & ( A != empty_set )
          & ( A != singleton(B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).

tff(f_44,axiom,
    ! [A,B] :
      ( ( set_difference(A,B) = empty_set )
    <=> subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

tff(f_33,axiom,
    ! [A,B] :
      ( subset(A,singleton(B))
    <=> ( ( A = empty_set )
        | ( A = singleton(B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).

tff(c_22,plain,
    empty_set != '#skF_3',
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_20,plain,
    singleton('#skF_4') != '#skF_3',
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_24,plain,
    set_difference('#skF_3',singleton('#skF_4')) = empty_set,
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_16,plain,
    ! [A_5,B_6] :
      ( subset(A_5,B_6)
      | ( set_difference(A_5,B_6) != empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_60,plain,
    ! [B_15,A_16] :
      ( ( singleton(B_15) = A_16 )
      | ( empty_set = A_16 )
      | ~ subset(A_16,singleton(B_15)) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_77,plain,
    ! [B_17,A_18] :
      ( ( singleton(B_17) = A_18 )
      | ( empty_set = A_18 )
      | ( set_difference(A_18,singleton(B_17)) != empty_set ) ),
    inference(resolution,[status(thm)],[c_16,c_60]) ).

tff(c_87,plain,
    ( ( singleton('#skF_4') = '#skF_3' )
    | ( empty_set = '#skF_3' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_77]) ).

tff(c_95,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22,c_20,c_87]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET923+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/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
% 0.18/0.35  % Computer : n007.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit : 300
% 0.18/0.35  % WCLimit  : 300
% 0.18/0.35  % DateTime : Thu Aug  3 16:51:53 EDT 2023
% 0.18/0.35  % CPUTime  : 
% 2.86/1.74  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.86/1.74  
% 2.86/1.74  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.86/1.77  
% 2.86/1.77  Inference rules
% 2.86/1.77  ----------------------
% 2.86/1.77  #Ref     : 0
% 2.86/1.77  #Sup     : 15
% 2.86/1.77  #Fact    : 0
% 2.86/1.77  #Define  : 0
% 2.86/1.77  #Split   : 0
% 2.86/1.77  #Chain   : 0
% 2.86/1.77  #Close   : 0
% 2.86/1.77  
% 2.86/1.77  Ordering : KBO
% 2.86/1.77  
% 2.86/1.77  Simplification rules
% 2.86/1.77  ----------------------
% 2.86/1.77  #Subsume      : 0
% 2.86/1.77  #Demod        : 1
% 2.86/1.77  #Tautology    : 12
% 2.86/1.77  #SimpNegUnit  : 1
% 2.86/1.77  #BackRed      : 0
% 2.86/1.77  
% 2.86/1.77  #Partial instantiations: 0
% 2.86/1.77  #Strategies tried      : 1
% 2.86/1.77  
% 2.86/1.77  Timing (in seconds)
% 2.86/1.77  ----------------------
% 2.86/1.77  Preprocessing        : 0.46
% 2.86/1.77  Parsing              : 0.23
% 2.86/1.77  CNF conversion       : 0.03
% 2.86/1.77  Main loop            : 0.17
% 2.86/1.77  Inferencing          : 0.06
% 2.86/1.77  Reduction            : 0.04
% 2.86/1.77  Demodulation         : 0.03
% 2.86/1.77  BG Simplification    : 0.01
% 2.86/1.77  Subsumption          : 0.04
% 2.86/1.77  Abstraction          : 0.01
% 2.86/1.77  MUC search           : 0.00
% 2.86/1.77  Cooper               : 0.00
% 2.86/1.77  Total                : 0.67
% 2.86/1.77  Index Insertion      : 0.00
% 2.86/1.77  Index Deletion       : 0.00
% 2.86/1.77  Index Matching       : 0.00
% 2.86/1.77  BG Taut test         : 0.00
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