TSTP Solution File: SET880+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET880+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 : n021.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 10:57:16 EDT 2023

% Result   : Theorem 2.68s 1.64s
% Output   : CNFRefutation 2.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   21 (   5 unt;  11 typ;   0 def)
%            Number of atoms       :   16 (  10 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   10 (   4   ~;   2   |;   0   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   11 (;  11   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > set_difference > #nlpp > singleton > empty_set > #skF_5 > #skF_6 > #skF_3 > #skF_4 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

tff(f_53,negated_conjecture,
    ~ ! [A,B] :
        ( ( set_difference(singleton(A),singleton(B)) = empty_set )
       => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).

tff(f_43,axiom,
    ! [A,B] :
      ( ( set_difference(singleton(A),B) = empty_set )
    <=> in(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).

tff(f_38,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

tff(c_26,plain,
    '#skF_5' != '#skF_6',
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_28,plain,
    set_difference(singleton('#skF_5'),singleton('#skF_6')) = empty_set,
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_45,plain,
    ! [A_16,B_17] :
      ( in(A_16,B_17)
      | ( set_difference(singleton(A_16),B_17) != empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_49,plain,
    in('#skF_5',singleton('#skF_6')),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_45]) ).

tff(c_4,plain,
    ! [C_7,A_3] :
      ( ( C_7 = A_3 )
      | ~ in(C_7,singleton(A_3)) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_52,plain,
    '#skF_5' = '#skF_6',
    inference(resolution,[status(thm)],[c_49,c_4]) ).

tff(c_58,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26,c_52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET880+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % 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 : n021.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 16:22:06 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 2.68/1.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.68/1.64  
% 2.68/1.64  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.68/1.66  
% 2.68/1.66  Inference rules
% 2.68/1.66  ----------------------
% 2.68/1.66  #Ref     : 0
% 2.68/1.66  #Sup     : 7
% 2.68/1.66  #Fact    : 0
% 2.68/1.66  #Define  : 0
% 2.68/1.66  #Split   : 0
% 2.68/1.66  #Chain   : 0
% 2.68/1.66  #Close   : 0
% 2.68/1.66  
% 2.68/1.66  Ordering : KBO
% 2.68/1.66  
% 2.68/1.66  Simplification rules
% 2.68/1.66  ----------------------
% 2.68/1.66  #Subsume      : 0
% 2.68/1.66  #Demod        : 0
% 2.68/1.66  #Tautology    : 3
% 2.68/1.66  #SimpNegUnit  : 1
% 2.68/1.66  #BackRed      : 0
% 2.68/1.66  
% 2.68/1.66  #Partial instantiations: 0
% 2.68/1.66  #Strategies tried      : 1
% 2.68/1.66  
% 2.68/1.66  Timing (in seconds)
% 2.68/1.66  ----------------------
% 2.68/1.67  Preprocessing        : 0.47
% 2.68/1.67  Parsing              : 0.23
% 2.68/1.67  CNF conversion       : 0.03
% 2.68/1.67  Main loop            : 0.14
% 2.68/1.67  Inferencing          : 0.05
% 2.68/1.67  Reduction            : 0.04
% 2.68/1.67  Demodulation         : 0.03
% 2.68/1.67  BG Simplification    : 0.01
% 2.68/1.67  Subsumption          : 0.04
% 2.68/1.67  Abstraction          : 0.01
% 2.68/1.67  MUC search           : 0.00
% 2.68/1.67  Cooper               : 0.00
% 2.68/1.67  Total                : 0.65
% 2.68/1.67  Index Insertion      : 0.00
% 2.68/1.67  Index Deletion       : 0.00
% 2.68/1.67  Index Matching       : 0.00
% 2.68/1.67  BG Taut test         : 0.00
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