TSTP Solution File: SET926+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET926+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 : n010.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 10:57:21 EDT 2023

% Result   : Theorem 2.53s 1.65s
% Output   : CNFRefutation 2.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   19 (   5 unt;   9 typ;   0 def)
%            Number of atoms       :   15 (   8 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   11 (   6   ~;   3   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   2 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   :   10 (;  10   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > 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(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(empty_set,type,
    empty_set: $i ).

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

tff(f_41,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_51,negated_conjecture,
    ~ ! [A,B] :
        ( ( set_difference(singleton(A),B) = empty_set )
        | ( set_difference(singleton(A),B) = singleton(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).

tff(f_37,axiom,
    ! [A,B] :
      ( ( set_difference(singleton(A),B) = singleton(A) )
    <=> ~ in(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).

tff(c_22,plain,
    ! [A_9,B_10] :
      ( ( set_difference(singleton(A_9),B_10) = empty_set )
      | ~ in(A_9,B_10) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_20,plain,
    set_difference(singleton('#skF_3'),'#skF_4') != empty_set,
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_36,plain,
    ~ in('#skF_3','#skF_4'),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_20]) ).

tff(c_43,plain,
    ! [A_13,B_14] :
      ( ( set_difference(singleton(A_13),B_14) = singleton(A_13) )
      | in(A_13,B_14) ),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_18,plain,
    set_difference(singleton('#skF_3'),'#skF_4') != singleton('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_55,plain,
    in('#skF_3','#skF_4'),
    inference(superposition,[status(thm),theory(equality)],[c_43,c_18]) ).

tff(c_69,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_55]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET926+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
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 16:19:59 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 2.53/1.65  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.53/1.65  
% 2.53/1.65  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.88/1.68  
% 2.88/1.68  Inference rules
% 2.88/1.68  ----------------------
% 2.88/1.68  #Ref     : 0
% 2.88/1.68  #Sup     : 12
% 2.88/1.68  #Fact    : 0
% 2.88/1.68  #Define  : 0
% 2.88/1.68  #Split   : 0
% 2.88/1.68  #Chain   : 0
% 2.88/1.68  #Close   : 0
% 2.88/1.68  
% 2.88/1.68  Ordering : KBO
% 2.88/1.68  
% 2.88/1.68  Simplification rules
% 2.88/1.68  ----------------------
% 2.88/1.68  #Subsume      : 1
% 2.88/1.68  #Demod        : 0
% 2.88/1.68  #Tautology    : 5
% 2.88/1.68  #SimpNegUnit  : 1
% 2.88/1.68  #BackRed      : 0
% 2.88/1.68  
% 2.88/1.68  #Partial instantiations: 0
% 2.88/1.68  #Strategies tried      : 1
% 2.88/1.68  
% 2.88/1.68  Timing (in seconds)
% 2.88/1.68  ----------------------
% 2.88/1.68  Preprocessing        : 0.47
% 2.88/1.68  Parsing              : 0.27
% 2.88/1.68  CNF conversion       : 0.03
% 2.88/1.68  Main loop            : 0.18
% 2.88/1.68  Inferencing          : 0.07
% 2.88/1.68  Reduction            : 0.04
% 2.88/1.68  Demodulation         : 0.03
% 2.88/1.68  BG Simplification    : 0.01
% 2.88/1.68  Subsumption          : 0.05
% 2.88/1.68  Abstraction          : 0.01
% 2.88/1.68  MUC search           : 0.00
% 2.88/1.68  Cooper               : 0.00
% 2.88/1.68  Total                : 0.70
% 2.88/1.68  Index Insertion      : 0.00
% 2.88/1.68  Index Deletion       : 0.00
% 2.88/1.68  Index Matching       : 0.00
% 2.88/1.68  BG Taut test         : 0.00
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