TSTP Solution File: SET977+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET977+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 : n017.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 10:57:27 EDT 2023

% Result   : Theorem 3.49s 2.01s
% Output   : CNFRefutation 3.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   32 (  10 unt;  12 typ;   0 def)
%            Number of atoms       :   33 (  14 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   26 (  13   ~;   6   |;   3   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   24 (;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > empty_set > #skF_1 > #skF_5 > #skF_2 > #skF_3 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

tff('#skF_2',type,
    '#skF_2': $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(cartesian_product2,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(f_72,negated_conjecture,
    ~ ! [A,B] :
        ( ( A != empty_set )
       => ( ( cartesian_product2(singleton(B),A) != empty_set )
          & ( cartesian_product2(A,singleton(B)) != empty_set ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).

tff(f_39,axiom,
    ! [A] :
      ( ( A = empty_set )
    <=> ! [B] : ~ in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

tff(f_56,axiom,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
    <=> ( ( A = C )
        & in(B,D) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).

tff(f_62,axiom,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
    <=> ( in(A,C)
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).

tff(c_34,plain,
    empty_set != '#skF_4',
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_8,plain,
    ! [A_5] :
      ( ( empty_set = A_5 )
      | in('#skF_1'(A_5),A_5) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_6,plain,
    ! [B_8] : ~ in(B_8,empty_set),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_32,plain,
    ( ( cartesian_product2('#skF_4',singleton('#skF_5')) = empty_set )
    | ( cartesian_product2(singleton('#skF_5'),'#skF_4') = empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_81,plain,
    cartesian_product2(singleton('#skF_5'),'#skF_4') = empty_set,
    inference(splitLeft,[status(thm)],[c_32]) ).

tff(c_267,plain,
    ! [C_46,B_47,D_48] :
      ( in(ordered_pair(C_46,B_47),cartesian_product2(singleton(C_46),D_48))
      | ~ in(B_47,D_48) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_279,plain,
    ! [B_47] :
      ( in(ordered_pair('#skF_5',B_47),empty_set)
      | ~ in(B_47,'#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_81,c_267]) ).

tff(c_285,plain,
    ! [B_49] : ~ in(B_49,'#skF_4'),
    inference(negUnitSimplification,[status(thm)],[c_6,c_279]) ).

tff(c_289,plain,
    empty_set = '#skF_4',
    inference(resolution,[status(thm)],[c_8,c_285]) ).

tff(c_293,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_34,c_289]) ).

tff(c_294,plain,
    cartesian_product2('#skF_4',singleton('#skF_5')) = empty_set,
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_484,plain,
    ! [A_71,D_72,C_73] :
      ( in(ordered_pair(A_71,D_72),cartesian_product2(C_73,singleton(D_72)))
      | ~ in(A_71,C_73) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_500,plain,
    ! [A_71] :
      ( in(ordered_pair(A_71,'#skF_5'),empty_set)
      | ~ in(A_71,'#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_294,c_484]) ).

tff(c_507,plain,
    ! [A_74] : ~ in(A_74,'#skF_4'),
    inference(negUnitSimplification,[status(thm)],[c_6,c_500]) ).

tff(c_511,plain,
    empty_set = '#skF_4',
    inference(resolution,[status(thm)],[c_8,c_507]) ).

tff(c_515,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_34,c_511]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET977+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
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 15:42:21 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 3.49/2.01  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.49/2.01  
% 3.49/2.01  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.49/2.03  
% 3.49/2.03  Inference rules
% 3.49/2.03  ----------------------
% 3.49/2.03  #Ref     : 0
% 3.49/2.03  #Sup     : 123
% 3.49/2.03  #Fact    : 0
% 3.49/2.03  #Define  : 0
% 3.49/2.03  #Split   : 1
% 3.49/2.03  #Chain   : 0
% 3.49/2.03  #Close   : 0
% 3.49/2.03  
% 3.49/2.03  Ordering : KBO
% 3.49/2.03  
% 3.49/2.03  Simplification rules
% 3.49/2.03  ----------------------
% 3.49/2.03  #Subsume      : 2
% 3.49/2.03  #Demod        : 24
% 3.49/2.03  #Tautology    : 63
% 3.49/2.03  #SimpNegUnit  : 4
% 3.49/2.03  #BackRed      : 0
% 3.49/2.03  
% 3.49/2.03  #Partial instantiations: 0
% 3.49/2.03  #Strategies tried      : 1
% 3.49/2.03  
% 3.49/2.03  Timing (in seconds)
% 3.49/2.03  ----------------------
% 3.49/2.04  Preprocessing        : 0.48
% 3.49/2.04  Parsing              : 0.26
% 3.49/2.04  CNF conversion       : 0.03
% 3.49/2.04  Main loop            : 0.36
% 3.49/2.04  Inferencing          : 0.13
% 3.49/2.04  Reduction            : 0.11
% 3.49/2.04  Demodulation         : 0.08
% 3.49/2.04  BG Simplification    : 0.02
% 3.49/2.04  Subsumption          : 0.07
% 3.49/2.04  Abstraction          : 0.02
% 3.49/2.04  MUC search           : 0.00
% 3.49/2.04  Cooper               : 0.00
% 3.49/2.04  Total                : 0.89
% 3.49/2.04  Index Insertion      : 0.00
% 3.49/2.04  Index Deletion       : 0.00
% 3.49/2.04  Index Matching       : 0.00
% 3.49/2.04  BG Taut test         : 0.00
%------------------------------------------------------------------------------