TSTP Solution File: SET983+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET983+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 10:57:27 EDT 2023

% Result   : Theorem 4.57s 2.26s
% Output   : CNFRefutation 5.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   27 (   9 unt;  13 typ;   0 def)
%            Number of atoms       :   24 (   5 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   19 (   9   ~;   5   |;   2   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   6   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-3 aty)
%            Number of variables   :   29 (;  29   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > set_intersection2 > cartesian_product2 > #nlpp > #skF_1 > #skF_7 > #skF_5 > #skF_6 > #skF_3 > #skF_2 > #skF_9 > #skF_8 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

tff(set_intersection2,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

tff('#skF_9',type,
    '#skF_9': $i ).

tff('#skF_8',type,
    '#skF_8': $i ).

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

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

tff(f_58,negated_conjecture,
    ~ ! [A,B,C,D,E] :
        ( ( in(A,cartesian_product2(B,C))
          & in(A,cartesian_product2(D,E)) )
       => in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).

tff(f_51,axiom,
    ! [A,B,C,D] : ( cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).

tff(f_42,axiom,
    ! [A,B,C] :
      ( ( C = set_intersection2(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

tff(f_33,axiom,
    ! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

tff(c_34,plain,
    in('#skF_5',cartesian_product2('#skF_8','#skF_9')),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_36,plain,
    in('#skF_5',cartesian_product2('#skF_6','#skF_7')),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_128,plain,
    ! [A_31,C_32,B_33,D_34] : ( set_intersection2(cartesian_product2(A_31,C_32),cartesian_product2(B_33,D_34)) = cartesian_product2(set_intersection2(A_31,B_33),set_intersection2(C_32,D_34)) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_6,plain,
    ! [D_10,A_5,B_6] :
      ( in(D_10,set_intersection2(A_5,B_6))
      | ~ in(D_10,B_6)
      | ~ in(D_10,A_5) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_1516,plain,
    ! [A_134,B_133,D_130,C_132,D_131] :
      ( in(D_131,cartesian_product2(set_intersection2(A_134,B_133),set_intersection2(C_132,D_130)))
      | ~ in(D_131,cartesian_product2(B_133,D_130))
      | ~ in(D_131,cartesian_product2(A_134,C_132)) ),
    inference(superposition,[status(thm),theory(equality)],[c_128,c_6]) ).

tff(c_4,plain,
    ! [B_4,A_3] : ( set_intersection2(B_4,A_3) = set_intersection2(A_3,B_4) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_32,plain,
    ~ in('#skF_5',cartesian_product2(set_intersection2('#skF_6','#skF_8'),set_intersection2('#skF_7','#skF_9'))),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_37,plain,
    ~ in('#skF_5',cartesian_product2(set_intersection2('#skF_8','#skF_6'),set_intersection2('#skF_9','#skF_7'))),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_32]) ).

tff(c_1560,plain,
    ( ~ in('#skF_5',cartesian_product2('#skF_6','#skF_7'))
    | ~ in('#skF_5',cartesian_product2('#skF_8','#skF_9')) ),
    inference(resolution,[status(thm)],[c_1516,c_37]) ).

tff(c_1631,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_36,c_1560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET983+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
% 0.13/0.34  % Computer : n021.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 16:38:06 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 4.57/2.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.57/2.26  
% 4.57/2.26  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.02/2.29  
% 5.02/2.29  Inference rules
% 5.02/2.29  ----------------------
% 5.02/2.29  #Ref     : 0
% 5.02/2.29  #Sup     : 407
% 5.02/2.29  #Fact    : 0
% 5.02/2.29  #Define  : 0
% 5.02/2.29  #Split   : 0
% 5.02/2.29  #Chain   : 0
% 5.02/2.29  #Close   : 0
% 5.02/2.29  
% 5.02/2.29  Ordering : KBO
% 5.02/2.29  
% 5.02/2.29  Simplification rules
% 5.02/2.29  ----------------------
% 5.02/2.29  #Subsume      : 106
% 5.02/2.29  #Demod        : 45
% 5.02/2.29  #Tautology    : 78
% 5.02/2.29  #SimpNegUnit  : 0
% 5.02/2.29  #BackRed      : 0
% 5.02/2.29  
% 5.02/2.29  #Partial instantiations: 0
% 5.02/2.29  #Strategies tried      : 1
% 5.02/2.29  
% 5.02/2.29  Timing (in seconds)
% 5.02/2.29  ----------------------
% 5.02/2.29  Preprocessing        : 0.49
% 5.02/2.29  Parsing              : 0.24
% 5.02/2.29  CNF conversion       : 0.03
% 5.02/2.29  Main loop            : 0.69
% 5.02/2.29  Inferencing          : 0.23
% 5.02/2.29  Reduction            : 0.24
% 5.02/2.29  Demodulation         : 0.20
% 5.02/2.29  BG Simplification    : 0.03
% 5.02/2.29  Subsumption          : 0.14
% 5.02/2.29  Abstraction          : 0.04
% 5.02/2.29  MUC search           : 0.00
% 5.02/2.29  Cooper               : 0.00
% 5.02/2.29  Total                : 1.22
% 5.02/2.29  Index Insertion      : 0.00
% 5.02/2.29  Index Deletion       : 0.00
% 5.02/2.29  Index Matching       : 0.00
% 5.02/2.29  BG Taut test         : 0.00
%------------------------------------------------------------------------------