TSTP Solution File: SET961+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : n005.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 10:57:25 EDT 2023

% Result   : Theorem 3.58s 1.99s
% Output   : CNFRefutation 3.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   51 (  14 unt;  14 typ;   0 def)
%            Number of atoms       :   74 (  22 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   65 (  28   ~;  31   |;   1   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   9   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :   49 (;  49   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > empty_set > #skF_6 > #skF_1 > #skF_5 > #skF_2 > #skF_3 > #skF_4 > #skF_7

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_6',type,
    '#skF_6': ( $i * $i ) > $i ).

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('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

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

tff(f_66,negated_conjecture,
    ~ ! [A,B] :
        ( ( cartesian_product2(A,B) = cartesian_product2(B,A) )
       => ( ( A = empty_set )
          | ( B = empty_set )
          | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).

tff(f_73,axiom,
    ! [A,B] :
      ( ! [C] :
          ( in(C,A)
        <=> in(C,B) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

tff(f_40,axiom,
    ! [A] :
      ( ( A = empty_set )
    <=> ! [B] : ~ in(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

tff(f_52,axiom,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).

tff(c_26,plain,
    '#skF_5' != '#skF_4',
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_28,plain,
    empty_set != '#skF_5',
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_294,plain,
    ! [A_53,B_54] :
      ( in('#skF_6'(A_53,B_54),B_54)
      | in('#skF_7'(A_53,B_54),A_53)
      | ( B_54 = A_53 ) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_6,plain,
    ! [B_8] : ~ in(B_8,empty_set),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_311,plain,
    ! [A_53] :
      ( in('#skF_7'(A_53,empty_set),A_53)
      | ( empty_set = A_53 ) ),
    inference(resolution,[status(thm)],[c_294,c_6]) ).

tff(c_348,plain,
    ! [A_65,B_66,C_67,D_68] :
      ( in(ordered_pair(A_65,B_66),cartesian_product2(C_67,D_68))
      | ~ in(B_66,D_68)
      | ~ in(A_65,C_67) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_32,plain,
    cartesian_product2('#skF_5','#skF_4') = cartesian_product2('#skF_4','#skF_5'),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_152,plain,
    ! [A_33,C_34,B_35,D_36] :
      ( in(A_33,C_34)
      | ~ in(ordered_pair(A_33,B_35),cartesian_product2(C_34,D_36)) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_155,plain,
    ! [A_33,B_35] :
      ( in(A_33,'#skF_5')
      | ~ in(ordered_pair(A_33,B_35),cartesian_product2('#skF_4','#skF_5')) ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_152]) ).

tff(c_370,plain,
    ! [A_65,B_66] :
      ( in(A_65,'#skF_5')
      | ~ in(B_66,'#skF_5')
      | ~ in(A_65,'#skF_4') ),
    inference(resolution,[status(thm)],[c_348,c_155]) ).

tff(c_458,plain,
    ! [B_77] : ~ in(B_77,'#skF_5'),
    inference(splitLeft,[status(thm)],[c_370]) ).

tff(c_462,plain,
    empty_set = '#skF_5',
    inference(resolution,[status(thm)],[c_311,c_458]) ).

tff(c_480,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28,c_462]) ).

tff(c_481,plain,
    ! [A_65] :
      ( in(A_65,'#skF_5')
      | ~ in(A_65,'#skF_4') ),
    inference(splitRight,[status(thm)],[c_370]) ).

tff(c_36,plain,
    ! [A_17,B_18] :
      ( in('#skF_6'(A_17,B_18),B_18)
      | ~ in('#skF_7'(A_17,B_18),B_18)
      | ( B_18 = A_17 ) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_30,plain,
    empty_set != '#skF_4',
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_271,plain,
    ! [B_43,D_44,A_45,C_46] :
      ( in(B_43,D_44)
      | ~ in(ordered_pair(A_45,B_43),cartesian_product2(C_46,D_44)) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_274,plain,
    ! [B_43,A_45] :
      ( in(B_43,'#skF_4')
      | ~ in(ordered_pair(A_45,B_43),cartesian_product2('#skF_4','#skF_5')) ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_271]) ).

tff(c_368,plain,
    ! [B_66,A_65] :
      ( in(B_66,'#skF_4')
      | ~ in(B_66,'#skF_5')
      | ~ in(A_65,'#skF_4') ),
    inference(resolution,[status(thm)],[c_348,c_274]) ).

tff(c_375,plain,
    ! [A_69] : ~ in(A_69,'#skF_4'),
    inference(splitLeft,[status(thm)],[c_368]) ).

tff(c_379,plain,
    empty_set = '#skF_4',
    inference(resolution,[status(thm)],[c_311,c_375]) ).

tff(c_397,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_30,c_379]) ).

tff(c_399,plain,
    ! [B_70] :
      ( in(B_70,'#skF_4')
      | ~ in(B_70,'#skF_5') ),
    inference(splitRight,[status(thm)],[c_368]) ).

tff(c_509,plain,
    ! [A_80] :
      ( in('#skF_6'(A_80,'#skF_5'),'#skF_4')
      | ~ in('#skF_7'(A_80,'#skF_5'),'#skF_5')
      | ( A_80 = '#skF_5' ) ),
    inference(resolution,[status(thm)],[c_36,c_399]) ).

tff(c_34,plain,
    ! [A_17,B_18] :
      ( ~ in('#skF_6'(A_17,B_18),A_17)
      | ~ in('#skF_7'(A_17,B_18),B_18)
      | ( B_18 = A_17 ) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_516,plain,
    ( ~ in('#skF_7'('#skF_4','#skF_5'),'#skF_5')
    | ( '#skF_5' = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_509,c_34]) ).

tff(c_523,plain,
    ~ in('#skF_7'('#skF_4','#skF_5'),'#skF_5'),
    inference(negUnitSimplification,[status(thm)],[c_26,c_26,c_516]) ).

tff(c_548,plain,
    ~ in('#skF_7'('#skF_4','#skF_5'),'#skF_4'),
    inference(resolution,[status(thm)],[c_481,c_523]) ).

tff(c_40,plain,
    ! [A_17,B_18] :
      ( in('#skF_6'(A_17,B_18),B_18)
      | in('#skF_7'(A_17,B_18),A_17)
      | ( B_18 = A_17 ) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_640,plain,
    ! [A_87] :
      ( in('#skF_6'(A_87,'#skF_5'),'#skF_4')
      | in('#skF_7'(A_87,'#skF_5'),A_87)
      | ( A_87 = '#skF_5' ) ),
    inference(resolution,[status(thm)],[c_40,c_399]) ).

tff(c_38,plain,
    ! [A_17,B_18] :
      ( ~ in('#skF_6'(A_17,B_18),A_17)
      | in('#skF_7'(A_17,B_18),A_17)
      | ( B_18 = A_17 ) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_648,plain,
    ( in('#skF_7'('#skF_4','#skF_5'),'#skF_4')
    | ( '#skF_5' = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_640,c_38]) ).

tff(c_670,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26,c_548,c_26,c_548,c_648]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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
% 0.18/0.36  % Computer : n005.cluster.edu
% 0.18/0.36  % Model    : x86_64 x86_64
% 0.18/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36  % Memory   : 8042.1875MB
% 0.18/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36  % CPULimit : 300
% 0.18/0.36  % WCLimit  : 300
% 0.18/0.36  % DateTime : Thu Aug  3 16:44:41 EDT 2023
% 0.18/0.36  % CPUTime  : 
% 3.58/1.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.94/1.99  
% 3.94/1.99  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.94/2.02  
% 3.94/2.02  Inference rules
% 3.94/2.02  ----------------------
% 3.94/2.02  #Ref     : 0
% 3.94/2.02  #Sup     : 141
% 3.94/2.02  #Fact    : 0
% 3.94/2.02  #Define  : 0
% 3.94/2.02  #Split   : 2
% 3.94/2.02  #Chain   : 0
% 3.94/2.02  #Close   : 0
% 3.94/2.02  
% 3.94/2.02  Ordering : KBO
% 3.94/2.02  
% 3.94/2.02  Simplification rules
% 3.94/2.02  ----------------------
% 3.94/2.02  #Subsume      : 8
% 3.94/2.02  #Demod        : 19
% 3.94/2.02  #Tautology    : 53
% 3.94/2.02  #SimpNegUnit  : 12
% 3.94/2.02  #BackRed      : 2
% 3.94/2.02  
% 3.94/2.02  #Partial instantiations: 0
% 3.94/2.02  #Strategies tried      : 1
% 3.94/2.02  
% 3.94/2.02  Timing (in seconds)
% 3.94/2.02  ----------------------
% 3.94/2.03  Preprocessing        : 0.49
% 3.94/2.03  Parsing              : 0.25
% 3.94/2.03  CNF conversion       : 0.04
% 3.94/2.03  Main loop            : 0.46
% 3.94/2.03  Inferencing          : 0.18
% 3.94/2.03  Reduction            : 0.13
% 3.94/2.03  Demodulation         : 0.09
% 3.94/2.03  BG Simplification    : 0.02
% 3.94/2.03  Subsumption          : 0.10
% 3.94/2.03  Abstraction          : 0.02
% 3.94/2.03  MUC search           : 0.00
% 3.94/2.03  Cooper               : 0.00
% 3.94/2.03  Total                : 1.00
% 3.94/2.03  Index Insertion      : 0.00
% 3.94/2.03  Index Deletion       : 0.00
% 3.94/2.03  Index Matching       : 0.00
% 3.94/2.03  BG Taut test         : 0.00
%------------------------------------------------------------------------------