TSTP Solution File: SEU171+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU171+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n031.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 10:57:54 EDT 2023

% Result   : Theorem 3.84s 2.11s
% Output   : CNFRefutation 4.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   50 (  18 unt;  17 typ;   0 def)
%            Number of atoms       :   60 (  13 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   50 (  23   ~;  13   |;   2   &)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  11   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :   25 (;  24   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > element > empty > subset_complement > set_difference > #nlpp > powerset > empty_set > #skF_1 > #skF_4 > #skF_7 > #skF_10 > #skF_5 > #skF_2 > #skF_9 > #skF_8 > #skF_3 > #skF_6

%Foreground sorts:

%Background operators:

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

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

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

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

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

tff('#skF_10',type,
    '#skF_10': $i ).

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

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

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

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

tff(powerset,type,
    powerset: $i > $i ).

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

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

tff(f_85,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_116,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_112,negated_conjecture,
    ~ ! [A] :
        ( ( A != empty_set )
       => ! [B] :
            ( element(B,powerset(A))
           => ! [C] :
                ( element(C,A)
               => ( ~ in(C,B)
                 => in(C,subset_complement(A,B)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).

tff(f_44,axiom,
    ! [A,B] :
      ( ( ~ empty(A)
       => ( element(B,A)
        <=> in(B,A) ) )
      & ( empty(A)
       => ( element(B,A)
        <=> empty(B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).

tff(f_54,axiom,
    ! [A,B,C] :
      ( ( C = set_difference(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & ~ in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

tff(f_58,axiom,
    ! [A,B] :
      ( element(B,powerset(A))
     => ( subset_complement(A,B) = set_difference(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).

tff(c_54,plain,
    empty('#skF_5'),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_91,plain,
    ! [A_39] :
      ( ( empty_set = A_39 )
      | ~ empty(A_39) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_102,plain,
    empty_set = '#skF_5',
    inference(resolution,[status(thm)],[c_54,c_91]) ).

tff(c_74,plain,
    empty_set != '#skF_8',
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_108,plain,
    '#skF_5' != '#skF_8',
    inference(demodulation,[status(thm),theory(equality)],[c_102,c_74]) ).

tff(c_70,plain,
    element('#skF_10','#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_167,plain,
    ! [B_54,A_55] :
      ( empty(B_54)
      | ~ element(B_54,A_55)
      | ~ empty(A_55) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_188,plain,
    ( empty('#skF_10')
    | ~ empty('#skF_8') ),
    inference(resolution,[status(thm)],[c_70,c_167]) ).

tff(c_189,plain,
    ~ empty('#skF_8'),
    inference(splitLeft,[status(thm)],[c_188]) ).

tff(c_6,plain,
    ! [B_4,A_3] :
      ( in(B_4,A_3)
      | ~ element(B_4,A_3)
      | empty(A_3) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_68,plain,
    ~ in('#skF_10','#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_649,plain,
    ! [D_102,A_103,B_104] :
      ( in(D_102,set_difference(A_103,B_104))
      | in(D_102,B_104)
      | ~ in(D_102,A_103) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_72,plain,
    element('#skF_9',powerset('#skF_8')),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_375,plain,
    ! [A_85,B_86] :
      ( ( subset_complement(A_85,B_86) = set_difference(A_85,B_86) )
      | ~ element(B_86,powerset(A_85)) ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_398,plain,
    subset_complement('#skF_8','#skF_9') = set_difference('#skF_8','#skF_9'),
    inference(resolution,[status(thm)],[c_72,c_375]) ).

tff(c_66,plain,
    ~ in('#skF_10',subset_complement('#skF_8','#skF_9')),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_433,plain,
    ~ in('#skF_10',set_difference('#skF_8','#skF_9')),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_66]) ).

tff(c_652,plain,
    ( in('#skF_10','#skF_9')
    | ~ in('#skF_10','#skF_8') ),
    inference(resolution,[status(thm)],[c_649,c_433]) ).

tff(c_681,plain,
    ~ in('#skF_10','#skF_8'),
    inference(negUnitSimplification,[status(thm)],[c_68,c_652]) ).

tff(c_690,plain,
    ( ~ element('#skF_10','#skF_8')
    | empty('#skF_8') ),
    inference(resolution,[status(thm)],[c_6,c_681]) ).

tff(c_693,plain,
    empty('#skF_8'),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_690]) ).

tff(c_695,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_189,c_693]) ).

tff(c_697,plain,
    empty('#skF_8'),
    inference(splitRight,[status(thm)],[c_188]) ).

tff(c_76,plain,
    ! [A_30] :
      ( ( empty_set = A_30 )
      | ~ empty(A_30) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_105,plain,
    ! [A_30] :
      ( ( A_30 = '#skF_5' )
      | ~ empty(A_30) ),
    inference(demodulation,[status(thm),theory(equality)],[c_102,c_76]) ).

tff(c_709,plain,
    '#skF_5' = '#skF_8',
    inference(resolution,[status(thm)],[c_697,c_105]) ).

tff(c_714,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_108,c_709]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SEU171+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15  % 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
% 0.15/0.36  % Computer : n031.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 12:32:59 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 3.84/2.11  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.41/2.11  
% 4.41/2.11  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.41/2.14  
% 4.41/2.14  Inference rules
% 4.41/2.14  ----------------------
% 4.41/2.14  #Ref     : 0
% 4.41/2.14  #Sup     : 144
% 4.41/2.14  #Fact    : 0
% 4.41/2.14  #Define  : 0
% 4.41/2.14  #Split   : 5
% 4.41/2.14  #Chain   : 0
% 4.41/2.14  #Close   : 0
% 4.41/2.14  
% 4.41/2.14  Ordering : KBO
% 4.41/2.14  
% 4.41/2.14  Simplification rules
% 4.41/2.14  ----------------------
% 4.41/2.14  #Subsume      : 19
% 4.41/2.14  #Demod        : 56
% 4.41/2.14  #Tautology    : 78
% 4.41/2.14  #SimpNegUnit  : 5
% 4.41/2.14  #BackRed      : 10
% 4.41/2.14  
% 4.41/2.14  #Partial instantiations: 0
% 4.41/2.14  #Strategies tried      : 1
% 4.41/2.14  
% 4.41/2.14  Timing (in seconds)
% 4.41/2.14  ----------------------
% 4.41/2.14  Preprocessing        : 0.53
% 4.41/2.14  Parsing              : 0.26
% 4.41/2.14  CNF conversion       : 0.04
% 4.41/2.14  Main loop            : 0.45
% 4.41/2.14  Inferencing          : 0.16
% 4.41/2.14  Reduction            : 0.13
% 4.41/2.14  Demodulation         : 0.09
% 4.41/2.14  BG Simplification    : 0.02
% 4.41/2.14  Subsumption          : 0.10
% 4.41/2.14  Abstraction          : 0.02
% 4.41/2.14  MUC search           : 0.00
% 4.41/2.14  Cooper               : 0.00
% 4.41/2.14  Total                : 1.02
% 4.41/2.14  Index Insertion      : 0.00
% 4.41/2.14  Index Deletion       : 0.00
% 4.41/2.14  Index Matching       : 0.00
% 4.41/2.14  BG Taut test         : 0.00
%------------------------------------------------------------------------------