TSTP Solution File: SET016+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 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 10:55:32 EDT 2023

% Result   : Theorem 4.11s 1.95s
% Output   : CNFRefutation 4.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   44 (  13 unt;  19 typ;   0 def)
%            Number of atoms       :   42 (  14 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   26 (   9   ~;  10   |;   1   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  14   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-2 aty)
%            Number of variables   :   33 (;  33   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(empty_set,type,
    empty_set: $i ).

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

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

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

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

tff(f_119,negated_conjecture,
    ~ ! [A,B,U,V] :
        ( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
       => ( A = U ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI50a) ).

tff(f_62,axiom,
    ! [A,B] :
      ( equal_set(A,B)
    <=> ( subset(A,B)
        & subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).

tff(f_98,axiom,
    ! [X,A,B] :
      ( member(X,unordered_pair(A,B))
    <=> ( ( X = A )
        | ( X = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).

tff(f_56,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( member(X,A)
         => member(X,B) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).

tff(f_92,axiom,
    ! [X,A] :
      ( member(X,singleton(A))
    <=> ( X = A ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).

tff(c_60,plain,
    '#skF_6' != '#skF_4',
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_62,plain,
    equal_set(unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5')),unordered_pair(singleton('#skF_6'),unordered_pair('#skF_6','#skF_7'))),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_10,plain,
    ! [B_7,A_6] :
      ( subset(B_7,A_6)
      | ~ equal_set(A_6,B_7) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_46,plain,
    ! [X_22,B_24] : member(X_22,unordered_pair(X_22,B_24)),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_146,plain,
    ! [X_75,B_76,A_77] :
      ( member(X_75,B_76)
      | ~ member(X_75,A_77)
      | ~ subset(A_77,B_76) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_188,plain,
    ! [X_86,B_87,B_88] :
      ( member(X_86,B_87)
      | ~ subset(unordered_pair(X_86,B_88),B_87) ),
    inference(resolution,[status(thm)],[c_46,c_146]) ).

tff(c_230,plain,
    ! [X_95,A_96,B_97] :
      ( member(X_95,A_96)
      | ~ equal_set(A_96,unordered_pair(X_95,B_97)) ),
    inference(resolution,[status(thm)],[c_10,c_188]) ).

tff(c_234,plain,
    member(singleton('#skF_6'),unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5'))),
    inference(resolution,[status(thm)],[c_62,c_230]) ).

tff(c_514,plain,
    ! [X_123,B_124,A_125] :
      ( ( X_123 = B_124 )
      | ( X_123 = A_125 )
      | ~ member(X_123,unordered_pair(A_125,B_124)) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_539,plain,
    ( ( unordered_pair('#skF_4','#skF_5') = singleton('#skF_6') )
    | ( singleton('#skF_6') = singleton('#skF_4') ) ),
    inference(resolution,[status(thm)],[c_234,c_514]) ).

tff(c_741,plain,
    singleton('#skF_6') = singleton('#skF_4'),
    inference(splitLeft,[status(thm)],[c_539]) ).

tff(c_40,plain,
    ! [X_20] : member(X_20,singleton(X_20)),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_763,plain,
    member('#skF_6',singleton('#skF_4')),
    inference(superposition,[status(thm),theory(equality)],[c_741,c_40]) ).

tff(c_38,plain,
    ! [X_20,A_21] :
      ( ( X_20 = A_21 )
      | ~ member(X_20,singleton(A_21)) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_773,plain,
    '#skF_6' = '#skF_4',
    inference(resolution,[status(thm)],[c_763,c_38]) ).

tff(c_779,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_60,c_773]) ).

tff(c_780,plain,
    unordered_pair('#skF_4','#skF_5') = singleton('#skF_6'),
    inference(splitRight,[status(thm)],[c_539]) ).

tff(c_837,plain,
    member('#skF_4',singleton('#skF_6')),
    inference(superposition,[status(thm),theory(equality)],[c_780,c_46]) ).

tff(c_906,plain,
    '#skF_6' = '#skF_4',
    inference(resolution,[status(thm)],[c_837,c_38]) ).

tff(c_913,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_60,c_906]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 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 16:27:51 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 4.11/1.95  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.11/1.96  
% 4.11/1.96  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.11/1.98  
% 4.11/1.98  Inference rules
% 4.11/1.98  ----------------------
% 4.11/1.98  #Ref     : 0
% 4.11/1.98  #Sup     : 187
% 4.11/1.98  #Fact    : 0
% 4.11/1.98  #Define  : 0
% 4.11/1.98  #Split   : 1
% 4.11/1.98  #Chain   : 0
% 4.11/1.98  #Close   : 0
% 4.11/1.98  
% 4.11/1.98  Ordering : KBO
% 4.11/1.98  
% 4.11/1.98  Simplification rules
% 4.11/1.98  ----------------------
% 4.11/1.98  #Subsume      : 0
% 4.11/1.98  #Demod        : 39
% 4.11/1.98  #Tautology    : 41
% 4.11/1.98  #SimpNegUnit  : 2
% 4.11/1.98  #BackRed      : 10
% 4.11/1.98  
% 4.11/1.98  #Partial instantiations: 0
% 4.11/1.98  #Strategies tried      : 1
% 4.11/1.98  
% 4.11/1.98  Timing (in seconds)
% 4.11/1.98  ----------------------
% 4.11/1.99  Preprocessing        : 0.48
% 4.11/1.99  Parsing              : 0.24
% 4.11/1.99  CNF conversion       : 0.03
% 4.11/1.99  Main loop            : 0.48
% 4.11/1.99  Inferencing          : 0.18
% 4.11/1.99  Reduction            : 0.13
% 4.11/1.99  Demodulation         : 0.09
% 4.11/1.99  BG Simplification    : 0.02
% 4.11/1.99  Subsumption          : 0.10
% 4.11/1.99  Abstraction          : 0.02
% 4.11/1.99  MUC search           : 0.00
% 4.11/1.99  Cooper               : 0.00
% 4.11/1.99  Total                : 1.00
% 4.11/1.99  Index Insertion      : 0.00
% 4.11/1.99  Index Deletion       : 0.00
% 4.11/1.99  Index Matching       : 0.00
% 4.11/1.99  BG Taut test         : 0.00
%------------------------------------------------------------------------------