TSTP Solution File: SET082+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n027.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 10:55:53 EDT 2023

% Result   : Theorem 6.69s 2.81s
% Output   : CNFRefutation 7.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   63 (  10 unt;  39 typ;   0 def)
%            Number of atoms       :   49 (  23 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   37 (  12   ~;  20   |;   2   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   47 (  31   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   34 (  34 usr;   8 con; 0-3 aty)
%            Number of variables   :   31 (;  30   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subclass > member > disjoint > inductive > function > restrict > unordered_pair > union > ordered_pair > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > range_of > power_class > inverse > flip > first > domain_of > complement > universal_class > successor_relation > null_class > identity_relation > element_relation > #skF_4 > #skF_7 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_5 > #skF_6

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_381,negated_conjecture,
    ~ ! [X] :
        ( ~ member(X,universal_class)
       => ( singleton(X) = null_class ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).

tff(f_100,axiom,
    ! [X] : ( singleton(X) = unordered_pair(X,X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).

tff(f_97,axiom,
    ! [X,Y] : member(unordered_pair(X,Y),universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair) ).

tff(f_372,axiom,
    ? [XF] :
      ( function(XF)
      & ! [Y] :
          ( member(Y,universal_class)
         => ( ( Y = null_class )
            | member(apply(XF,Y),Y) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',choice) ).

tff(f_87,axiom,
    ! [U,X,Y] :
      ( member(U,unordered_pair(X,Y))
    <=> ( member(U,universal_class)
        & ( ( U = X )
          | ( U = Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).

tff(c_180,plain,
    singleton('#skF_8') != null_class,
    inference(cnfTransformation,[status(thm)],[f_381]) ).

tff(c_204,plain,
    ! [X_103] : ( unordered_pair(X_103,X_103) = singleton(X_103) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_24,plain,
    ! [X_12,Y_13] : member(unordered_pair(X_12,Y_13),universal_class),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_209,plain,
    ! [X_103] : member(singleton(X_103),universal_class),
    inference(superposition,[status(thm),theory(equality)],[c_204,c_24]) ).

tff(c_3275,plain,
    ! [Y_349] :
      ( member(apply('#skF_7',Y_349),Y_349)
      | ( null_class = Y_349 )
      | ~ member(Y_349,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_372]) ).

tff(c_26,plain,
    ! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_2146,plain,
    ! [Y_284,U_285,X_286] :
      ( ( Y_284 = U_285 )
      | ( X_286 = U_285 )
      | ~ member(U_285,unordered_pair(X_286,Y_284)) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_2171,plain,
    ! [X_14,U_285] :
      ( ( X_14 = U_285 )
      | ( X_14 = U_285 )
      | ~ member(U_285,singleton(X_14)) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_2146]) ).

tff(c_3292,plain,
    ! [X_14] :
      ( ( apply('#skF_7',singleton(X_14)) = X_14 )
      | ( singleton(X_14) = null_class )
      | ~ member(singleton(X_14),universal_class) ),
    inference(resolution,[status(thm)],[c_3275,c_2171]) ).

tff(c_4647,plain,
    ! [X_458] :
      ( ( apply('#skF_7',singleton(X_458)) = X_458 )
      | ( singleton(X_458) = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_209,c_3292]) ).

tff(c_176,plain,
    ! [Y_94] :
      ( member(apply('#skF_7',Y_94),Y_94)
      | ( null_class = Y_94 )
      | ~ member(Y_94,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_372]) ).

tff(c_4653,plain,
    ! [X_458] :
      ( member(X_458,singleton(X_458))
      | ( singleton(X_458) = null_class )
      | ~ member(singleton(X_458),universal_class)
      | ( singleton(X_458) = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4647,c_176]) ).

tff(c_4665,plain,
    ! [X_463] :
      ( member(X_463,singleton(X_463))
      | ( singleton(X_463) = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_209,c_4653]) ).

tff(c_344,plain,
    ! [U_138,X_139,Y_140] :
      ( member(U_138,universal_class)
      | ~ member(U_138,unordered_pair(X_139,Y_140)) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_350,plain,
    ! [U_138,X_14] :
      ( member(U_138,universal_class)
      | ~ member(U_138,singleton(X_14)) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_344]) ).

tff(c_4713,plain,
    ! [X_464] :
      ( member(X_464,universal_class)
      | ( singleton(X_464) = null_class ) ),
    inference(resolution,[status(thm)],[c_4665,c_350]) ).

tff(c_182,plain,
    ~ member('#skF_8',universal_class),
    inference(cnfTransformation,[status(thm)],[f_381]) ).

tff(c_4753,plain,
    singleton('#skF_8') = null_class,
    inference(resolution,[status(thm)],[c_4713,c_182]) ).

tff(c_4770,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_180,c_4753]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13  % 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
% 0.13/0.34  % Computer : n027.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 16:34:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 6.69/2.81  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.69/2.82  
% 6.69/2.82  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.27/2.86  
% 7.27/2.86  Inference rules
% 7.27/2.86  ----------------------
% 7.27/2.86  #Ref     : 0
% 7.27/2.86  #Sup     : 1004
% 7.27/2.86  #Fact    : 0
% 7.27/2.86  #Define  : 0
% 7.27/2.86  #Split   : 23
% 7.27/2.86  #Chain   : 0
% 7.27/2.86  #Close   : 0
% 7.27/2.86  
% 7.27/2.86  Ordering : KBO
% 7.27/2.86  
% 7.27/2.86  Simplification rules
% 7.27/2.86  ----------------------
% 7.27/2.86  #Subsume      : 181
% 7.27/2.86  #Demod        : 176
% 7.27/2.86  #Tautology    : 156
% 7.27/2.86  #SimpNegUnit  : 11
% 7.27/2.86  #BackRed      : 3
% 7.27/2.86  
% 7.27/2.86  #Partial instantiations: 0
% 7.27/2.86  #Strategies tried      : 1
% 7.27/2.86  
% 7.27/2.86  Timing (in seconds)
% 7.27/2.86  ----------------------
% 7.27/2.86  Preprocessing        : 0.65
% 7.27/2.86  Parsing              : 0.34
% 7.27/2.86  CNF conversion       : 0.05
% 7.27/2.86  Main loop            : 1.05
% 7.27/2.86  Inferencing          : 0.37
% 7.27/2.86  Reduction            : 0.31
% 7.27/2.86  Demodulation         : 0.21
% 7.27/2.86  BG Simplification    : 0.05
% 7.27/2.86  Subsumption          : 0.24
% 7.27/2.86  Abstraction          : 0.04
% 7.27/2.86  MUC search           : 0.00
% 7.27/2.86  Cooper               : 0.00
% 7.27/2.86  Total                : 1.77
% 7.27/2.86  Index Insertion      : 0.00
% 7.27/2.86  Index Deletion       : 0.00
% 7.27/2.86  Index Matching       : 0.00
% 7.27/2.87  BG Taut test         : 0.00
%------------------------------------------------------------------------------