TSTP Solution File: SET096+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET096+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/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 : n028.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 10:55:57 EDT 2023

% Result   : Theorem 14.45s 5.30s
% Output   : CNFRefutation 14.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   47
% Syntax   : Number of formulae    :   77 (  12 unt;  40 typ;   0 def)
%            Number of atoms       :   78 (  25 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   66 (  25   ~;  29   |;   5   &)
%                                         (   4 <=>;   3  =>;   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    :   35 (  35 usr;   9 con; 0-3 aty)
%            Number of variables   :   49 (;  48   !;   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_9 > #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('#skF_9',type,
    '#skF_9': $i ).

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_382,negated_conjecture,
    ~ ! [X,Y] :
        ( subclass(X,singleton(Y))
       => ( ( X = null_class )
          | ( singleton(Y) = X ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_subsets_of_singleton) ).

tff(f_78,axiom,
    ! [X,Y] :
      ( ( X = Y )
    <=> ( subclass(X,Y)
        & subclass(Y,X) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',extensionality) ).

tff(f_359,axiom,
    ! [X] :
      ( ( X != null_class )
     => ? [U] :
          ( member(U,universal_class)
          & member(U,X)
          & disjoint(U,X) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',regularity) ).

tff(f_67,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( member(U,X)
         => member(U,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',subclass_defn) ).

tff(f_346,axiom,
    ! [X,Y] :
      ( disjoint(X,Y)
    <=> ! [U] :
          ~ ( member(U,X)
            & member(U,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',disjoint_defn) ).

tff(f_100,axiom,
    ! [X] : ( singleton(X) = unordered_pair(X,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).

tff(f_87,axiom,
    ! [U,X,Y] :
      ( member(U,unordered_pair(X,Y))
    <=> ( member(U,universal_class)
        & ( ( U = X )
          | ( U = Y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).

tff(c_180,plain,
    singleton('#skF_9') != '#skF_8',
    inference(cnfTransformation,[status(thm)],[f_382]) ).

tff(c_184,plain,
    subclass('#skF_8',singleton('#skF_9')),
    inference(cnfTransformation,[status(thm)],[f_382]) ).

tff(c_495,plain,
    ! [Y_166,X_167] :
      ( ( Y_166 = X_167 )
      | ~ subclass(Y_166,X_167)
      | ~ subclass(X_167,Y_166) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_513,plain,
    ( ( singleton('#skF_9') = '#skF_8' )
    | ~ subclass(singleton('#skF_9'),'#skF_8') ),
    inference(resolution,[status(thm)],[c_184,c_495]) ).

tff(c_528,plain,
    ~ subclass(singleton('#skF_9'),'#skF_8'),
    inference(negUnitSimplification,[status(thm)],[c_180,c_513]) ).

tff(c_182,plain,
    null_class != '#skF_8',
    inference(cnfTransformation,[status(thm)],[f_382]) ).

tff(c_170,plain,
    ! [X_89] :
      ( member('#skF_6'(X_89),X_89)
      | ( null_class = X_89 ) ),
    inference(cnfTransformation,[status(thm)],[f_359]) ).

tff(c_2188,plain,
    ! [U_281,Y_282,X_283] :
      ( member(U_281,Y_282)
      | ~ member(U_281,X_283)
      | ~ subclass(X_283,Y_282) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_2249,plain,
    ! [X_89,Y_282] :
      ( member('#skF_6'(X_89),Y_282)
      | ~ subclass(X_89,Y_282)
      | ( null_class = X_89 ) ),
    inference(resolution,[status(thm)],[c_170,c_2188]) ).

tff(c_2530,plain,
    ! [U_293,Y_294,X_295] :
      ( ~ member(U_293,Y_294)
      | ~ member(U_293,X_295)
      | ~ disjoint(X_295,Y_294) ),
    inference(cnfTransformation,[status(thm)],[f_346]) ).

tff(c_6542,plain,
    ! [X_563,X_564] :
      ( ~ member('#skF_6'(X_563),X_564)
      | ~ disjoint(X_564,X_563)
      | ( null_class = X_563 ) ),
    inference(resolution,[status(thm)],[c_170,c_2530]) ).

tff(c_6698,plain,
    ! [Y_571,X_572] :
      ( ~ disjoint(Y_571,X_572)
      | ~ subclass(X_572,Y_571)
      | ( null_class = X_572 ) ),
    inference(resolution,[status(thm)],[c_2249,c_6542]) ).

tff(c_6737,plain,
    ( ~ disjoint(singleton('#skF_9'),'#skF_8')
    | ( null_class = '#skF_8' ) ),
    inference(resolution,[status(thm)],[c_184,c_6698]) ).

tff(c_6761,plain,
    ~ disjoint(singleton('#skF_9'),'#skF_8'),
    inference(negUnitSimplification,[status(thm)],[c_182,c_6737]) ).

tff(c_166,plain,
    ! [X_84,Y_85] :
      ( member('#skF_5'(X_84,Y_85),X_84)
      | disjoint(X_84,Y_85) ),
    inference(cnfTransformation,[status(thm)],[f_346]) ).

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

tff(c_824,plain,
    ! [Y_206,U_207,X_208] :
      ( ( Y_206 = U_207 )
      | ( X_208 = U_207 )
      | ~ member(U_207,unordered_pair(X_208,Y_206)) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_2138,plain,
    ! [X_278,U_279] :
      ( ( X_278 = U_279 )
      | ( X_278 = U_279 )
      | ~ member(U_279,singleton(X_278)) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_824]) ).

tff(c_8647,plain,
    ! [X_651,Y_652] :
      ( ( '#skF_5'(singleton(X_651),Y_652) = X_651 )
      | disjoint(singleton(X_651),Y_652) ),
    inference(resolution,[status(thm)],[c_166,c_2138]) ).

tff(c_8726,plain,
    '#skF_5'(singleton('#skF_9'),'#skF_8') = '#skF_9',
    inference(resolution,[status(thm)],[c_8647,c_6761]) ).

tff(c_164,plain,
    ! [X_84,Y_85] :
      ( member('#skF_5'(X_84,Y_85),Y_85)
      | disjoint(X_84,Y_85) ),
    inference(cnfTransformation,[status(thm)],[f_346]) ).

tff(c_8916,plain,
    ( member('#skF_9','#skF_8')
    | disjoint(singleton('#skF_9'),'#skF_8') ),
    inference(superposition,[status(thm),theory(equality)],[c_8726,c_164]) ).

tff(c_8922,plain,
    member('#skF_9','#skF_8'),
    inference(negUnitSimplification,[status(thm)],[c_6761,c_8916]) ).

tff(c_6,plain,
    ! [X_1,Y_2] :
      ( member('#skF_1'(X_1,Y_2),X_1)
      | subclass(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_19823,plain,
    ! [X_1013,Y_1014] :
      ( ( '#skF_1'(singleton(X_1013),Y_1014) = X_1013 )
      | subclass(singleton(X_1013),Y_1014) ),
    inference(resolution,[status(thm)],[c_6,c_2138]) ).

tff(c_19906,plain,
    '#skF_1'(singleton('#skF_9'),'#skF_8') = '#skF_9',
    inference(resolution,[status(thm)],[c_19823,c_528]) ).

tff(c_4,plain,
    ! [X_1,Y_2] :
      ( ~ member('#skF_1'(X_1,Y_2),Y_2)
      | subclass(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_19920,plain,
    ( ~ member('#skF_9','#skF_8')
    | subclass(singleton('#skF_9'),'#skF_8') ),
    inference(superposition,[status(thm),theory(equality)],[c_19906,c_4]) ).

tff(c_19931,plain,
    subclass(singleton('#skF_9'),'#skF_8'),
    inference(demodulation,[status(thm),theory(equality)],[c_8922,c_19920]) ).

tff(c_19933,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_528,c_19931]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET096+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.14  % 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
% 0.18/0.36  % Computer : n028.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 17:09:09 EDT 2023
% 0.18/0.36  % CPUTime  : 
% 14.45/5.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.45/5.30  
% 14.45/5.30  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.45/5.33  
% 14.45/5.33  Inference rules
% 14.45/5.33  ----------------------
% 14.45/5.33  #Ref     : 0
% 14.45/5.33  #Sup     : 4473
% 14.45/5.33  #Fact    : 0
% 14.45/5.33  #Define  : 0
% 14.45/5.33  #Split   : 81
% 14.45/5.33  #Chain   : 0
% 14.45/5.33  #Close   : 0
% 14.45/5.33  
% 14.45/5.33  Ordering : KBO
% 14.45/5.33  
% 14.45/5.33  Simplification rules
% 14.45/5.33  ----------------------
% 14.45/5.33  #Subsume      : 1278
% 14.45/5.33  #Demod        : 968
% 14.45/5.33  #Tautology    : 578
% 14.45/5.33  #SimpNegUnit  : 141
% 14.45/5.33  #BackRed      : 169
% 14.45/5.33  
% 14.45/5.33  #Partial instantiations: 0
% 14.45/5.33  #Strategies tried      : 1
% 14.45/5.33  
% 14.45/5.33  Timing (in seconds)
% 14.45/5.33  ----------------------
% 14.45/5.34  Preprocessing        : 0.65
% 14.45/5.34  Parsing              : 0.33
% 14.45/5.34  CNF conversion       : 0.05
% 14.45/5.34  Main loop            : 3.62
% 14.45/5.34  Inferencing          : 0.92
% 14.45/5.34  Reduction            : 1.28
% 14.45/5.34  Demodulation         : 0.78
% 14.45/5.34  BG Simplification    : 0.07
% 14.45/5.34  Subsumption          : 1.04
% 14.45/5.34  Abstraction          : 0.07
% 14.45/5.34  MUC search           : 0.00
% 14.45/5.34  Cooper               : 0.00
% 14.45/5.34  Total                : 4.32
% 14.45/5.34  Index Insertion      : 0.00
% 14.45/5.34  Index Deletion       : 0.00
% 14.45/5.34  Index Matching       : 0.00
% 14.45/5.34  BG Taut test         : 0.00
%------------------------------------------------------------------------------