TSTP Solution File: SET027-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET027-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n009.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 10:55:37 EDT 2023

% Result   : Unsatisfiable 235.03s 206.57s
% Output   : CNFRefutation 235.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   88 (  11 unt;  50 typ;   0 def)
%            Number of atoms       :   73 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   64 (  29   ~;  35   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   65 (  39   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   41 (  41 usr;  11 con; 0-3 aty)
%            Number of variables   :   64 (;  64   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ homomorphism > compatible > subclass > member > single_valued_class > operation > one_to_one > inductive > function > restrict > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordered_pair > not_subclass_element > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > complement > cantor > z > y > x > universal_class > successor_relation > subset_relation > omega > null_class > identity_relation > element_relation > choice

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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(symmetric_difference,type,
    symmetric_difference: ( $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(choice,type,
    choice: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(not_homomorphism2,type,
    not_homomorphism2: ( $i * $i * $i ) > $i ).

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

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

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

tff(not_homomorphism1,type,
    not_homomorphism1: ( $i * $i * $i ) > $i ).

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

tff(f_647,axiom,
    ~ subclass(x,z),
    file(unknown,unknown) ).

tff(f_644,axiom,
    subclass(x,y),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file(unknown,unknown) ).

tff(f_199,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,X)
      | ~ member(Z,Y)
      | member(Z,intersection(X,Y)) ),
    file(unknown,unknown) ).

tff(f_66,axiom,
    ! [X,Y] :
      ( ~ member(not_subclass_element(X,Y),Y)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_191,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    file(unknown,unknown) ).

tff(f_91,axiom,
    ! [X,Y] :
      ( ~ subclass(X,Y)
      | ~ subclass(Y,X)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_185,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    file(unknown,unknown) ).

tff(f_645,axiom,
    subclass(y,z),
    file(unknown,unknown) ).

tff(c_188,plain,
    ~ subclass(x,z),
    inference(cnfTransformation,[status(thm)],[f_647]) ).

tff(c_184,plain,
    subclass(x,y),
    inference(cnfTransformation,[status(thm)],[f_644]) ).

tff(c_4,plain,
    ! [X_4,Y_5] :
      ( subclass(X_4,Y_5)
      | member(not_subclass_element(X_4,Y_5),X_4) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_793,plain,
    ! [U_285,Y_286,X_287] :
      ( member(U_285,Y_286)
      | ~ member(U_285,X_287)
      | ~ subclass(X_287,Y_286) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_820,plain,
    ! [X_4,Y_5,Y_286] :
      ( member(not_subclass_element(X_4,Y_5),Y_286)
      | ~ subclass(X_4,Y_286)
      | subclass(X_4,Y_5) ),
    inference(resolution,[status(thm)],[c_4,c_793]) ).

tff(c_1814,plain,
    ! [Z_369,X_370,Y_371] :
      ( member(Z_369,intersection(X_370,Y_371))
      | ~ member(Z_369,Y_371)
      | ~ member(Z_369,X_370) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_6,plain,
    ! [X_6,Y_7] :
      ( subclass(X_6,Y_7)
      | ~ member(not_subclass_element(X_6,Y_7),Y_7) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_841696,plain,
    ! [X_18538,X_18539,Y_18540] :
      ( subclass(X_18538,intersection(X_18539,Y_18540))
      | ~ member(not_subclass_element(X_18538,intersection(X_18539,Y_18540)),Y_18540)
      | ~ member(not_subclass_element(X_18538,intersection(X_18539,Y_18540)),X_18539) ),
    inference(resolution,[status(thm)],[c_1814,c_6]) ).

tff(c_858454,plain,
    ! [X_18988,X_18989] :
      ( ~ member(not_subclass_element(X_18988,intersection(X_18989,X_18988)),X_18989)
      | subclass(X_18988,intersection(X_18989,X_18988)) ),
    inference(resolution,[status(thm)],[c_4,c_841696]) ).

tff(c_861065,plain,
    ! [X_19026,Y_19027] :
      ( ~ subclass(X_19026,Y_19027)
      | subclass(X_19026,intersection(Y_19027,X_19026)) ),
    inference(resolution,[status(thm)],[c_820,c_858454]) ).

tff(c_421,plain,
    ! [X_244,Y_245] :
      ( subclass(X_244,Y_245)
      | member(not_subclass_element(X_244,Y_245),X_244) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_44,plain,
    ! [Z_49,Y_51,X_50] :
      ( member(Z_49,Y_51)
      | ~ member(Z_49,intersection(X_50,Y_51)) ),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_626892,plain,
    ! [X_13931,Y_13932,Y_13933] :
      ( member(not_subclass_element(intersection(X_13931,Y_13932),Y_13933),Y_13932)
      | subclass(intersection(X_13931,Y_13932),Y_13933) ),
    inference(resolution,[status(thm)],[c_421,c_44]) ).

tff(c_627070,plain,
    ! [X_13934,Y_13935] : subclass(intersection(X_13934,Y_13935),Y_13935),
    inference(resolution,[status(thm)],[c_626892,c_6]) ).

tff(c_14,plain,
    ! [Y_14,X_13] :
      ( ( Y_14 = X_13 )
      | ~ subclass(Y_14,X_13)
      | ~ subclass(X_13,Y_14) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_627149,plain,
    ! [X_13934,Y_13935] :
      ( ( intersection(X_13934,Y_13935) = Y_13935 )
      | ~ subclass(Y_13935,intersection(X_13934,Y_13935)) ),
    inference(resolution,[status(thm)],[c_627070,c_14]) ).

tff(c_861442,plain,
    ! [Y_19028,X_19029] :
      ( ( intersection(Y_19028,X_19029) = X_19029 )
      | ~ subclass(X_19029,Y_19028) ),
    inference(resolution,[status(thm)],[c_861065,c_627149]) ).

tff(c_861713,plain,
    intersection(y,x) = x,
    inference(resolution,[status(thm)],[c_184,c_861442]) ).

tff(c_42,plain,
    ! [Z_46,X_47,Y_48] :
      ( member(Z_46,X_47)
      | ~ member(Z_46,intersection(X_47,Y_48)) ),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_435,plain,
    ! [X_47,Y_48,Y_245] :
      ( member(not_subclass_element(intersection(X_47,Y_48),Y_245),X_47)
      | subclass(intersection(X_47,Y_48),Y_245) ),
    inference(resolution,[status(thm)],[c_421,c_42]) ).

tff(c_861811,plain,
    ! [Y_245] :
      ( member(not_subclass_element(x,Y_245),y)
      | subclass(intersection(y,x),Y_245) ),
    inference(superposition,[status(thm),theory(equality)],[c_861713,c_435]) ).

tff(c_861856,plain,
    ! [Y_245] :
      ( member(not_subclass_element(x,Y_245),y)
      | subclass(x,Y_245) ),
    inference(demodulation,[status(thm),theory(equality)],[c_861713,c_861811]) ).

tff(c_186,plain,
    subclass(y,z),
    inference(cnfTransformation,[status(thm)],[f_645]) ).

tff(c_861717,plain,
    intersection(z,y) = y,
    inference(resolution,[status(thm)],[c_186,c_861442]) ).

tff(c_863333,plain,
    ! [Z_19035] :
      ( member(Z_19035,z)
      | ~ member(Z_19035,y) ),
    inference(superposition,[status(thm),theory(equality)],[c_861717,c_42]) ).

tff(c_875896,plain,
    ! [X_19196] :
      ( subclass(X_19196,z)
      | ~ member(not_subclass_element(X_19196,z),y) ),
    inference(resolution,[status(thm)],[c_863333,c_6]) ).

tff(c_875900,plain,
    subclass(x,z),
    inference(resolution,[status(thm)],[c_861856,c_875896]) ).

tff(c_875931,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_188,c_188,c_875900]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET027-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n009.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 16:15:24 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 235.03/206.57  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 235.03/206.58  
% 235.03/206.58  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 235.03/206.61  
% 235.03/206.61  Inference rules
% 235.03/206.61  ----------------------
% 235.03/206.61  #Ref     : 5
% 235.03/206.61  #Sup     : 236114
% 235.03/206.61  #Fact    : 76
% 235.03/206.61  #Define  : 0
% 235.03/206.61  #Split   : 1356
% 235.03/206.61  #Chain   : 0
% 235.03/206.61  #Close   : 0
% 235.03/206.61  
% 235.03/206.61  Ordering : KBO
% 235.03/206.61  
% 235.03/206.61  Simplification rules
% 235.03/206.61  ----------------------
% 235.03/206.61  #Subsume      : 68633
% 235.03/206.61  #Demod        : 118290
% 235.03/206.61  #Tautology    : 37489
% 235.03/206.61  #SimpNegUnit  : 5649
% 235.03/206.61  #BackRed      : 2299
% 235.03/206.61  
% 235.03/206.61  #Partial instantiations: 0
% 235.03/206.61  #Strategies tried      : 1
% 235.03/206.61  
% 235.03/206.61  Timing (in seconds)
% 235.03/206.61  ----------------------
% 235.03/206.61  Preprocessing        : 0.69
% 235.03/206.61  Parsing              : 0.36
% 235.03/206.61  CNF conversion       : 0.05
% 235.03/206.61  Main loop            : 204.80
% 235.03/206.61  Inferencing          : 25.66
% 235.03/206.61  Reduction            : 95.52
% 235.03/206.61  Demodulation         : 70.42
% 235.03/206.61  BG Simplification    : 1.06
% 235.03/206.61  Subsumption          : 63.70
% 235.03/206.61  Abstraction          : 1.82
% 235.03/206.61  MUC search           : 0.00
% 235.03/206.61  Cooper               : 0.00
% 235.03/206.61  Total                : 205.55
% 235.03/206.61  Index Insertion      : 0.00
% 235.03/206.61  Index Deletion       : 0.00
% 235.03/206.61  Index Matching       : 0.00
% 235.03/206.61  BG Taut test         : 0.00
%------------------------------------------------------------------------------