TSTP Solution File: SET085-7 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET085-7 : 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 : n022.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 10:55:54 EDT 2023

% Result   : Unsatisfiable 6.06s 2.40s
% Output   : CNFRefutation 6.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   86 (  22 unt;  50 typ;   0 def)
%            Number of atoms       :   50 (  21 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   33 (  19   ~;  14   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   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   :   21 (;  21   !;   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_869,axiom,
    x != y,
    file(unknown,unknown) ).

tff(f_871,axiom,
    x != z,
    file(unknown,unknown) ).

tff(f_867,axiom,
    member(x,universal_class),
    file(unknown,unknown) ).

tff(f_835,axiom,
    ! [X] :
      ( ~ member(X,universal_class)
      | ( singleton(X) != null_class ) ),
    file(unknown,unknown) ).

tff(f_848,axiom,
    ! [X] :
      ( member(X,universal_class)
      | ( singleton(X) = null_class ) ),
    file(unknown,unknown) ).

tff(f_866,axiom,
    unordered_pair(y,z) = singleton(x),
    file(unknown,unknown) ).

tff(f_117,axiom,
    ! [Y,X] :
      ( ~ member(Y,universal_class)
      | member(Y,unordered_pair(X,Y)) ),
    file(unknown,unknown) ).

tff(f_758,axiom,
    ! [X,Y] :
      ( member(X,universal_class)
      | ( unordered_pair(X,Y) = singleton(Y) ) ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | member(X,unordered_pair(X,Y)) ),
    file(unknown,unknown) ).

tff(f_843,axiom,
    ! [Y,X] :
      ( ~ member(Y,singleton(X))
      | ( Y = X ) ),
    file(unknown,unknown) ).

tff(c_262,plain,
    y != x,
    inference(cnfTransformation,[status(thm)],[f_869]) ).

tff(c_264,plain,
    z != x,
    inference(cnfTransformation,[status(thm)],[f_871]) ).

tff(c_260,plain,
    member(x,universal_class),
    inference(cnfTransformation,[status(thm)],[f_867]) ).

tff(c_363,plain,
    ! [X_272] :
      ( ( singleton(X_272) != null_class )
      | ~ member(X_272,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_835]) ).

tff(c_392,plain,
    singleton(x) != null_class,
    inference(resolution,[status(thm)],[c_260,c_363]) ).

tff(c_252,plain,
    ! [X_247] :
      ( ( singleton(X_247) = null_class )
      | member(X_247,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_848]) ).

tff(c_258,plain,
    unordered_pair(y,z) = singleton(x),
    inference(cnfTransformation,[status(thm)],[f_866]) ).

tff(c_816,plain,
    ! [Y_332,X_333] :
      ( member(Y_332,unordered_pair(X_333,Y_332))
      | ~ member(Y_332,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_828,plain,
    ( member(z,singleton(x))
    | ~ member(z,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_258,c_816]) ).

tff(c_980,plain,
    ~ member(z,universal_class),
    inference(splitLeft,[status(thm)],[c_828]) ).

tff(c_984,plain,
    singleton(z) = null_class,
    inference(resolution,[status(thm)],[c_252,c_980]) ).

tff(c_1188,plain,
    ! [X_364,Y_365] :
      ( ( unordered_pair(X_364,Y_365) = singleton(Y_365) )
      | member(X_364,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_758]) ).

tff(c_722,plain,
    ! [X_324,Y_325] :
      ( member(X_324,unordered_pair(X_324,Y_325))
      | ~ member(X_324,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_734,plain,
    ( member(y,singleton(x))
    | ~ member(y,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_258,c_722]) ).

tff(c_829,plain,
    ~ member(y,universal_class),
    inference(splitLeft,[status(thm)],[c_734]) ).

tff(c_1366,plain,
    ! [Y_369] : ( unordered_pair(y,Y_369) = singleton(Y_369) ),
    inference(resolution,[status(thm)],[c_1188,c_829]) ).

tff(c_1413,plain,
    singleton(z) = singleton(x),
    inference(superposition,[status(thm),theory(equality)],[c_1366,c_258]) ).

tff(c_1445,plain,
    singleton(x) = null_class,
    inference(demodulation,[status(thm),theory(equality)],[c_984,c_1413]) ).

tff(c_1447,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_392,c_1445]) ).

tff(c_1448,plain,
    member(z,singleton(x)),
    inference(splitRight,[status(thm)],[c_828]) ).

tff(c_250,plain,
    ! [Y_245,X_246] :
      ( ( Y_245 = X_246 )
      | ~ member(Y_245,singleton(X_246)) ),
    inference(cnfTransformation,[status(thm)],[f_843]) ).

tff(c_1460,plain,
    z = x,
    inference(resolution,[status(thm)],[c_1448,c_250]) ).

tff(c_1464,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_264,c_1460]) ).

tff(c_1465,plain,
    member(y,singleton(x)),
    inference(splitRight,[status(thm)],[c_734]) ).

tff(c_1473,plain,
    y = x,
    inference(resolution,[status(thm)],[c_1465,c_250]) ).

tff(c_1477,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_262,c_1473]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET085-7 : 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 : n022.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 16:24:18 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 6.06/2.40  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.06/2.41  
% 6.06/2.41  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.06/2.43  
% 6.06/2.43  Inference rules
% 6.06/2.43  ----------------------
% 6.06/2.43  #Ref     : 0
% 6.06/2.44  #Sup     : 294
% 6.06/2.44  #Fact    : 0
% 6.06/2.44  #Define  : 0
% 6.06/2.44  #Split   : 6
% 6.06/2.44  #Chain   : 0
% 6.06/2.44  #Close   : 0
% 6.06/2.44  
% 6.06/2.44  Ordering : KBO
% 6.06/2.44  
% 6.06/2.44  Simplification rules
% 6.06/2.44  ----------------------
% 6.06/2.44  #Subsume      : 55
% 6.06/2.44  #Demod        : 94
% 6.06/2.44  #Tautology    : 139
% 6.06/2.44  #SimpNegUnit  : 8
% 6.06/2.44  #BackRed      : 4
% 6.06/2.44  
% 6.06/2.44  #Partial instantiations: 0
% 6.06/2.44  #Strategies tried      : 1
% 6.06/2.44  
% 6.06/2.44  Timing (in seconds)
% 6.06/2.44  ----------------------
% 6.06/2.44  Preprocessing        : 0.74
% 6.06/2.44  Parsing              : 0.36
% 6.06/2.44  CNF conversion       : 0.05
% 6.06/2.44  Main loop            : 0.63
% 6.06/2.44  Inferencing          : 0.21
% 6.06/2.44  Reduction            : 0.22
% 6.06/2.44  Demodulation         : 0.15
% 6.06/2.44  BG Simplification    : 0.05
% 6.06/2.44  Subsumption          : 0.12
% 6.06/2.44  Abstraction          : 0.02
% 6.06/2.44  MUC search           : 0.00
% 6.06/2.44  Cooper               : 0.00
% 6.06/2.44  Total                : 1.42
% 6.06/2.44  Index Insertion      : 0.00
% 6.06/2.44  Index Deletion       : 0.00
% 6.06/2.44  Index Matching       : 0.00
% 6.06/2.44  BG Taut test         : 0.00
%------------------------------------------------------------------------------