TSTP Solution File: SET085-6 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET085-6 : 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 : n004.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 5.58s 2.22s
% Output   : CNFRefutation 5.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   57
% Syntax   : Number of formulae    :   69 (  11 unt;  50 typ;   0 def)
%            Number of atoms       :   31 (  18 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   23 (  11   ~;  12   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 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   :   14 (;  14   !;   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,
    x != y,
    file(unknown,unknown) ).

tff(f_649,axiom,
    x != z,
    file(unknown,unknown) ).

tff(f_645,axiom,
    member(x,universal_class),
    file(unknown,unknown) ).

tff(f_123,axiom,
    ! [X] : ( unordered_pair(X,X) = singleton(X) ),
    file(unknown,unknown) ).

tff(f_109,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | member(X,unordered_pair(X,Y)) ),
    file(unknown,unknown) ).

tff(f_644,axiom,
    unordered_pair(y,z) = singleton(x),
    file(unknown,unknown) ).

tff(f_102,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | ( U = X )
      | ( U = Y ) ),
    file(unknown,unknown) ).

tff(c_188,plain,
    y != x,
    inference(cnfTransformation,[status(thm)],[f_647]) ).

tff(c_190,plain,
    z != x,
    inference(cnfTransformation,[status(thm)],[f_649]) ).

tff(c_186,plain,
    member(x,universal_class),
    inference(cnfTransformation,[status(thm)],[f_645]) ).

tff(c_24,plain,
    ! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_402,plain,
    ! [X_236,Y_237] :
      ( member(X_236,unordered_pair(X_236,Y_237))
      | ~ member(X_236,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_405,plain,
    ! [X_24] :
      ( member(X_24,singleton(X_24))
      | ~ member(X_24,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_402]) ).

tff(c_184,plain,
    unordered_pair(y,z) = singleton(x),
    inference(cnfTransformation,[status(thm)],[f_644]) ).

tff(c_745,plain,
    ! [Y_269,U_270,X_271] :
      ( ( Y_269 = U_270 )
      | ( X_271 = U_270 )
      | ~ member(U_270,unordered_pair(X_271,Y_269)) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_1060,plain,
    ! [U_298] :
      ( ( z = U_298 )
      | ( y = U_298 )
      | ~ member(U_298,singleton(x)) ),
    inference(superposition,[status(thm),theory(equality)],[c_184,c_745]) ).

tff(c_1076,plain,
    ( ( z = x )
    | ( y = x )
    | ~ member(x,universal_class) ),
    inference(resolution,[status(thm)],[c_405,c_1060]) ).

tff(c_1090,plain,
    ( ( z = x )
    | ( y = x ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_186,c_1076]) ).

tff(c_1092,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_188,c_190,c_1090]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET085-6 : 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 : n004.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 16:26:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 5.58/2.22  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.58/2.23  
% 5.58/2.23  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.70/2.25  
% 5.70/2.25  Inference rules
% 5.70/2.25  ----------------------
% 5.70/2.25  #Ref     : 0
% 5.70/2.25  #Sup     : 204
% 5.70/2.25  #Fact    : 0
% 5.70/2.25  #Define  : 0
% 5.70/2.25  #Split   : 11
% 5.70/2.25  #Chain   : 0
% 5.70/2.25  #Close   : 0
% 5.70/2.25  
% 5.70/2.25  Ordering : KBO
% 5.70/2.25  
% 5.70/2.25  Simplification rules
% 5.70/2.25  ----------------------
% 5.70/2.25  #Subsume      : 24
% 5.70/2.25  #Demod        : 23
% 5.70/2.25  #Tautology    : 53
% 5.70/2.25  #SimpNegUnit  : 2
% 5.70/2.25  #BackRed      : 1
% 5.70/2.25  
% 5.70/2.25  #Partial instantiations: 0
% 5.70/2.25  #Strategies tried      : 1
% 5.70/2.25  
% 5.70/2.25  Timing (in seconds)
% 5.70/2.25  ----------------------
% 5.70/2.26  Preprocessing        : 0.68
% 5.70/2.26  Parsing              : 0.35
% 5.70/2.26  CNF conversion       : 0.05
% 5.70/2.26  Main loop            : 0.54
% 5.70/2.26  Inferencing          : 0.17
% 5.70/2.26  Reduction            : 0.17
% 5.70/2.26  Demodulation         : 0.12
% 5.70/2.26  BG Simplification    : 0.04
% 5.70/2.26  Subsumption          : 0.12
% 5.70/2.26  Abstraction          : 0.02
% 5.70/2.26  MUC search           : 0.00
% 5.70/2.26  Cooper               : 0.00
% 5.70/2.26  Total                : 1.26
% 5.70/2.26  Index Insertion      : 0.00
% 5.70/2.26  Index Deletion       : 0.00
% 5.70/2.26  Index Matching       : 0.00
% 5.70/2.26  BG Taut test         : 0.00
%------------------------------------------------------------------------------