TSTP Solution File: SET108-7 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET108-7 : 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 : 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 10:56:00 EDT 2023

% Result   : Unsatisfiable 30.36s 15.81s
% Output   : CNFRefutation 30.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   54
% Syntax   : Number of formulae    :   60 (   7 unt;  51 typ;   0 def)
%            Number of atoms       :   11 (   3 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   5   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   67 (  41   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   42 (  42 usr;  10 con; 0-3 aty)
%            Number of variables   :    6 (;   6   !;   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 > member_of1 > member_of > inverse > flip > first > domain_of > diagonalise > complement > cantor > z > y > 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(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(member_of1,type,
    member_of1: $i > $i ).

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

tff(member_of,type,
    member_of: $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_1020,axiom,
    member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
    file(unknown,unknown) ).

tff(f_162,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,cross_product(X,Y))
      | ( ordered_pair(first(Z),second(Z)) = Z ) ),
    file(unknown,unknown) ).

tff(f_1026,axiom,
    ~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
    file(unknown,unknown) ).

tff(c_306,plain,
    member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
    inference(cnfTransformation,[status(thm)],[f_1020]) ).

tff(c_6066,plain,
    ! [Z_618,X_619,Y_620] :
      ( ( ordered_pair(first(Z_618),second(Z_618)) = Z_618 )
      | ~ member(Z_618,cross_product(X_619,Y_620)) ),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_6099,plain,
    ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))) = ordered_pair(y,z),
    inference(resolution,[status(thm)],[c_306,c_6066]) ).

tff(c_308,plain,
    ~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
    inference(cnfTransformation,[status(thm)],[f_1026]) ).

tff(c_75201,plain,
    ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
    inference(demodulation,[status(thm),theory(equality)],[c_6099,c_308]) ).

tff(c_75204,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_306,c_75201]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET108-7 : 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
% 0.12/0.34  % Computer : n004.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 16:31:41 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 30.36/15.81  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.36/15.81  
% 30.36/15.81  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.49/15.84  
% 30.49/15.84  Inference rules
% 30.49/15.84  ----------------------
% 30.49/15.84  #Ref     : 43
% 30.49/15.84  #Sup     : 19091
% 30.49/15.84  #Fact    : 20
% 30.49/15.84  #Define  : 0
% 30.49/15.84  #Split   : 79
% 30.49/15.84  #Chain   : 0
% 30.49/15.84  #Close   : 0
% 30.49/15.84  
% 30.49/15.84  Ordering : KBO
% 30.49/15.84  
% 30.49/15.84  Simplification rules
% 30.49/15.84  ----------------------
% 30.49/15.84  #Subsume      : 5938
% 30.49/15.84  #Demod        : 8551
% 30.49/15.84  #Tautology    : 4731
% 30.49/15.84  #SimpNegUnit  : 1499
% 30.49/15.84  #BackRed      : 595
% 30.49/15.84  
% 30.49/15.84  #Partial instantiations: 0
% 30.49/15.84  #Strategies tried      : 1
% 30.49/15.84  
% 30.49/15.84  Timing (in seconds)
% 30.49/15.84  ----------------------
% 30.49/15.84  Preprocessing        : 0.80
% 30.49/15.84  Parsing              : 0.37
% 30.49/15.84  CNF conversion       : 0.06
% 30.49/15.84  Main loop            : 13.99
% 30.49/15.84  Inferencing          : 2.25
% 30.49/15.84  Reduction            : 6.08
% 30.49/15.84  Demodulation         : 4.31
% 30.49/15.84  BG Simplification    : 0.16
% 30.49/15.84  Subsumption          : 4.03
% 30.49/15.84  Abstraction          : 0.19
% 30.49/15.84  MUC search           : 0.00
% 30.49/15.84  Cooper               : 0.00
% 30.49/15.84  Total                : 14.83
% 30.49/15.84  Index Insertion      : 0.00
% 30.49/15.84  Index Deletion       : 0.00
% 30.49/15.84  Index Matching       : 0.00
% 30.49/15.84  BG Taut test         : 0.00
%------------------------------------------------------------------------------