TSTP Solution File: SET242-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET242-6 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n029.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 10:56:15 EDT 2023

% Result   : Unsatisfiable 17.69s 6.33s
% Output   : CNFRefutation 17.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   65
% Syntax   : Number of formulae    :   73 (   9 unt;  60 typ;   0 def)
%            Number of atoms       :   20 (   2 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   17 (  10   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   72 (  44   >;  28   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   50 (  50 usr;  16 con; 0-3 aty)
%            Number of variables   :   16 (;  16   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ maps > 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 > single_valued3 > single_valued2 > single_valued1 > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > compose_class > complement > cantor > z > y > xr > x > universal_class > successor_relation > subset_relation > singleton_relation > omega > null_class > identity_relation > element_relation > domain_relation > composition_function > choice > application_function

%Foreground sorts:

%Background operators:

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

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

tff(xr,type,
    xr: $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(single_valued3,type,
    single_valued3: $i > $i ).

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

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

tff(compose_class,type,
    compose_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(singleton_relation,type,
    singleton_relation: $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(application_function,type,
    application_function: $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(single_valued2,type,
    single_valued2: $i > $i ).

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(composition_function,type,
    composition_function: $i ).

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

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

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

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

tff(single_valued1,type,
    single_valued1: $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_780,axiom,
    member(z,xr),
    file(unknown,unknown) ).

tff(f_781,axiom,
    member(z,cross_product(x,y)),
    file(unknown,unknown) ).

tff(f_239,axiom,
    ! [Xr,X,Y] : ( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
    file(unknown,unknown) ).

tff(f_210,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,X)
      | ~ member(Z,Y)
      | member(Z,intersection(X,Y)) ),
    file(unknown,unknown) ).

tff(f_783,axiom,
    ~ member(z,restrict(xr,x,y)),
    file(unknown,unknown) ).

tff(c_226,plain,
    member(z,xr),
    inference(cnfTransformation,[status(thm)],[f_780]) ).

tff(c_228,plain,
    member(z,cross_product(x,y)),
    inference(cnfTransformation,[status(thm)],[f_781]) ).

tff(c_56,plain,
    ! [Xr_63,X_64,Y_65] : ( intersection(Xr_63,cross_product(X_64,Y_65)) = restrict(Xr_63,X_64,Y_65) ),
    inference(cnfTransformation,[status(thm)],[f_239]) ).

tff(c_1759,plain,
    ! [Z_421,X_422,Y_423] :
      ( member(Z_421,intersection(X_422,Y_423))
      | ~ member(Z_421,Y_423)
      | ~ member(Z_421,X_422) ),
    inference(cnfTransformation,[status(thm)],[f_210]) ).

tff(c_19747,plain,
    ! [Z_1114,Xr_1115,X_1116,Y_1117] :
      ( member(Z_1114,restrict(Xr_1115,X_1116,Y_1117))
      | ~ member(Z_1114,cross_product(X_1116,Y_1117))
      | ~ member(Z_1114,Xr_1115) ),
    inference(superposition,[status(thm),theory(equality)],[c_56,c_1759]) ).

tff(c_230,plain,
    ~ member(z,restrict(xr,x,y)),
    inference(cnfTransformation,[status(thm)],[f_783]) ).

tff(c_19800,plain,
    ( ~ member(z,cross_product(x,y))
    | ~ member(z,xr) ),
    inference(resolution,[status(thm)],[c_19747,c_230]) ).

tff(c_19834,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_226,c_228,c_19800]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET242-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 16:25:22 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 17.69/6.33  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.69/6.34  
% 17.69/6.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.69/6.36  
% 17.69/6.36  Inference rules
% 17.69/6.36  ----------------------
% 17.69/6.36  #Ref     : 1
% 17.69/6.36  #Sup     : 4870
% 17.69/6.36  #Fact    : 0
% 17.69/6.36  #Define  : 0
% 17.69/6.36  #Split   : 119
% 17.69/6.36  #Chain   : 0
% 17.69/6.36  #Close   : 0
% 17.69/6.36  
% 17.69/6.36  Ordering : KBO
% 17.69/6.36  
% 17.69/6.36  Simplification rules
% 17.69/6.36  ----------------------
% 17.69/6.36  #Subsume      : 1237
% 17.69/6.36  #Demod        : 1626
% 17.69/6.36  #Tautology    : 626
% 17.69/6.36  #SimpNegUnit  : 111
% 17.69/6.36  #BackRed      : 306
% 17.69/6.36  
% 17.69/6.36  #Partial instantiations: 0
% 17.69/6.36  #Strategies tried      : 1
% 17.69/6.36  
% 17.69/6.36  Timing (in seconds)
% 17.69/6.36  ----------------------
% 17.69/6.37  Preprocessing        : 0.74
% 17.69/6.37  Parsing              : 0.40
% 17.69/6.37  CNF conversion       : 0.05
% 17.69/6.37  Main loop            : 4.50
% 17.69/6.37  Inferencing          : 1.10
% 17.69/6.37  Reduction            : 1.74
% 17.69/6.37  Demodulation         : 1.19
% 17.69/6.37  BG Simplification    : 0.09
% 17.69/6.37  Subsumption          : 1.12
% 17.69/6.37  Abstraction          : 0.08
% 17.69/6.37  MUC search           : 0.00
% 17.69/6.37  Cooper               : 0.00
% 17.69/6.37  Total                : 5.28
% 17.69/6.37  Index Insertion      : 0.00
% 17.69/6.37  Index Deletion       : 0.00
% 17.69/6.37  Index Matching       : 0.00
% 17.69/6.37  BG Taut test         : 0.00
%------------------------------------------------------------------------------