TSTP Solution File: SET204-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET204-6 : 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 : n008.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 10:56:12 EDT 2023

% Result   : Unsatisfiable 7.50s 2.75s
% Output   : CNFRefutation 7.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   65
% Syntax   : Number of formulae    :   74 (   7 unt;  60 typ;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   21 (  12   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   72 (  44   >;  28   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   50 (  50 usr;  16 con; 0-3 aty)
%            Number of variables   :   24 (;  24   !;   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 > y > x > v > universal_class > u > 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(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(u,type,
    u: $i ).

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(v,type,
    v: $i ).

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(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_778,axiom,
    member(ordered_pair(u,v),cross_product(x,y)),
    file(unknown,unknown) ).

tff(f_151,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,Y) ),
    file(unknown,unknown) ).

tff(f_145,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    file(unknown,unknown) ).

tff(f_159,axiom,
    ! [U,X,V,Y] :
      ( ~ member(U,X)
      | ~ member(V,Y)
      | member(ordered_pair(U,V),cross_product(X,Y)) ),
    file(unknown,unknown) ).

tff(f_780,axiom,
    ~ member(ordered_pair(v,u),cross_product(y,x)),
    file(unknown,unknown) ).

tff(c_226,plain,
    member(ordered_pair(u,v),cross_product(x,y)),
    inference(cnfTransformation,[status(thm)],[f_778]) ).

tff(c_1619,plain,
    ! [V_410,Y_411,U_412,X_413] :
      ( member(V_410,Y_411)
      | ~ member(ordered_pair(U_412,V_410),cross_product(X_413,Y_411)) ),
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_1628,plain,
    member(v,y),
    inference(resolution,[status(thm)],[c_226,c_1619]) ).

tff(c_1567,plain,
    ! [U_404,X_405,V_406,Y_407] :
      ( member(U_404,X_405)
      | ~ member(ordered_pair(U_404,V_406),cross_product(X_405,Y_407)) ),
    inference(cnfTransformation,[status(thm)],[f_145]) ).

tff(c_1576,plain,
    member(u,x),
    inference(resolution,[status(thm)],[c_226,c_1567]) ).

tff(c_2512,plain,
    ! [U_469,V_470,X_471,Y_472] :
      ( member(ordered_pair(U_469,V_470),cross_product(X_471,Y_472))
      | ~ member(V_470,Y_472)
      | ~ member(U_469,X_471) ),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_228,plain,
    ~ member(ordered_pair(v,u),cross_product(y,x)),
    inference(cnfTransformation,[status(thm)],[f_780]) ).

tff(c_2525,plain,
    ( ~ member(u,x)
    | ~ member(v,y) ),
    inference(resolution,[status(thm)],[c_2512,c_228]) ).

tff(c_2536,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1628,c_1576,c_2525]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET204-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.15/0.35  % Computer : n008.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 16:57:03 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 7.50/2.75  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.50/2.75  
% 7.50/2.75  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.57/2.78  
% 7.57/2.78  Inference rules
% 7.57/2.78  ----------------------
% 7.57/2.78  #Ref     : 0
% 7.57/2.78  #Sup     : 548
% 7.57/2.78  #Fact    : 0
% 7.57/2.78  #Define  : 0
% 7.57/2.78  #Split   : 28
% 7.57/2.78  #Chain   : 0
% 7.57/2.78  #Close   : 0
% 7.57/2.78  
% 7.57/2.78  Ordering : KBO
% 7.57/2.78  
% 7.57/2.78  Simplification rules
% 7.57/2.78  ----------------------
% 7.57/2.78  #Subsume      : 60
% 7.57/2.78  #Demod        : 83
% 7.57/2.78  #Tautology    : 110
% 7.57/2.78  #SimpNegUnit  : 1
% 7.57/2.78  #BackRed      : 5
% 7.57/2.78  
% 7.57/2.78  #Partial instantiations: 0
% 7.57/2.78  #Strategies tried      : 1
% 7.57/2.78  
% 7.57/2.78  Timing (in seconds)
% 7.57/2.78  ----------------------
% 7.57/2.78  Preprocessing        : 0.72
% 7.57/2.78  Parsing              : 0.38
% 7.57/2.78  CNF conversion       : 0.05
% 7.57/2.78  Main loop            : 0.95
% 7.57/2.78  Inferencing          : 0.32
% 7.57/2.78  Reduction            : 0.31
% 7.57/2.78  Demodulation         : 0.21
% 7.57/2.78  BG Simplification    : 0.05
% 7.57/2.78  Subsumption          : 0.20
% 7.57/2.78  Abstraction          : 0.03
% 7.57/2.78  MUC search           : 0.00
% 7.57/2.78  Cooper               : 0.00
% 7.57/2.78  Total                : 1.72
% 7.57/2.79  Index Insertion      : 0.00
% 7.57/2.79  Index Deletion       : 0.00
% 7.57/2.79  Index Matching       : 0.00
% 7.57/2.79  BG Taut test         : 0.00
%------------------------------------------------------------------------------