TSTP Solution File: SET020-7 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET020-7 : 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 : n012.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 10:55:35 EDT 2023

% Result   : Unsatisfiable 39.13s 24.53s
% Output   : CNFRefutation 39.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   56
% Syntax   : Number of formulae    :   67 (   8 unt;  51 typ;   0 def)
%            Number of atoms       :   26 (  14 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   23 (  13   ~;  10   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 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   :   27 (;  27   !;   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 > v > universal_class > u > 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(u,type,
    u: $i ).

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(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(v,type,
    v: $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(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_1047,axiom,
    first(ordered_pair(u,v)) != u,
    file(unknown,unknown) ).

tff(f_1045,axiom,
    member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
    file(unknown,unknown) ).

tff(f_159,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,cross_product(X,Y))
      | ( ordered_pair(first(Z),second(Z)) = Z ) ),
    file(unknown,unknown) ).

tff(f_136,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    file(unknown,unknown) ).

tff(f_1007,axiom,
    ! [W,X,Y,Z] :
      ( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
      | ~ member(W,universal_class)
      | ( W = Y ) ),
    file(unknown,unknown) ).

tff(c_318,plain,
    first(ordered_pair(u,v)) != u,
    inference(cnfTransformation,[status(thm)],[f_1047]) ).

tff(c_316,plain,
    member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
    inference(cnfTransformation,[status(thm)],[f_1045]) ).

tff(c_5482,plain,
    ! [Z_597,X_598,Y_599] :
      ( ( ordered_pair(first(Z_597),second(Z_597)) = Z_597 )
      | ~ member(Z_597,cross_product(X_598,Y_599)) ),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_5523,plain,
    ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v),
    inference(resolution,[status(thm)],[c_316,c_5482]) ).

tff(c_4897,plain,
    ! [U_573,X_574,V_575,Y_576] :
      ( member(U_573,X_574)
      | ~ member(ordered_pair(U_573,V_575),cross_product(X_574,Y_576)) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_4912,plain,
    member(u,universal_class),
    inference(resolution,[status(thm)],[c_316,c_4897]) ).

tff(c_5251,plain,
    ! [Y_593,W_594,Z_595,X_596] :
      ( ( Y_593 = W_594 )
      | ~ member(W_594,universal_class)
      | ( ordered_pair(Y_593,Z_595) != ordered_pair(W_594,X_596) ) ),
    inference(cnfTransformation,[status(thm)],[f_1007]) ).

tff(c_5330,plain,
    ! [Y_593,X_596,Z_595] :
      ( ( u = Y_593 )
      | ( ordered_pair(u,X_596) != ordered_pair(Y_593,Z_595) ) ),
    inference(resolution,[status(thm)],[c_4912,c_5251]) ).

tff(c_96534,plain,
    ! [X_596] :
      ( ( first(ordered_pair(u,v)) = u )
      | ( ordered_pair(u,v) != ordered_pair(u,X_596) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_5523,c_5330]) ).

tff(c_96647,plain,
    ! [X_596] : ( ordered_pair(u,v) != ordered_pair(u,X_596) ),
    inference(negUnitSimplification,[status(thm)],[c_318,c_96534]) ).

tff(c_96794,plain,
    $false,
    inference(reflexivity,[status(thm),theory(equality)],[c_96647]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET020-7 : 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
% 0.16/0.35  % Computer : n012.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Thu Aug  3 16:11:37 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 39.13/24.53  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.13/24.54  
% 39.13/24.54  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.18/24.57  
% 39.18/24.57  Inference rules
% 39.18/24.57  ----------------------
% 39.18/24.57  #Ref     : 41
% 39.18/24.57  #Sup     : 24589
% 39.18/24.57  #Fact    : 12
% 39.18/24.57  #Define  : 0
% 39.18/24.57  #Split   : 122
% 39.18/24.57  #Chain   : 0
% 39.18/24.57  #Close   : 0
% 39.18/24.57  
% 39.18/24.57  Ordering : KBO
% 39.18/24.57  
% 39.18/24.57  Simplification rules
% 39.18/24.57  ----------------------
% 39.18/24.57  #Subsume      : 7104
% 39.18/24.57  #Demod        : 11516
% 39.18/24.57  #Tautology    : 6043
% 39.18/24.57  #SimpNegUnit  : 1995
% 39.18/24.57  #BackRed      : 460
% 39.18/24.57  
% 39.18/24.57  #Partial instantiations: 0
% 39.18/24.57  #Strategies tried      : 1
% 39.18/24.57  
% 39.18/24.57  Timing (in seconds)
% 39.18/24.57  ----------------------
% 39.18/24.57  Preprocessing        : 0.93
% 39.18/24.57  Parsing              : 0.44
% 39.18/24.57  CNF conversion       : 0.07
% 39.18/24.57  Main loop            : 22.50
% 39.18/24.57  Inferencing          : 3.25
% 39.18/24.57  Reduction            : 10.34
% 39.18/24.57  Demodulation         : 7.45
% 39.18/24.57  BG Simplification    : 0.18
% 39.18/24.57  Subsumption          : 6.80
% 39.18/24.57  Abstraction          : 0.23
% 39.18/24.57  MUC search           : 0.00
% 39.18/24.57  Cooper               : 0.00
% 39.18/24.57  Total                : 23.48
% 39.18/24.57  Index Insertion      : 0.00
% 39.18/24.57  Index Deletion       : 0.00
% 39.18/24.57  Index Matching       : 0.00
% 39.18/24.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------