TSTP Solution File: SET072-7 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET072-7 : 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/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 : n005.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 10:55:49 EDT 2023

% Result   : Unsatisfiable 6.50s 2.48s
% Output   : CNFRefutation 6.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   90 (  23 unt;  50 typ;   0 def)
%            Number of atoms       :   62 (  21 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   42 (  20   ~;  22   |;   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   :   47 (;  47   !;   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_777,axiom,
    x != y,
    file(unknown,unknown) ).

tff(f_747,axiom,
    ! [X,Y] : subclass(singleton(X),unordered_pair(X,Y)),
    file(unknown,unknown) ).

tff(f_775,axiom,
    member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
    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_123,axiom,
    ! [X] : ( unordered_pair(X,X) = singleton(X) ),
    file(unknown,unknown) ).

tff(f_774,axiom,
    unordered_pair(x,z) = unordered_pair(y,z),
    file(unknown,unknown) ).

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

tff(f_142,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,Y) ),
    file(unknown,unknown) ).

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

tff(f_57,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file(unknown,unknown) ).

tff(c_234,plain,
    y != x,
    inference(cnfTransformation,[status(thm)],[f_777]) ).

tff(c_218,plain,
    ! [X_213,Y_214] : subclass(singleton(X_213),unordered_pair(X_213,Y_214)),
    inference(cnfTransformation,[status(thm)],[f_747]) ).

tff(c_232,plain,
    member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
    inference(cnfTransformation,[status(thm)],[f_775]) ).

tff(c_1875,plain,
    ! [U_375,X_376,V_377,Y_378] :
      ( member(U_375,X_376)
      | ~ member(ordered_pair(U_375,V_377),cross_product(X_376,Y_378)) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_1879,plain,
    member(x,universal_class),
    inference(resolution,[status(thm)],[c_232,c_1875]) ).

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

tff(c_230,plain,
    unordered_pair(y,z) = unordered_pair(x,z),
    inference(cnfTransformation,[status(thm)],[f_774]) ).

tff(c_538,plain,
    ! [X_282,Y_283] :
      ( member(X_282,unordered_pair(X_282,Y_283))
      | ~ member(X_282,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_547,plain,
    ( member(y,unordered_pair(x,z))
    | ~ member(y,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_230,c_538]) ).

tff(c_1424,plain,
    ~ member(y,universal_class),
    inference(splitLeft,[status(thm)],[c_547]) ).

tff(c_1712,plain,
    ! [V_367,Y_368,U_369,X_370] :
      ( member(V_367,Y_368)
      | ~ member(ordered_pair(U_369,V_367),cross_product(X_370,Y_368)) ),
    inference(cnfTransformation,[status(thm)],[f_142]) ).

tff(c_1715,plain,
    member(y,universal_class),
    inference(resolution,[status(thm)],[c_232,c_1712]) ).

tff(c_1719,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1424,c_1715]) ).

tff(c_1720,plain,
    member(y,unordered_pair(x,z)),
    inference(splitRight,[status(thm)],[c_547]) ).

tff(c_1753,plain,
    ! [Y_372,U_373,X_374] :
      ( ( Y_372 = U_373 )
      | ( X_374 = U_373 )
      | ~ member(U_373,unordered_pair(X_374,Y_372)) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_1756,plain,
    ( ( z = y )
    | ( y = x ) ),
    inference(resolution,[status(thm)],[c_1720,c_1753]) ).

tff(c_1807,plain,
    z = y,
    inference(negUnitSimplification,[status(thm)],[c_234,c_1756]) ).

tff(c_1820,plain,
    unordered_pair(y,y) = unordered_pair(x,y),
    inference(demodulation,[status(thm),theory(equality)],[c_1807,c_1807,c_230]) ).

tff(c_1822,plain,
    unordered_pair(x,y) = singleton(y),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_1820]) ).

tff(c_18,plain,
    ! [X_18,Y_19] :
      ( member(X_18,unordered_pair(X_18,Y_19))
      | ~ member(X_18,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_1853,plain,
    ( member(x,singleton(y))
    | ~ member(x,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_1822,c_18]) ).

tff(c_2049,plain,
    member(x,singleton(y)),
    inference(demodulation,[status(thm),theory(equality)],[c_1879,c_1853]) ).

tff(c_2,plain,
    ! [U_3,Y_2,X_1] :
      ( member(U_3,Y_2)
      | ~ member(U_3,X_1)
      | ~ subclass(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_2094,plain,
    ! [Y_390] :
      ( member(x,Y_390)
      | ~ subclass(singleton(y),Y_390) ),
    inference(resolution,[status(thm)],[c_2049,c_2]) ).

tff(c_2133,plain,
    ! [Y_391] : member(x,unordered_pair(y,Y_391)),
    inference(resolution,[status(thm)],[c_218,c_2094]) ).

tff(c_16,plain,
    ! [Y_17,U_15,X_16] :
      ( ( Y_17 = U_15 )
      | ( X_16 = U_15 )
      | ~ member(U_15,unordered_pair(X_16,Y_17)) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_2136,plain,
    ! [Y_391] :
      ( ( x = Y_391 )
      | ( y = x ) ),
    inference(resolution,[status(thm)],[c_2133,c_16]) ).

tff(c_2163,plain,
    ! [Y_392] : ( x = Y_392 ),
    inference(negUnitSimplification,[status(thm)],[c_234,c_2136]) ).

tff(c_2384,plain,
    y = x,
    inference(superposition,[status(thm),theory(equality)],[c_2163,c_1807]) ).

tff(c_2642,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_234,c_2384]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET072-7 : 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 : n005.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 16:38:41 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 6.50/2.48  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.50/2.49  
% 6.50/2.49  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.50/2.52  
% 6.50/2.52  Inference rules
% 6.50/2.52  ----------------------
% 6.50/2.52  #Ref     : 0
% 6.50/2.52  #Sup     : 652
% 6.50/2.52  #Fact    : 0
% 6.50/2.52  #Define  : 0
% 6.50/2.52  #Split   : 7
% 6.50/2.52  #Chain   : 0
% 6.50/2.52  #Close   : 0
% 6.50/2.52  
% 6.50/2.52  Ordering : KBO
% 6.50/2.52  
% 6.50/2.52  Simplification rules
% 6.50/2.52  ----------------------
% 6.50/2.52  #Subsume      : 61
% 6.50/2.52  #Demod        : 96
% 6.50/2.52  #Tautology    : 167
% 6.50/2.52  #SimpNegUnit  : 9
% 6.50/2.52  #BackRed      : 8
% 6.50/2.52  
% 6.50/2.52  #Partial instantiations: 960
% 6.50/2.52  #Strategies tried      : 1
% 6.50/2.52  
% 6.50/2.52  Timing (in seconds)
% 6.50/2.52  ----------------------
% 6.50/2.52  Preprocessing        : 0.68
% 6.50/2.52  Parsing              : 0.33
% 6.50/2.52  CNF conversion       : 0.05
% 6.50/2.52  Main loop            : 0.81
% 6.50/2.52  Inferencing          : 0.30
% 6.50/2.52  Reduction            : 0.25
% 6.50/2.52  Demodulation         : 0.18
% 6.50/2.52  BG Simplification    : 0.05
% 6.50/2.52  Subsumption          : 0.14
% 6.50/2.52  Abstraction          : 0.03
% 6.50/2.52  MUC search           : 0.00
% 6.50/2.52  Cooper               : 0.00
% 6.50/2.52  Total                : 1.53
% 6.50/2.52  Index Insertion      : 0.00
% 6.50/2.52  Index Deletion       : 0.00
% 6.50/2.52  Index Matching       : 0.00
% 6.50/2.52  BG Taut test         : 0.00
%------------------------------------------------------------------------------