TSTP Solution File: SET230-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET230-6 : 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 : n032.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 10:56:13 EDT 2023

% Result   : Unsatisfiable 26.63s 14.44s
% Output   : CNFRefutation 26.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   74
% Syntax   : Number of formulae    :  182 (  48 unt;  58 typ;   0 def)
%            Number of atoms       :  224 (  40 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  210 ( 110   ~; 100   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 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    :   48 (  48 usr;  14 con; 0-3 aty)
%            Number of variables   :  151 (; 151   !;   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 > w > 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(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(w,type,
    w: $i ).

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(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(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_70,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_479,axiom,
    ! [X] :
      ( ( X = null_class )
      | member(regular(X),X) ),
    file(unknown,unknown) ).

tff(f_194,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    file(unknown,unknown) ).

tff(f_80,axiom,
    ! [X] : subclass(X,universal_class),
    file(unknown,unknown) ).

tff(f_66,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file(unknown,unknown) ).

tff(f_216,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,X) ),
    file(unknown,unknown) ).

tff(f_200,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    file(unknown,unknown) ).

tff(f_75,axiom,
    ! [X,Y] :
      ( ~ member(not_subclass_element(X,Y),Y)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_780,axiom,
    u != w,
    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_778,axiom,
    cross_product(u,u) = cross_product(w,w),
    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_151,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(V,Y) ),
    file(unknown,unknown) ).

tff(f_100,axiom,
    ! [X,Y] :
      ( ~ subclass(X,Y)
      | ~ subclass(Y,X)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_523,axiom,
    intersection(inverse(subset_relation),subset_relation) = identity_relation,
    file(unknown,unknown) ).

tff(f_483,axiom,
    ! [X] :
      ( ( X = null_class )
      | ( intersection(X,regular(X)) = null_class ) ),
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [X_4,Y_5] :
      ( subclass(X_4,Y_5)
      | member(not_subclass_element(X_4,Y_5),X_4) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_132,plain,
    ! [X_131] :
      ( member(regular(X_131),X_131)
      | ( null_class = X_131 ) ),
    inference(cnfTransformation,[status(thm)],[f_479]) ).

tff(c_414,plain,
    ! [Z_273,X_274,Y_275] :
      ( member(Z_273,X_274)
      | ~ member(Z_273,intersection(X_274,Y_275)) ),
    inference(cnfTransformation,[status(thm)],[f_194]) ).

tff(c_30421,plain,
    ! [X_1497,Y_1498] :
      ( member(regular(intersection(X_1497,Y_1498)),X_1497)
      | ( intersection(X_1497,Y_1498) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_414]) ).

tff(c_8,plain,
    ! [X_8] : subclass(X_8,universal_class),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_758,plain,
    ! [U_320,Y_321,X_322] :
      ( member(U_320,Y_321)
      | ~ member(U_320,X_322)
      | ~ subclass(X_322,Y_321) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_799,plain,
    ! [X_131,Y_321] :
      ( member(regular(X_131),Y_321)
      | ~ subclass(X_131,Y_321)
      | ( null_class = X_131 ) ),
    inference(resolution,[status(thm)],[c_132,c_758]) ).

tff(c_1446,plain,
    ! [X_382,Y_383] :
      ( member(regular(X_382),Y_383)
      | ~ subclass(X_382,Y_383)
      | ( null_class = X_382 ) ),
    inference(resolution,[status(thm)],[c_132,c_758]) ).

tff(c_340,plain,
    ! [Z_256,X_257] :
      ( ~ member(Z_256,X_257)
      | ~ member(Z_256,complement(X_257)) ),
    inference(cnfTransformation,[status(thm)],[f_216]) ).

tff(c_355,plain,
    ! [X_257] :
      ( ~ member(regular(complement(X_257)),X_257)
      | ( complement(X_257) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_340]) ).

tff(c_1501,plain,
    ! [Y_384] :
      ( ~ subclass(complement(Y_384),Y_384)
      | ( complement(Y_384) = null_class ) ),
    inference(resolution,[status(thm)],[c_1446,c_355]) ).

tff(c_1523,plain,
    complement(universal_class) = null_class,
    inference(resolution,[status(thm)],[c_8,c_1501]) ).

tff(c_48,plain,
    ! [Z_55,X_56] :
      ( ~ member(Z_55,X_56)
      | ~ member(Z_55,complement(X_56)) ),
    inference(cnfTransformation,[status(thm)],[f_216]) ).

tff(c_1580,plain,
    ! [Z_386] :
      ( ~ member(Z_386,universal_class)
      | ~ member(Z_386,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_1523,c_48]) ).

tff(c_1584,plain,
    ! [X_131] :
      ( ~ member(regular(X_131),null_class)
      | ~ subclass(X_131,universal_class)
      | ( null_class = X_131 ) ),
    inference(resolution,[status(thm)],[c_799,c_1580]) ).

tff(c_1628,plain,
    ! [X_131] :
      ( ~ member(regular(X_131),null_class)
      | ( null_class = X_131 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_1584]) ).

tff(c_30538,plain,
    ! [Y_1499] : ( intersection(null_class,Y_1499) = null_class ),
    inference(resolution,[status(thm)],[c_30421,c_1628]) ).

tff(c_44,plain,
    ! [Z_49,Y_51,X_50] :
      ( member(Z_49,Y_51)
      | ~ member(Z_49,intersection(X_50,Y_51)) ),
    inference(cnfTransformation,[status(thm)],[f_200]) ).

tff(c_30825,plain,
    ! [Z_1506,Y_1507] :
      ( member(Z_1506,Y_1507)
      | ~ member(Z_1506,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_30538,c_44]) ).

tff(c_41062,plain,
    ! [Y_1872,Y_1873] :
      ( member(not_subclass_element(null_class,Y_1872),Y_1873)
      | subclass(null_class,Y_1872) ),
    inference(resolution,[status(thm)],[c_4,c_30825]) ).

tff(c_6,plain,
    ! [X_6,Y_7] :
      ( subclass(X_6,Y_7)
      | ~ member(not_subclass_element(X_6,Y_7),Y_7) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_41157,plain,
    ! [Y_1873] : subclass(null_class,Y_1873),
    inference(resolution,[status(thm)],[c_41062,c_6]) ).

tff(c_228,plain,
    w != u,
    inference(cnfTransformation,[status(thm)],[f_780]) ).

tff(c_32,plain,
    ! [U_35,V_37,X_36,Y_38] :
      ( member(ordered_pair(U_35,V_37),cross_product(X_36,Y_38))
      | ~ member(V_37,Y_38)
      | ~ member(U_35,X_36) ),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_226,plain,
    cross_product(w,w) = cross_product(u,u),
    inference(cnfTransformation,[status(thm)],[f_778]) ).

tff(c_1647,plain,
    ! [U_387,X_388,V_389,Y_390] :
      ( member(U_387,X_388)
      | ~ member(ordered_pair(U_387,V_389),cross_product(X_388,Y_390)) ),
    inference(cnfTransformation,[status(thm)],[f_145]) ).

tff(c_3755,plain,
    ! [U_604,V_605] :
      ( member(U_604,w)
      | ~ member(ordered_pair(U_604,V_605),cross_product(u,u)) ),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_1647]) ).

tff(c_3764,plain,
    ! [U_35,V_37] :
      ( member(U_35,w)
      | ~ member(V_37,u)
      | ~ member(U_35,u) ),
    inference(resolution,[status(thm)],[c_32,c_3755]) ).

tff(c_3772,plain,
    ! [V_607] : ~ member(V_607,u),
    inference(splitLeft,[status(thm)],[c_3764]) ).

tff(c_3811,plain,
    u = null_class,
    inference(resolution,[status(thm)],[c_132,c_3772]) ).

tff(c_3818,plain,
    w != null_class,
    inference(demodulation,[status(thm),theory(equality)],[c_3811,c_228]) ).

tff(c_3771,plain,
    ! [V_37] : ~ member(V_37,u),
    inference(splitLeft,[status(thm)],[c_3764]) ).

tff(c_3813,plain,
    ! [V_37] : ~ member(V_37,null_class),
    inference(demodulation,[status(thm),theory(equality)],[c_3811,c_3771]) ).

tff(c_2597,plain,
    ! [U_479,V_480,X_481,Y_482] :
      ( member(ordered_pair(U_479,V_480),cross_product(X_481,Y_482))
      | ~ member(V_480,Y_482)
      | ~ member(U_479,X_481) ),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_2613,plain,
    ! [U_479,V_480] :
      ( member(ordered_pair(U_479,V_480),cross_product(u,u))
      | ~ member(V_480,w)
      | ~ member(U_479,w) ),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_2597]) ).

tff(c_30119,plain,
    ! [U_1493,V_1494] :
      ( member(ordered_pair(U_1493,V_1494),cross_product(null_class,null_class))
      | ~ member(V_1494,w)
      | ~ member(U_1493,w) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3811,c_3811,c_2613]) ).

tff(c_30,plain,
    ! [V_32,Y_34,U_31,X_33] :
      ( member(V_32,Y_34)
      | ~ member(ordered_pair(U_31,V_32),cross_product(X_33,Y_34)) ),
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_30132,plain,
    ! [V_1494,U_1493] :
      ( member(V_1494,null_class)
      | ~ member(V_1494,w)
      | ~ member(U_1493,w) ),
    inference(resolution,[status(thm)],[c_30119,c_30]) ).

tff(c_30159,plain,
    ! [V_1494,U_1493] :
      ( ~ member(V_1494,w)
      | ~ member(U_1493,w) ),
    inference(negUnitSimplification,[status(thm)],[c_3813,c_30132]) ).

tff(c_30167,plain,
    ! [U_1495] : ~ member(U_1495,w),
    inference(splitLeft,[status(thm)],[c_30159]) ).

tff(c_30259,plain,
    w = null_class,
    inference(resolution,[status(thm)],[c_132,c_30167]) ).

tff(c_30291,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3818,c_30259]) ).

tff(c_30295,plain,
    ! [V_1496] : ~ member(V_1496,w),
    inference(splitRight,[status(thm)],[c_30159]) ).

tff(c_30387,plain,
    w = null_class,
    inference(resolution,[status(thm)],[c_132,c_30295]) ).

tff(c_30419,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3818,c_30387]) ).

tff(c_30798,plain,
    ! [U_1505] :
      ( member(U_1505,w)
      | ~ member(U_1505,u) ),
    inference(splitRight,[status(thm)],[c_3764]) ).

tff(c_30989,plain,
    ! [X_1511] :
      ( subclass(X_1511,w)
      | ~ member(not_subclass_element(X_1511,w),u) ),
    inference(resolution,[status(thm)],[c_30798,c_6]) ).

tff(c_30994,plain,
    subclass(u,w),
    inference(resolution,[status(thm)],[c_4,c_30989]) ).

tff(c_14,plain,
    ! [Y_14,X_13] :
      ( ( Y_14 = X_13 )
      | ~ subclass(Y_14,X_13)
      | ~ subclass(X_13,Y_14) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_30999,plain,
    ( ( w = u )
    | ~ subclass(w,u) ),
    inference(resolution,[status(thm)],[c_30994,c_14]) ).

tff(c_31003,plain,
    ~ subclass(w,u),
    inference(negUnitSimplification,[status(thm)],[c_228,c_30999]) ).

tff(c_67444,plain,
    ! [U_2576,V_2577] :
      ( member(ordered_pair(U_2576,V_2577),cross_product(u,u))
      | ~ member(V_2577,w)
      | ~ member(U_2576,w) ),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_2597]) ).

tff(c_67485,plain,
    ! [V_2577,U_2576] :
      ( member(V_2577,u)
      | ~ member(V_2577,w)
      | ~ member(U_2576,w) ),
    inference(resolution,[status(thm)],[c_67444,c_30]) ).

tff(c_67493,plain,
    ! [U_2578] : ~ member(U_2578,w),
    inference(splitLeft,[status(thm)],[c_67485]) ).

tff(c_67637,plain,
    w = null_class,
    inference(resolution,[status(thm)],[c_132,c_67493]) ).

tff(c_53997,plain,
    ! [U_2266,V_2267] :
      ( member(ordered_pair(U_2266,V_2267),cross_product(u,u))
      | ~ member(V_2267,w)
      | ~ member(U_2266,w) ),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_2597]) ).

tff(c_54032,plain,
    ! [V_2267,U_2266] :
      ( member(V_2267,u)
      | ~ member(V_2267,w)
      | ~ member(U_2266,w) ),
    inference(resolution,[status(thm)],[c_53997,c_30]) ).

tff(c_54040,plain,
    ! [U_2268] : ~ member(U_2268,w),
    inference(splitLeft,[status(thm)],[c_54032]) ).

tff(c_54164,plain,
    w = null_class,
    inference(resolution,[status(thm)],[c_132,c_54040]) ).

tff(c_44815,plain,
    ! [X_2002,Y_2003,Y_2004] :
      ( member(not_subclass_element(X_2002,Y_2003),Y_2004)
      | ~ subclass(X_2002,Y_2004)
      | subclass(X_2002,Y_2003) ),
    inference(resolution,[status(thm)],[c_4,c_758]) ).

tff(c_150,plain,
    intersection(inverse(subset_relation),subset_relation) = identity_relation,
    inference(cnfTransformation,[status(thm)],[f_523]) ).

tff(c_572,plain,
    ! [Z_298,Y_299,X_300] :
      ( member(Z_298,Y_299)
      | ~ member(Z_298,intersection(X_300,Y_299)) ),
    inference(cnfTransformation,[status(thm)],[f_200]) ).

tff(c_594,plain,
    ! [Z_301] :
      ( member(Z_301,subset_relation)
      | ~ member(Z_301,identity_relation) ),
    inference(superposition,[status(thm),theory(equality)],[c_150,c_572]) ).

tff(c_599,plain,
    ! [X_6] :
      ( subclass(X_6,subset_relation)
      | ~ member(not_subclass_element(X_6,subset_relation),identity_relation) ),
    inference(resolution,[status(thm)],[c_594,c_6]) ).

tff(c_44992,plain,
    ! [X_2005] :
      ( ~ subclass(X_2005,identity_relation)
      | subclass(X_2005,subset_relation) ),
    inference(resolution,[status(thm)],[c_44815,c_599]) ).

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_66]) ).

tff(c_30821,plain,
    ! [U_1505,Y_2] :
      ( member(U_1505,Y_2)
      | ~ subclass(w,Y_2)
      | ~ member(U_1505,u) ),
    inference(resolution,[status(thm)],[c_30798,c_2]) ).

tff(c_45051,plain,
    ! [U_1505] :
      ( member(U_1505,subset_relation)
      | ~ member(U_1505,u)
      | ~ subclass(w,identity_relation) ),
    inference(resolution,[status(thm)],[c_44992,c_30821]) ).

tff(c_46391,plain,
    ~ subclass(w,identity_relation),
    inference(splitLeft,[status(thm)],[c_45051]) ).

tff(c_54174,plain,
    ~ subclass(null_class,identity_relation),
    inference(demodulation,[status(thm),theory(equality)],[c_54164,c_46391]) ).

tff(c_54193,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_41157,c_54174]) ).

tff(c_54355,plain,
    ! [V_2270] :
      ( member(V_2270,u)
      | ~ member(V_2270,w) ),
    inference(splitRight,[status(thm)],[c_54032]) ).

tff(c_54613,plain,
    ! [Y_2272] :
      ( member(not_subclass_element(w,Y_2272),u)
      | subclass(w,Y_2272) ),
    inference(resolution,[status(thm)],[c_4,c_54355]) ).

tff(c_54623,plain,
    subclass(w,u),
    inference(resolution,[status(thm)],[c_54613,c_6]) ).

tff(c_54630,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_31003,c_31003,c_54623]) ).

tff(c_54658,plain,
    ! [U_2274] :
      ( member(U_2274,subset_relation)
      | ~ member(U_2274,u) ),
    inference(splitRight,[status(thm)],[c_45051]) ).

tff(c_54750,plain,
    ( member(regular(u),subset_relation)
    | ( u = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_54658]) ).

tff(c_54753,plain,
    u = null_class,
    inference(splitLeft,[status(thm)],[c_54750]) ).

tff(c_42339,plain,
    ! [U_1915,Y_1916] :
      ( member(U_1915,Y_1916)
      | ~ subclass(w,Y_1916)
      | ~ member(U_1915,u) ),
    inference(resolution,[status(thm)],[c_30798,c_2]) ).

tff(c_42353,plain,
    ! [U_1918] :
      ( member(U_1918,universal_class)
      | ~ member(U_1918,u) ),
    inference(resolution,[status(thm)],[c_8,c_42339]) ).

tff(c_1566,plain,
    ! [Z_55] :
      ( ~ member(Z_55,universal_class)
      | ~ member(Z_55,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_1523,c_48]) ).

tff(c_42394,plain,
    ! [U_1919] :
      ( ~ member(U_1919,null_class)
      | ~ member(U_1919,u) ),
    inference(resolution,[status(thm)],[c_42353,c_1566]) ).

tff(c_42467,plain,
    ! [Y_5] :
      ( ~ member(not_subclass_element(u,Y_5),null_class)
      | subclass(u,Y_5) ),
    inference(resolution,[status(thm)],[c_4,c_42394]) ).

tff(c_44964,plain,
    ! [Y_2003] :
      ( ~ subclass(u,null_class)
      | subclass(u,Y_2003) ),
    inference(resolution,[status(thm)],[c_44815,c_42467]) ).

tff(c_45193,plain,
    ~ subclass(u,null_class),
    inference(splitLeft,[status(thm)],[c_44964]) ).

tff(c_54762,plain,
    ~ subclass(null_class,null_class),
    inference(demodulation,[status(thm),theory(equality)],[c_54753,c_45193]) ).

tff(c_54783,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_41157,c_54762]) ).

tff(c_54785,plain,
    u != null_class,
    inference(splitRight,[status(thm)],[c_54750]) ).

tff(c_134,plain,
    ! [X_132] :
      ( ( intersection(X_132,regular(X_132)) = null_class )
      | ( null_class = X_132 ) ),
    inference(cnfTransformation,[status(thm)],[f_483]) ).

tff(c_56204,plain,
    ! [X_2305,Y_2306,Y_2307] :
      ( member(not_subclass_element(intersection(X_2305,Y_2306),Y_2307),X_2305)
      | subclass(intersection(X_2305,Y_2306),Y_2307) ),
    inference(resolution,[status(thm)],[c_4,c_414]) ).

tff(c_30823,plain,
    ! [X_6] :
      ( subclass(X_6,w)
      | ~ member(not_subclass_element(X_6,w),u) ),
    inference(resolution,[status(thm)],[c_30798,c_6]) ).

tff(c_56569,plain,
    ! [Y_2314] : subclass(intersection(u,Y_2314),w),
    inference(resolution,[status(thm)],[c_56204,c_30823]) ).

tff(c_58617,plain,
    ! [Y_2386] :
      ( ( intersection(u,Y_2386) = w )
      | ~ subclass(w,intersection(u,Y_2386)) ),
    inference(resolution,[status(thm)],[c_56569,c_14]) ).

tff(c_58629,plain,
    ( ( intersection(u,regular(u)) = w )
    | ~ subclass(w,null_class)
    | ( u = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_134,c_58617]) ).

tff(c_58632,plain,
    ( ( intersection(u,regular(u)) = w )
    | ~ subclass(w,null_class) ),
    inference(negUnitSimplification,[status(thm)],[c_54785,c_58629]) ).

tff(c_58633,plain,
    ~ subclass(w,null_class),
    inference(splitLeft,[status(thm)],[c_58632]) ).

tff(c_67642,plain,
    ~ subclass(null_class,null_class),
    inference(demodulation,[status(thm),theory(equality)],[c_67637,c_58633]) ).

tff(c_67666,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_41157,c_67642]) ).

tff(c_67848,plain,
    ! [V_2580] :
      ( member(V_2580,u)
      | ~ member(V_2580,w) ),
    inference(splitRight,[status(thm)],[c_67485]) ).

tff(c_68042,plain,
    ! [Y_2582] :
      ( member(not_subclass_element(w,Y_2582),u)
      | subclass(w,Y_2582) ),
    inference(resolution,[status(thm)],[c_4,c_67848]) ).

tff(c_68058,plain,
    subclass(w,u),
    inference(resolution,[status(thm)],[c_68042,c_6]) ).

tff(c_68067,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_31003,c_31003,c_68058]) ).

tff(c_68069,plain,
    subclass(w,null_class),
    inference(splitRight,[status(thm)],[c_58632]) ).

tff(c_1824,plain,
    ! [X_412] :
      ( ~ member(regular(X_412),null_class)
      | ( null_class = X_412 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_1584]) ).

tff(c_1836,plain,
    ! [X_131] :
      ( ~ subclass(X_131,null_class)
      | ( null_class = X_131 ) ),
    inference(resolution,[status(thm)],[c_799,c_1824]) ).

tff(c_68091,plain,
    w = null_class,
    inference(resolution,[status(thm)],[c_68069,c_1836]) ).

tff(c_68113,plain,
    ~ subclass(null_class,u),
    inference(demodulation,[status(thm),theory(equality)],[c_68091,c_31003]) ).

tff(c_68133,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_41157,c_68113]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET230-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12  % 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
% 0.11/0.32  % Computer : n032.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu Aug  3 16:15:36 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 26.63/14.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.63/14.46  
% 26.63/14.46  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.63/14.50  
% 26.63/14.50  Inference rules
% 26.63/14.50  ----------------------
% 26.63/14.50  #Ref     : 2
% 26.63/14.50  #Sup     : 17063
% 26.63/14.50  #Fact    : 0
% 26.63/14.50  #Define  : 0
% 26.63/14.50  #Split   : 330
% 26.63/14.50  #Chain   : 0
% 26.63/14.50  #Close   : 0
% 26.63/14.50  
% 26.63/14.50  Ordering : KBO
% 26.63/14.50  
% 26.63/14.50  Simplification rules
% 26.63/14.50  ----------------------
% 26.63/14.50  #Subsume      : 4050
% 26.63/14.50  #Demod        : 5348
% 26.63/14.50  #Tautology    : 2237
% 26.63/14.50  #SimpNegUnit  : 470
% 26.63/14.50  #BackRed      : 809
% 26.63/14.50  
% 26.63/14.50  #Partial instantiations: 0
% 26.63/14.50  #Strategies tried      : 1
% 26.63/14.50  
% 26.63/14.50  Timing (in seconds)
% 26.63/14.50  ----------------------
% 26.63/14.51  Preprocessing        : 0.74
% 26.63/14.51  Parsing              : 0.39
% 26.63/14.51  CNF conversion       : 0.05
% 26.63/14.51  Main loop            : 12.81
% 26.63/14.51  Inferencing          : 2.75
% 26.63/14.51  Reduction            : 5.39
% 26.63/14.51  Demodulation         : 3.66
% 26.63/14.51  BG Simplification    : 0.14
% 26.63/14.51  Subsumption          : 3.63
% 26.63/14.51  Abstraction          : 0.17
% 26.63/14.51  MUC search           : 0.00
% 26.63/14.51  Cooper               : 0.00
% 26.63/14.51  Total                : 13.62
% 26.63/14.51  Index Insertion      : 0.00
% 26.63/14.51  Index Deletion       : 0.00
% 26.63/14.51  Index Matching       : 0.00
% 26.63/14.51  BG Taut test         : 0.00
%------------------------------------------------------------------------------