TSTP Solution File: SET154-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET154-6 : 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 : n010.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 10:56:06 EDT 2023

% Result   : Unsatisfiable 110.86s 91.01s
% Output   : CNFRefutation 110.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   72
% Syntax   : Number of formulae    :  155 (  39 unt;  57 typ;   0 def)
%            Number of atoms       :  172 (  51 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  146 (  72   ~;  74   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    5 (   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    :   47 (  47 usr;  13 con; 0-3 aty)
%            Number of variables   :  133 (; 133   !;   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 > 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(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(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_81,axiom,
    ! [X] : subclass(X,universal_class),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file(unknown,unknown) ).

tff(f_240,axiom,
    ! [X,Y,Xr] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
    file(unknown,unknown) ).

tff(f_480,axiom,
    ! [X] :
      ( ( X = null_class )
      | member(regular(X),X) ),
    file(unknown,unknown) ).

tff(f_201,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    file(unknown,unknown) ).

tff(f_217,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,X) ),
    file(unknown,unknown) ).

tff(f_224,axiom,
    ! [Z,X] :
      ( ~ member(Z,universal_class)
      | member(Z,complement(X))
      | member(Z,X) ),
    file(unknown,unknown) ).

tff(f_76,axiom,
    ! [X,Y] :
      ( ~ member(not_subclass_element(X,Y),Y)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_195,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    file(unknown,unknown) ).

tff(f_251,axiom,
    ! [X,Z] :
      ( ( restrict(X,singleton(Z),universal_class) != null_class )
      | ~ member(Z,domain_of(X)) ),
    file(unknown,unknown) ).

tff(f_528,axiom,
    ! [Xr] : ( complement(domain_of(intersection(Xr,identity_relation))) = diagonalise(Xr) ),
    file(unknown,unknown) ).

tff(f_101,axiom,
    ! [X,Y] :
      ( ~ subclass(X,Y)
      | ~ subclass(Y,X)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_229,axiom,
    ! [X,Y] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
    file(unknown,unknown) ).

tff(f_780,axiom,
    union(complement(x),x) != universal_class,
    file(unknown,unknown) ).

tff(c_8,plain,
    ! [X_8] : subclass(X_8,universal_class),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

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_71]) ).

tff(c_787,plain,
    ! [U_321,Y_322,X_323] :
      ( member(U_321,Y_322)
      | ~ member(U_321,X_323)
      | ~ subclass(X_323,Y_322) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_824,plain,
    ! [X_4,Y_5,Y_322] :
      ( member(not_subclass_element(X_4,Y_5),Y_322)
      | ~ subclass(X_4,Y_322)
      | subclass(X_4,Y_5) ),
    inference(resolution,[status(thm)],[c_4,c_787]) ).

tff(c_58,plain,
    ! [X_66,Y_67,Xr_68] : ( intersection(cross_product(X_66,Y_67),Xr_68) = restrict(Xr_68,X_66,Y_67) ),
    inference(cnfTransformation,[status(thm)],[f_240]) ).

tff(c_132,plain,
    ! [X_131] :
      ( member(regular(X_131),X_131)
      | ( null_class = X_131 ) ),
    inference(cnfTransformation,[status(thm)],[f_480]) ).

tff(c_566,plain,
    ! [Z_292,Y_293,X_294] :
      ( member(Z_292,Y_293)
      | ~ member(Z_292,intersection(X_294,Y_293)) ),
    inference(cnfTransformation,[status(thm)],[f_201]) ).

tff(c_67889,plain,
    ! [X_2517,Y_2518] :
      ( member(regular(intersection(X_2517,Y_2518)),Y_2518)
      | ( intersection(X_2517,Y_2518) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_566]) ).

tff(c_828,plain,
    ! [X_131,Y_322] :
      ( member(regular(X_131),Y_322)
      | ~ subclass(X_131,Y_322)
      | ( null_class = X_131 ) ),
    inference(resolution,[status(thm)],[c_132,c_787]) ).

tff(c_1378,plain,
    ! [X_387,Y_388] :
      ( member(regular(X_387),Y_388)
      | ~ subclass(X_387,Y_388)
      | ( null_class = X_387 ) ),
    inference(resolution,[status(thm)],[c_132,c_787]) ).

tff(c_344,plain,
    ! [Z_257,X_258] :
      ( ~ member(Z_257,X_258)
      | ~ member(Z_257,complement(X_258)) ),
    inference(cnfTransformation,[status(thm)],[f_217]) ).

tff(c_359,plain,
    ! [X_258] :
      ( ~ member(regular(complement(X_258)),X_258)
      | ( complement(X_258) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_344]) ).

tff(c_1433,plain,
    ! [Y_389] :
      ( ~ subclass(complement(Y_389),Y_389)
      | ( complement(Y_389) = null_class ) ),
    inference(resolution,[status(thm)],[c_1378,c_359]) ).

tff(c_1455,plain,
    complement(universal_class) = null_class,
    inference(resolution,[status(thm)],[c_8,c_1433]) ).

tff(c_48,plain,
    ! [Z_55,X_56] :
      ( ~ member(Z_55,X_56)
      | ~ member(Z_55,complement(X_56)) ),
    inference(cnfTransformation,[status(thm)],[f_217]) ).

tff(c_1492,plain,
    ! [Z_390] :
      ( ~ member(Z_390,universal_class)
      | ~ member(Z_390,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_1455,c_48]) ).

tff(c_1496,plain,
    ! [X_131] :
      ( ~ member(regular(X_131),null_class)
      | ~ subclass(X_131,universal_class)
      | ( null_class = X_131 ) ),
    inference(resolution,[status(thm)],[c_828,c_1492]) ).

tff(c_1544,plain,
    ! [X_131] :
      ( ~ member(regular(X_131),null_class)
      | ( null_class = X_131 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_1496]) ).

tff(c_68008,plain,
    ! [X_2519] : ( intersection(X_2519,null_class) = null_class ),
    inference(resolution,[status(thm)],[c_67889,c_1544]) ).

tff(c_68045,plain,
    ! [X_66,Y_67] : ( restrict(null_class,X_66,Y_67) = null_class ),
    inference(superposition,[status(thm),theory(equality)],[c_58,c_68008]) ).

tff(c_1566,plain,
    ! [Z_391,X_392] :
      ( member(Z_391,X_392)
      | member(Z_391,complement(X_392))
      | ~ member(Z_391,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_224]) ).

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_76]) ).

tff(c_237271,plain,
    ! [X_6519,X_6520] :
      ( subclass(X_6519,complement(X_6520))
      | member(not_subclass_element(X_6519,complement(X_6520)),X_6520)
      | ~ member(not_subclass_element(X_6519,complement(X_6520)),universal_class) ),
    inference(resolution,[status(thm)],[c_1566,c_6]) ).

tff(c_237288,plain,
    ! [X_4,X_6520] :
      ( member(not_subclass_element(X_4,complement(X_6520)),X_6520)
      | ~ subclass(X_4,universal_class)
      | subclass(X_4,complement(X_6520)) ),
    inference(resolution,[status(thm)],[c_824,c_237271]) ).

tff(c_237338,plain,
    ! [X_6521,X_6522] :
      ( member(not_subclass_element(X_6521,complement(X_6522)),X_6522)
      | subclass(X_6521,complement(X_6522)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_237288]) ).

tff(c_42,plain,
    ! [Z_46,X_47,Y_48] :
      ( member(Z_46,X_47)
      | ~ member(Z_46,intersection(X_47,Y_48)) ),
    inference(cnfTransformation,[status(thm)],[f_195]) ).

tff(c_205215,plain,
    ! [Z_5566,X_5567] :
      ( member(Z_5566,X_5567)
      | ~ member(Z_5566,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_68008,c_42]) ).

tff(c_210862,plain,
    ! [Y_5748,X_5749] :
      ( member(not_subclass_element(null_class,Y_5748),X_5749)
      | subclass(null_class,Y_5748) ),
    inference(resolution,[status(thm)],[c_4,c_205215]) ).

tff(c_543,plain,
    ! [X_288,Y_289] :
      ( subclass(X_288,Y_289)
      | member(not_subclass_element(X_288,Y_289),X_288) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_210770,plain,
    ! [X_5743,Y_5744] :
      ( ~ member(not_subclass_element(complement(X_5743),Y_5744),X_5743)
      | subclass(complement(X_5743),Y_5744) ),
    inference(resolution,[status(thm)],[c_543,c_48]) ).

tff(c_210812,plain,
    ! [Y_5744] :
      ( ~ member(not_subclass_element(null_class,Y_5744),universal_class)
      | subclass(complement(universal_class),Y_5744) ),
    inference(superposition,[status(thm),theory(equality)],[c_1455,c_210770]) ).

tff(c_210842,plain,
    ! [Y_5744] :
      ( ~ member(not_subclass_element(null_class,Y_5744),universal_class)
      | subclass(null_class,Y_5744) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1455,c_210812]) ).

tff(c_210955,plain,
    ! [Y_5748] : subclass(null_class,Y_5748),
    inference(resolution,[status(thm)],[c_210862,c_210842]) ).

tff(c_1665,plain,
    ! [Z_400,X_401] :
      ( ~ member(Z_400,domain_of(X_401))
      | ( restrict(X_401,singleton(Z_400),universal_class) != null_class ) ),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_215217,plain,
    ! [X_5889] :
      ( ( restrict(X_5889,singleton(regular(domain_of(X_5889))),universal_class) != null_class )
      | ( domain_of(X_5889) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_1665]) ).

tff(c_215231,plain,
    domain_of(null_class) = null_class,
    inference(superposition,[status(thm),theory(equality)],[c_68045,c_215217]) ).

tff(c_500,plain,
    ! [Z_278,X_279,Y_280] :
      ( member(Z_278,X_279)
      | ~ member(Z_278,intersection(X_279,Y_280)) ),
    inference(cnfTransformation,[status(thm)],[f_195]) ).

tff(c_205492,plain,
    ! [X_5575,Y_5576] :
      ( member(regular(intersection(X_5575,Y_5576)),X_5575)
      | ( intersection(X_5575,Y_5576) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_500]) ).

tff(c_205595,plain,
    ! [Y_5576] : ( intersection(null_class,Y_5576) = null_class ),
    inference(resolution,[status(thm)],[c_205492,c_1544]) ).

tff(c_152,plain,
    ! [Xr_139] : ( complement(domain_of(intersection(Xr_139,identity_relation))) = diagonalise(Xr_139) ),
    inference(cnfTransformation,[status(thm)],[f_528]) ).

tff(c_210337,plain,
    ! [Z_5725,Xr_5726] :
      ( ~ member(Z_5725,domain_of(intersection(Xr_5726,identity_relation)))
      | ~ member(Z_5725,diagonalise(Xr_5726)) ),
    inference(superposition,[status(thm),theory(equality)],[c_152,c_344]) ).

tff(c_210462,plain,
    ! [Z_5728] :
      ( ~ member(Z_5728,domain_of(null_class))
      | ~ member(Z_5728,diagonalise(null_class)) ),
    inference(superposition,[status(thm),theory(equality)],[c_205595,c_210337]) ).

tff(c_210547,plain,
    ( ~ member(regular(domain_of(null_class)),diagonalise(null_class))
    | ( domain_of(null_class) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_210462]) ).

tff(c_212612,plain,
    ~ member(regular(domain_of(null_class)),diagonalise(null_class)),
    inference(splitLeft,[status(thm)],[c_210547]) ).

tff(c_212616,plain,
    ( ~ subclass(domain_of(null_class),diagonalise(null_class))
    | ( domain_of(null_class) = null_class ) ),
    inference(resolution,[status(thm)],[c_828,c_212612]) ).

tff(c_212617,plain,
    ~ subclass(domain_of(null_class),diagonalise(null_class)),
    inference(splitLeft,[status(thm)],[c_212616]) ).

tff(c_215236,plain,
    ~ subclass(null_class,diagonalise(null_class)),
    inference(demodulation,[status(thm),theory(equality)],[c_215231,c_212617]) ).

tff(c_215249,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_210955,c_215236]) ).

tff(c_215250,plain,
    domain_of(null_class) = null_class,
    inference(splitRight,[status(thm)],[c_212616]) ).

tff(c_60,plain,
    ! [Z_70,X_69] :
      ( ~ member(Z_70,domain_of(X_69))
      | ( restrict(X_69,singleton(Z_70),universal_class) != null_class ) ),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_215323,plain,
    ! [Z_70] :
      ( ~ member(Z_70,null_class)
      | ( restrict(null_class,singleton(Z_70),universal_class) != null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_215250,c_60]) ).

tff(c_215349,plain,
    ! [Z_70] : ~ member(Z_70,null_class),
    inference(demodulation,[status(thm),theory(equality)],[c_68045,c_215323]) ).

tff(c_237573,plain,
    ! [X_6523] : subclass(X_6523,complement(null_class)),
    inference(resolution,[status(thm)],[c_237338,c_215349]) ).

tff(c_368,plain,
    ! [Y_260,X_261] :
      ( ( Y_260 = X_261 )
      | ~ subclass(Y_260,X_261)
      | ~ subclass(X_261,Y_260) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_403,plain,
    ! [X_8] :
      ( ( universal_class = X_8 )
      | ~ subclass(universal_class,X_8) ),
    inference(resolution,[status(thm)],[c_8,c_368]) ).

tff(c_237845,plain,
    complement(null_class) = universal_class,
    inference(resolution,[status(thm)],[c_237573,c_403]) ).

tff(c_589,plain,
    ! [X_294,Y_293] :
      ( member(regular(intersection(X_294,Y_293)),Y_293)
      | ( intersection(X_294,Y_293) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_566]) ).

tff(c_290422,plain,
    ! [X_7331,Y_7332] :
      ( ~ member(regular(intersection(complement(X_7331),Y_7332)),X_7331)
      | ( intersection(complement(X_7331),Y_7332) = null_class ) ),
    inference(resolution,[status(thm)],[c_205492,c_48]) ).

tff(c_290763,plain,
    ! [Y_7333] : ( intersection(complement(Y_7333),Y_7333) = null_class ),
    inference(resolution,[status(thm)],[c_589,c_290422]) ).

tff(c_52,plain,
    ! [X_59,Y_60] : ( complement(intersection(complement(X_59),complement(Y_60))) = union(X_59,Y_60) ),
    inference(cnfTransformation,[status(thm)],[f_229]) ).

tff(c_291276,plain,
    ! [Y_60] : ( union(complement(Y_60),Y_60) = complement(null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_290763,c_52]) ).

tff(c_291501,plain,
    ! [Y_60] : ( union(complement(Y_60),Y_60) = universal_class ),
    inference(demodulation,[status(thm),theory(equality)],[c_237845,c_291276]) ).

tff(c_226,plain,
    union(complement(x),x) != universal_class,
    inference(cnfTransformation,[status(thm)],[f_780]) ).

tff(c_291580,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_291501,c_226]) ).

tff(c_291581,plain,
    domain_of(null_class) = null_class,
    inference(splitRight,[status(thm)],[c_210547]) ).

tff(c_291729,plain,
    ! [Z_70] :
      ( ~ member(Z_70,null_class)
      | ( restrict(null_class,singleton(Z_70),universal_class) != null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_291581,c_60]) ).

tff(c_291755,plain,
    ! [Z_70] : ~ member(Z_70,null_class),
    inference(demodulation,[status(thm),theory(equality)],[c_68045,c_291729]) ).

tff(c_205613,plain,
    ! [Y_5577] : ( intersection(null_class,Y_5577) = null_class ),
    inference(resolution,[status(thm)],[c_205492,c_1544]) ).

tff(c_205674,plain,
    complement(domain_of(null_class)) = diagonalise(null_class),
    inference(superposition,[status(thm),theory(equality)],[c_205613,c_152]) ).

tff(c_291667,plain,
    diagonalise(null_class) = complement(null_class),
    inference(demodulation,[status(thm),theory(equality)],[c_291581,c_205674]) ).

tff(c_306390,plain,
    ! [Z_7772,Xr_7773] :
      ( member(Z_7772,domain_of(intersection(Xr_7773,identity_relation)))
      | member(Z_7772,diagonalise(Xr_7773))
      | ~ member(Z_7772,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_152,c_1566]) ).

tff(c_306465,plain,
    ! [Z_7772] :
      ( member(Z_7772,domain_of(null_class))
      | member(Z_7772,diagonalise(null_class))
      | ~ member(Z_7772,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_205595,c_306390]) ).

tff(c_306517,plain,
    ! [Z_7772] :
      ( member(Z_7772,null_class)
      | member(Z_7772,complement(null_class))
      | ~ member(Z_7772,universal_class) ),
    inference(demodulation,[status(thm),theory(equality)],[c_291667,c_291581,c_306465]) ).

tff(c_306519,plain,
    ! [Z_7774] :
      ( member(Z_7774,complement(null_class))
      | ~ member(Z_7774,universal_class) ),
    inference(negUnitSimplification,[status(thm)],[c_291755,c_306517]) ).

tff(c_315006,plain,
    ! [X_7994] :
      ( subclass(X_7994,complement(null_class))
      | ~ member(not_subclass_element(X_7994,complement(null_class)),universal_class) ),
    inference(resolution,[status(thm)],[c_306519,c_6]) ).

tff(c_315018,plain,
    ! [X_4] :
      ( ~ subclass(X_4,universal_class)
      | subclass(X_4,complement(null_class)) ),
    inference(resolution,[status(thm)],[c_824,c_315006]) ).

tff(c_315050,plain,
    ! [X_7995] : subclass(X_7995,complement(null_class)),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_315018]) ).

tff(c_315345,plain,
    complement(null_class) = universal_class,
    inference(resolution,[status(thm)],[c_315050,c_403]) ).

tff(c_346243,plain,
    ! [X_8512,Y_8513] :
      ( ~ member(regular(intersection(complement(X_8512),Y_8513)),X_8512)
      | ( intersection(complement(X_8512),Y_8513) = null_class ) ),
    inference(resolution,[status(thm)],[c_205492,c_48]) ).

tff(c_346541,plain,
    ! [Y_8514] : ( intersection(complement(Y_8514),Y_8514) = null_class ),
    inference(resolution,[status(thm)],[c_589,c_346243]) ).

tff(c_346957,plain,
    ! [Y_60] : ( union(complement(Y_60),Y_60) = complement(null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_346541,c_52]) ).

tff(c_347143,plain,
    ! [Y_60] : ( union(complement(Y_60),Y_60) = universal_class ),
    inference(demodulation,[status(thm),theory(equality)],[c_315345,c_346957]) ).

tff(c_347205,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_347143,c_226]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET154-6 : 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
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 16:04:13 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 110.86/91.01  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 110.86/91.03  
% 110.86/91.03  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 110.86/91.07  
% 110.86/91.07  Inference rules
% 110.86/91.07  ----------------------
% 110.86/91.07  #Ref     : 6
% 110.86/91.07  #Sup     : 92298
% 110.86/91.07  #Fact    : 22
% 110.86/91.07  #Define  : 0
% 110.86/91.07  #Split   : 840
% 110.86/91.07  #Chain   : 0
% 110.86/91.07  #Close   : 0
% 110.86/91.07  
% 110.86/91.07  Ordering : KBO
% 110.86/91.07  
% 110.86/91.07  Simplification rules
% 110.86/91.07  ----------------------
% 110.86/91.07  #Subsume      : 29211
% 110.86/91.07  #Demod        : 38998
% 110.86/91.07  #Tautology    : 12197
% 110.86/91.07  #SimpNegUnit  : 2570
% 110.86/91.07  #BackRed      : 1241
% 110.86/91.07  
% 110.86/91.07  #Partial instantiations: 0
% 110.86/91.07  #Strategies tried      : 1
% 110.86/91.07  
% 110.86/91.07  Timing (in seconds)
% 110.86/91.07  ----------------------
% 110.86/91.07  Preprocessing        : 0.74
% 110.86/91.07  Parsing              : 0.39
% 110.86/91.07  CNF conversion       : 0.05
% 110.86/91.08  Main loop            : 89.21
% 110.86/91.08  Inferencing          : 11.69
% 110.86/91.08  Reduction            : 40.78
% 110.86/91.08  Demodulation         : 29.19
% 110.86/91.08  BG Simplification    : 0.46
% 110.86/91.08  Subsumption          : 27.82
% 110.86/91.08  Abstraction          : 0.76
% 110.86/91.08  MUC search           : 0.00
% 110.86/91.08  Cooper               : 0.00
% 110.86/91.08  Total                : 90.02
% 110.86/91.08  Index Insertion      : 0.00
% 110.86/91.08  Index Deletion       : 0.00
% 110.86/91.08  Index Matching       : 0.00
% 110.86/91.08  BG Taut test         : 0.00
%------------------------------------------------------------------------------