TSTP Solution File: SET516-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET516-6 : 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 : n022.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 10:56:32 EDT 2023

% Result   : Unsatisfiable 15.24s 5.30s
% Output   : CNFRefutation 15.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   74
% Syntax   : Number of formulae    :  158 (  38 unt;  57 typ;   0 def)
%            Number of atoms       :  182 (  62 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  142 (  61   ~;  81   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 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   :   92 (;  92   !;   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_778,axiom,
    singleton(x) = x,
    file(unknown,unknown) ).

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

tff(f_132,axiom,
    ! [X] : ( unordered_pair(X,X) = singleton(X) ),
    file(unknown,unknown) ).

tff(f_111,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | ( U = X )
      | ( U = Y ) ),
    file(unknown,unknown) ).

tff(f_128,axiom,
    ! [X,Y] : member(unordered_pair(X,Y),universal_class),
    file(unknown,unknown) ).

tff(f_118,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | member(X,unordered_pair(X,Y)) ),
    file(unknown,unknown) ).

tff(f_70,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_523,axiom,
    intersection(inverse(subset_relation),subset_relation) = identity_relation,
    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_483,axiom,
    ! [X] :
      ( ( X = null_class )
      | ( intersection(X,regular(X)) = null_class ) ),
    file(unknown,unknown) ).

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

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

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

tff(f_729,axiom,
    intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
    file(unknown,unknown) ).

tff(f_498,axiom,
    ! [Y] :
      ( ~ member(Y,universal_class)
      | ( Y = null_class )
      | member(apply(choice,Y),Y) ),
    file(unknown,unknown) ).

tff(f_208,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,X)
      | ~ member(Z,Y)
      | member(Z,intersection(X,Y)) ),
    file(unknown,unknown) ).

tff(c_226,plain,
    singleton(x) = x,
    inference(cnfTransformation,[status(thm)],[f_778]) ).

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

tff(c_24,plain,
    ! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
    inference(cnfTransformation,[status(thm)],[f_132]) ).

tff(c_788,plain,
    ! [Y_319,U_320,X_321] :
      ( ( Y_319 = U_320 )
      | ( X_321 = U_320 )
      | ~ member(U_320,unordered_pair(X_321,Y_319)) ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_845,plain,
    ! [X_326,U_327] :
      ( ( X_326 = U_327 )
      | ( X_326 = U_327 )
      | ~ member(U_327,singleton(X_326)) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_788]) ).

tff(c_899,plain,
    ! [X_331] :
      ( ( regular(singleton(X_331)) = X_331 )
      | ( singleton(X_331) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_845]) ).

tff(c_914,plain,
    ( ( regular(x) = x )
    | ( singleton(x) = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_899]) ).

tff(c_917,plain,
    ( ( regular(x) = x )
    | ( x = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_226,c_914]) ).

tff(c_918,plain,
    x = null_class,
    inference(splitLeft,[status(thm)],[c_917]) ).

tff(c_263,plain,
    ! [X_224,Y_225] : member(unordered_pair(X_224,Y_225),universal_class),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_266,plain,
    ! [X_226] : member(singleton(X_226),universal_class),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_263]) ).

tff(c_268,plain,
    member(x,universal_class),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_266]) ).

tff(c_400,plain,
    ! [X_269,Y_270] :
      ( member(X_269,unordered_pair(X_269,Y_270))
      | ~ member(X_269,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_416,plain,
    ! [X_272] :
      ( member(X_272,singleton(X_272))
      | ~ member(X_272,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_400]) ).

tff(c_419,plain,
    ( member(x,x)
    | ~ member(x,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_416]) ).

tff(c_421,plain,
    member(x,x),
    inference(demodulation,[status(thm),theory(equality)],[c_268,c_419]) ).

tff(c_920,plain,
    member(null_class,null_class),
    inference(demodulation,[status(thm),theory(equality)],[c_918,c_918,c_421]) ).

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_150,plain,
    intersection(inverse(subset_relation),subset_relation) = identity_relation,
    inference(cnfTransformation,[status(thm)],[f_523]) ).

tff(c_518,plain,
    ! [Z_286,Y_287,X_288] :
      ( member(Z_286,Y_287)
      | ~ member(Z_286,intersection(X_288,Y_287)) ),
    inference(cnfTransformation,[status(thm)],[f_200]) ).

tff(c_553,plain,
    ! [Z_290] :
      ( member(Z_290,subset_relation)
      | ~ member(Z_290,identity_relation) ),
    inference(superposition,[status(thm),theory(equality)],[c_150,c_518]) ).

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_782,plain,
    ! [X_318] :
      ( subclass(X_318,subset_relation)
      | ~ member(not_subclass_element(X_318,subset_relation),identity_relation) ),
    inference(resolution,[status(thm)],[c_553,c_6]) ).

tff(c_787,plain,
    subclass(identity_relation,subset_relation),
    inference(resolution,[status(thm)],[c_4,c_782]) ).

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_432,plain,
    ! [Z_275,X_276,Y_277] :
      ( member(Z_275,X_276)
      | ~ member(Z_275,intersection(X_276,Y_277)) ),
    inference(cnfTransformation,[status(thm)],[f_194]) ).

tff(c_435,plain,
    ! [Z_275,X_132] :
      ( member(Z_275,X_132)
      | ~ member(Z_275,null_class)
      | ( null_class = X_132 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_134,c_432]) ).

tff(c_1011,plain,
    ! [X_132] :
      ( member(null_class,X_132)
      | ( null_class = X_132 ) ),
    inference(resolution,[status(thm)],[c_920,c_435]) ).

tff(c_532,plain,
    ! [Z_286] :
      ( member(Z_286,subset_relation)
      | ~ member(Z_286,identity_relation) ),
    inference(superposition,[status(thm),theory(equality)],[c_150,c_518]) ).

tff(c_1030,plain,
    ! [X_336] :
      ( member(null_class,X_336)
      | ( null_class = X_336 ) ),
    inference(resolution,[status(thm)],[c_920,c_435]) ).

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_1226,plain,
    ! [X_344] :
      ( ~ member(null_class,X_344)
      | ( complement(X_344) = null_class ) ),
    inference(resolution,[status(thm)],[c_1030,c_48]) ).

tff(c_1266,plain,
    ( ( complement(subset_relation) = null_class )
    | ~ member(null_class,identity_relation) ),
    inference(resolution,[status(thm)],[c_532,c_1226]) ).

tff(c_1614,plain,
    ~ member(null_class,identity_relation),
    inference(splitLeft,[status(thm)],[c_1266]) ).

tff(c_1621,plain,
    null_class = identity_relation,
    inference(resolution,[status(thm)],[c_1011,c_1614]) ).

tff(c_1623,plain,
    ~ member(identity_relation,identity_relation),
    inference(demodulation,[status(thm),theory(equality)],[c_1621,c_1614]) ).

tff(c_1642,plain,
    member(identity_relation,identity_relation),
    inference(demodulation,[status(thm),theory(equality)],[c_1621,c_1621,c_920]) ).

tff(c_1742,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1623,c_1642]) ).

tff(c_1744,plain,
    member(null_class,identity_relation),
    inference(splitRight,[status(thm)],[c_1266]) ).

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_1841,plain,
    ! [Y_369] :
      ( member(null_class,Y_369)
      | ~ subclass(identity_relation,Y_369) ),
    inference(resolution,[status(thm)],[c_1744,c_2]) ).

tff(c_1857,plain,
    member(null_class,subset_relation),
    inference(resolution,[status(thm)],[c_787,c_1841]) ).

tff(c_1743,plain,
    complement(subset_relation) = null_class,
    inference(splitRight,[status(thm)],[c_1266]) ).

tff(c_1872,plain,
    ! [Z_370] :
      ( ~ member(Z_370,subset_relation)
      | ~ member(Z_370,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_1743,c_48]) ).

tff(c_1875,plain,
    ~ member(null_class,null_class),
    inference(resolution,[status(thm)],[c_1857,c_1872]) ).

tff(c_1898,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_920,c_1875]) ).

tff(c_1900,plain,
    x != null_class,
    inference(splitRight,[status(thm)],[c_917]) ).

tff(c_2099,plain,
    ! [U_381] :
      ( ( x = U_381 )
      | ( x = U_381 )
      | ~ member(U_381,x) ),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_845]) ).

tff(c_2215,plain,
    ! [Y_388] :
      ( ( not_subclass_element(x,Y_388) = x )
      | subclass(x,Y_388) ),
    inference(resolution,[status(thm)],[c_4,c_2099]) ).

tff(c_1914,plain,
    ! [U_371,Y_372,X_373] :
      ( member(U_371,Y_372)
      | ~ member(U_371,X_373)
      | ~ subclass(X_373,Y_372) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_1955,plain,
    ! [Y_372] :
      ( member(x,Y_372)
      | ~ subclass(x,Y_372) ),
    inference(resolution,[status(thm)],[c_421,c_1914]) ).

tff(c_2230,plain,
    ! [Y_392] :
      ( member(x,Y_392)
      | ( not_subclass_element(x,Y_392) = x ) ),
    inference(resolution,[status(thm)],[c_2215,c_1955]) ).

tff(c_208,plain,
    intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
    inference(cnfTransformation,[status(thm)],[f_729]) ).

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_652,plain,
    ! [Z_307] :
      ( member(Z_307,element_relation)
      | ~ member(Z_307,singleton_relation) ),
    inference(superposition,[status(thm),theory(equality)],[c_208,c_44]) ).

tff(c_666,plain,
    ( member(regular(singleton_relation),element_relation)
    | ( singleton_relation = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_652]) ).

tff(c_668,plain,
    singleton_relation = null_class,
    inference(splitLeft,[status(thm)],[c_666]) ).

tff(c_641,plain,
    ! [Z_49] :
      ( member(Z_49,element_relation)
      | ~ member(Z_49,singleton_relation) ),
    inference(superposition,[status(thm),theory(equality)],[c_208,c_44]) ).

tff(c_669,plain,
    ! [Z_49] :
      ( member(Z_49,element_relation)
      | ~ member(Z_49,null_class) ),
    inference(demodulation,[status(thm),theory(equality)],[c_668,c_641]) ).

tff(c_2276,plain,
    ( member(x,element_relation)
    | ( not_subclass_element(x,null_class) = x ) ),
    inference(resolution,[status(thm)],[c_2230,c_669]) ).

tff(c_2305,plain,
    not_subclass_element(x,null_class) = x,
    inference(splitLeft,[status(thm)],[c_2276]) ).

tff(c_2312,plain,
    ( subclass(x,null_class)
    | ~ member(x,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_2305,c_6]) ).

tff(c_2317,plain,
    ~ member(x,null_class),
    inference(splitLeft,[status(thm)],[c_2312]) ).

tff(c_2596,plain,
    ! [Y_424] :
      ( member(apply(choice,Y_424),Y_424)
      | ( null_class = Y_424 )
      | ~ member(Y_424,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_863,plain,
    ! [U_327] :
      ( ( x = U_327 )
      | ( x = U_327 )
      | ~ member(U_327,x) ),
    inference(superposition,[status(thm),theory(equality)],[c_226,c_845]) ).

tff(c_2604,plain,
    ( ( apply(choice,x) = x )
    | ( x = null_class )
    | ~ member(x,universal_class) ),
    inference(resolution,[status(thm)],[c_2596,c_863]) ).

tff(c_2640,plain,
    ( ( apply(choice,x) = x )
    | ( x = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_268,c_2604]) ).

tff(c_2641,plain,
    apply(choice,x) = x,
    inference(negUnitSimplification,[status(thm)],[c_1900,c_2640]) ).

tff(c_140,plain,
    ! [Y_135] :
      ( member(apply(choice,Y_135),Y_135)
      | ( null_class = Y_135 )
      | ~ member(Y_135,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_498]) ).

tff(c_1899,plain,
    regular(x) = x,
    inference(splitRight,[status(thm)],[c_917]) ).

tff(c_1904,plain,
    ( ( intersection(x,x) = null_class )
    | ( x = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1899,c_134]) ).

tff(c_1910,plain,
    intersection(x,x) = null_class,
    inference(negUnitSimplification,[status(thm)],[c_1900,c_1904]) ).

tff(c_2976,plain,
    ! [Z_459,X_460,Y_461] :
      ( member(Z_459,intersection(X_460,Y_461))
      | ~ member(Z_459,Y_461)
      | ~ member(Z_459,X_460) ),
    inference(cnfTransformation,[status(thm)],[f_208]) ).

tff(c_16188,plain,
    ! [Z_1039] :
      ( member(Z_1039,null_class)
      | ~ member(Z_1039,x)
      | ~ member(Z_1039,x) ),
    inference(superposition,[status(thm),theory(equality)],[c_1910,c_2976]) ).

tff(c_16221,plain,
    ( member(apply(choice,x),null_class)
    | ~ member(apply(choice,x),x)
    | ( x = null_class )
    | ~ member(x,universal_class) ),
    inference(resolution,[status(thm)],[c_140,c_16188]) ).

tff(c_16259,plain,
    ( member(x,null_class)
    | ( x = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_268,c_421,c_2641,c_2641,c_16221]) ).

tff(c_16261,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1900,c_2317,c_16259]) ).

tff(c_16263,plain,
    member(x,null_class),
    inference(splitRight,[status(thm)],[c_2312]) ).

tff(c_16292,plain,
    ! [X_1040] :
      ( member(x,X_1040)
      | ( null_class = X_1040 ) ),
    inference(resolution,[status(thm)],[c_16263,c_435]) ).

tff(c_16423,plain,
    ! [X_1051] :
      ( ~ member(x,X_1051)
      | ( complement(X_1051) = null_class ) ),
    inference(resolution,[status(thm)],[c_16292,c_48]) ).

tff(c_16468,plain,
    complement(null_class) = null_class,
    inference(resolution,[status(thm)],[c_16263,c_16423]) ).

tff(c_17379,plain,
    ! [Z_1078] :
      ( ~ member(Z_1078,null_class)
      | ~ member(Z_1078,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_16468,c_48]) ).

tff(c_17387,plain,
    ~ member(x,null_class),
    inference(resolution,[status(thm)],[c_16263,c_17379]) ).

tff(c_17414,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16263,c_17387]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET516-6 : 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
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 16:40:33 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 15.24/5.30  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.24/5.33  
% 15.24/5.33  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.24/5.37  
% 15.24/5.37  Inference rules
% 15.24/5.37  ----------------------
% 15.24/5.37  #Ref     : 0
% 15.24/5.37  #Sup     : 4252
% 15.24/5.37  #Fact    : 0
% 15.24/5.37  #Define  : 0
% 15.24/5.37  #Split   : 101
% 15.24/5.37  #Chain   : 0
% 15.24/5.37  #Close   : 0
% 15.24/5.37  
% 15.24/5.37  Ordering : KBO
% 15.24/5.37  
% 15.24/5.37  Simplification rules
% 15.24/5.37  ----------------------
% 15.24/5.37  #Subsume      : 980
% 15.24/5.37  #Demod        : 1351
% 15.24/5.37  #Tautology    : 906
% 15.24/5.37  #SimpNegUnit  : 111
% 15.24/5.37  #BackRed      : 220
% 15.24/5.37  
% 15.24/5.37  #Partial instantiations: 0
% 15.24/5.37  #Strategies tried      : 1
% 15.24/5.37  
% 15.24/5.37  Timing (in seconds)
% 15.24/5.37  ----------------------
% 15.24/5.37  Preprocessing        : 0.73
% 15.24/5.37  Parsing              : 0.39
% 15.24/5.37  CNF conversion       : 0.05
% 15.24/5.37  Main loop            : 3.56
% 15.24/5.37  Inferencing          : 1.04
% 15.24/5.37  Reduction            : 1.31
% 15.24/5.37  Demodulation         : 0.88
% 15.24/5.37  BG Simplification    : 0.09
% 15.24/5.37  Subsumption          : 0.83
% 15.24/5.37  Abstraction          : 0.07
% 15.24/5.37  MUC search           : 0.00
% 15.24/5.37  Cooper               : 0.00
% 15.24/5.37  Total                : 4.37
% 15.24/5.37  Index Insertion      : 0.00
% 15.24/5.37  Index Deletion       : 0.00
% 15.24/5.37  Index Matching       : 0.00
% 15.24/5.37  BG Taut test         : 0.00
%------------------------------------------------------------------------------