TSTP Solution File: SET060-7 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET060-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n023.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 May 21 03:15:44 EDT 2024

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  103
% Syntax   : Number of formulae    :  178 (  71 unt;   0 def)
%            Number of atoms       :  350 (  30 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  286 ( 114   ~; 121   |;   0   &)
%                                         (  51 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   62 (  60 usr;  52 prp; 0-3 aty)
%            Number of functors    :   24 (  24 usr;  10 con; 0-3 aty)
%            Number of variables   :  180 ( 180   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f469,plain,
    $false,
    inference(avatar_sat_refutation,[],[f183,f188,f193,f197,f202,f206,f210,f214,f218,f223,f228,f232,f236,f240,f244,f248,f252,f256,f260,f264,f270,f274,f278,f282,f286,f290,f294,f298,f302,f306,f310,f322,f330,f334,f338,f342,f347,f352,f386,f390,f394,f403,f407,f411,f415,f419,f423,f427,f457,f461,f467,f468]) ).

fof(f468,plain,
    ( ~ spl0_38
    | ~ spl0_17
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f439,f319,f250,f349]) ).

fof(f349,plain,
    ( spl0_38
  <=> member(y,x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f250,plain,
    ( spl0_17
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f319,plain,
    ( spl0_32
  <=> member(y,complement(x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f439,plain,
    ( ~ member(y,x)
    | ~ spl0_17
    | ~ spl0_32 ),
    inference(resolution,[],[f321,f251]) ).

fof(f251,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f321,plain,
    ( member(y,complement(x))
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f319]) ).

fof(f467,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f98,f465]) ).

fof(f465,plain,
    ( spl0_51
  <=> ! [X0,X1] :
        ( X0 = X1
        | member(not_subclass_element(X1,X0),X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f98,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | member(not_subclass_element(X1,X0),X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).

fof(f461,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f119,f459]) ).

fof(f459,plain,
    ( spl0_50
  <=> ! [X8] :
        ( ~ operation(X8)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f119,plain,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f80,f104]) ).

fof(f104,plain,
    ! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
    inference(definition_unfolding,[],[f39,f38]) ).

fof(f38,axiom,
    ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).

fof(f39,axiom,
    ! [X4] : domain_of(inverse(X4)) = range_of(X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).

fof(f80,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(range_of(X8),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).

fof(f457,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f79,f455]) ).

fof(f455,plain,
    ( spl0_49
  <=> ! [X8] :
        ( ~ operation(X8)
        | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f79,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation2) ).

fof(f427,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f160,f425]) ).

fof(f425,plain,
    ( spl0_48
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f160,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f123,f114]) ).

fof(f114,plain,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
    inference(definition_unfolding,[],[f28,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).

fof(f28,axiom,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).

fof(f123,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
    inference(definition_unfolding,[],[f54,f103]) ).

fof(f103,plain,
    ! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
    inference(definition_unfolding,[],[f53,f29]) ).

fof(f53,axiom,
    ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).

fof(f54,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).

fof(f423,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f121,f421]) ).

fof(f421,plain,
    ( spl0_47
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f121,plain,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f61,f38]) ).

fof(f61,axiom,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class2) ).

fof(f419,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f120,f417]) ).

fof(f417,plain,
    ( spl0_46
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f120,plain,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f63,f38]) ).

fof(f63,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).

fof(f415,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f116,f413]) ).

fof(f413,plain,
    ( spl0_45
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f116,plain,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f60,f38]) ).

fof(f60,axiom,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class1) ).

fof(f411,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f114,f409]) ).

fof(f409,plain,
    ( spl0_44
  <=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f407,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f23,f405]) ).

fof(f405,plain,
    ( spl0_43
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,X0)
        | ~ member(X4,X1)
        | member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f23,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,X1)
      | member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).

fof(f403,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f8,f401]) ).

fof(f401,plain,
    ( spl0_42
  <=> ! [X2,X0,X1] :
        ( X1 = X2
        | X0 = X2
        | ~ member(X2,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( X1 = X2
      | X0 = X2
      | ~ member(X2,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).

fof(f394,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f138,f392]) ).

fof(f392,plain,
    ( spl0_41
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f138,plain,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f73,f38]) ).

fof(f73,axiom,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(inverse(X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one3) ).

fof(f390,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f83,f388]) ).

fof(f388,plain,
    ( spl0_40
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f83,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) = domain_of(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible2) ).

fof(f386,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f25,f384]) ).

fof(f384,plain,
    ( spl0_39
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,X0)
        | member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f25,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,X0)
      | member(X4,complement(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).

fof(f352,plain,
    ( spl0_38
    | ~ spl0_1
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f326,f292,f180,f349]) ).

fof(f180,plain,
    ( spl0_1
  <=> member(y,intersection(complement(x),x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f292,plain,
    ( spl0_27
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f326,plain,
    ( member(y,x)
    | ~ spl0_1
    | ~ spl0_27 ),
    inference(resolution,[],[f293,f182]) ).

fof(f182,plain,
    ( member(y,intersection(complement(x),x))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f180]) ).

fof(f293,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X1) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f292]) ).

fof(f347,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f113,f344]) ).

fof(f344,plain,
    ( spl0_37
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f113,plain,
    identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
    inference(definition_unfolding,[],[f75,f38]) ).

fof(f75,axiom,
    identity_relation = intersection(inverse(subset_relation),subset_relation),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).

fof(f342,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f97,f340]) ).

fof(f340,plain,
    ( spl0_36
  <=> ! [X4,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X4)
        | subclass(X0,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f97,axiom,
    ! [X0,X1,X4] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X4)
      | subclass(X0,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subclass) ).

fof(f338,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f67,f336]) ).

fof(f336,plain,
    ( spl0_35
  <=> ! [X0] :
        ( null_class = X0
        | null_class = intersection(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).

fof(f334,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f7,f332]) ).

fof(f332,plain,
    ( spl0_34
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f330,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f1,f328]) ).

fof(f328,plain,
    ( spl0_33
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).

fof(f322,plain,
    ( spl0_32
    | ~ spl0_1
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f317,f284,f180,f319]) ).

fof(f284,plain,
    ( spl0_25
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f317,plain,
    ( member(y,complement(x))
    | ~ spl0_1
    | ~ spl0_25 ),
    inference(resolution,[],[f285,f182]) ).

fof(f285,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f284]) ).

fof(f310,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f117,f308]) ).

fof(f308,plain,
    ( spl0_31
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f117,plain,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f72,f38]) ).

fof(f72,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(inverse(X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).

fof(f306,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f88,f304]) ).

fof(f304,plain,
    ( spl0_30
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).

fof(f302,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f35,f300]) ).

fof(f300,plain,
    ( spl0_29
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f35,axiom,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).

fof(f298,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f32,f296]) ).

fof(f296,plain,
    ( spl0_28
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f32,axiom,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate1) ).

fof(f294,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f22,f292]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).

fof(f290,plain,
    ( spl0_26
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f265,f250,f230,f288]) ).

fof(f288,plain,
    ( spl0_26
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f230,plain,
    ( spl0_12
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f265,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(resolution,[],[f251,f231]) ).

fof(f231,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f230]) ).

fof(f286,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f21,f284]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).

fof(f282,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f10,f280]) ).

fof(f280,plain,
    ( spl0_24
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).

fof(f278,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f9,f276]) ).

fof(f276,plain,
    ( spl0_23
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).

fof(f274,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f3,f272]) ).

fof(f272,plain,
    ( spl0_22
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).

fof(f270,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f2,f268]) ).

fof(f268,plain,
    ( spl0_21
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).

fof(f264,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f66,f262]) ).

fof(f262,plain,
    ( spl0_20
  <=> ! [X0] :
        ( null_class = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).

fof(f260,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f62,f258]) ).

fof(f258,plain,
    ( spl0_19
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).

fof(f256,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f57,f254]) ).

fof(f254,plain,
    ( spl0_18
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).

fof(f252,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f24,f250]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).

fof(f248,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f87,f246]) ).

fof(f246,plain,
    ( spl0_16
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).

fof(f244,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f86,f242]) ).

fof(f242,plain,
    ( spl0_15
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).

fof(f240,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f82,f238]) ).

fof(f238,plain,
    ( spl0_14
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).

fof(f236,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f51,f234]) ).

fof(f234,plain,
    ( spl0_13
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f232,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f47,f230]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).

fof(f228,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f44,f225]) ).

fof(f225,plain,
    ( spl0_11
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).

fof(f223,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f18,f220]) ).

fof(f220,plain,
    ( spl0_10
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).

fof(f218,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f11,f216]) ).

fof(f216,plain,
    ( spl0_9
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f214,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f78,f212]) ).

fof(f212,plain,
    ( spl0_8
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).

fof(f210,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f71,f208]) ).

fof(f208,plain,
    ( spl0_7
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).

fof(f206,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f96,f204]) ).

fof(f204,plain,
    ( spl0_6
  <=> ! [X0] : subclass(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f96,axiom,
    ! [X0] : subclass(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).

fof(f202,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f52,f199]) ).

fof(f199,plain,
    ( spl0_5
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f197,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f4,f195]) ).

fof(f195,plain,
    ( spl0_4
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f193,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f69,f190]) ).

fof(f190,plain,
    ( spl0_3
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).

fof(f188,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f50,f185]) ).

fof(f185,plain,
    ( spl0_2
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f183,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f102,f180]) ).

fof(f102,axiom,
    member(y,intersection(complement(x),x)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_special_classes_lemma_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SET060-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.12/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 11:41:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (23185)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (23190)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.38  % (23192)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.38  % (23187)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38  % (23186)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38  % (23190)First to succeed.
% 0.13/0.39  % (23191)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.39  % (23190)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23185"
% 0.13/0.39  % (23189)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39  % (23190)Refutation found. Thanks to Tanya!
% 0.13/0.39  % SZS status Unsatisfiable for theBenchmark
% 0.13/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.39  % (23190)------------------------------
% 0.13/0.39  % (23190)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.39  % (23190)Termination reason: Refutation
% 0.13/0.39  
% 0.13/0.39  % (23190)Memory used [KB]: 1064
% 0.13/0.39  % (23190)Time elapsed: 0.014 s
% 0.13/0.39  % (23190)Instructions burned: 25 (million)
% 0.13/0.39  % (23185)Success in time 0.041 s
%------------------------------------------------------------------------------