TSTP Solution File: SET102-6 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET102-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 Apr 30 15:05:41 EDT 2024

% Result   : Unsatisfiable 0.20s 0.39s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   73
% Syntax   : Number of formulae    :  125 (  54 unt;   0 def)
%            Number of atoms       :  231 (  16 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  177 (  71   ~;  70   |;   0   &)
%                                         (  36 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   46 (  44 usr;  37 prp; 0-3 aty)
%            Number of functors    :   23 (  23 usr;  10 con; 0-2 aty)
%            Number of variables   :  116 ( 116   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f339,plain,
    $false,
    inference(avatar_sat_refutation,[],[f170,f175,f179,f184,f188,f193,f197,f201,f205,f210,f215,f219,f223,f227,f231,f235,f239,f243,f247,f251,f257,f261,f265,f269,f273,f277,f281,f285,f289,f293,f297,f309,f316,f320,f324,f329,f338]) ).

fof(f338,plain,
    ( ~ spl0_9
    | spl0_32 ),
    inference(avatar_contradiction_clause,[],[f337]) ).

fof(f337,plain,
    ( $false
    | ~ spl0_9
    | spl0_32 ),
    inference(resolution,[],[f308,f204]) ).

fof(f204,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f203]) ).

fof(f203,plain,
    ( spl0_9
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f308,plain,
    ( ~ member(unordered_pair(x,unordered_pair(y,y)),universal_class)
    | spl0_32 ),
    inference(avatar_component_clause,[],[f306]) ).

fof(f306,plain,
    ( spl0_32
  <=> member(unordered_pair(x,unordered_pair(y,y)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f329,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f104,f326]) ).

fof(f326,plain,
    ( spl0_36
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f104,plain,
    identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
    inference(definition_unfolding,[],[f75,f38]) ).

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

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

fof(f324,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f67,f322]) ).

fof(f322,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(f320,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f7,f318]) ).

fof(f318,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(f316,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f1,f314]) ).

fof(f314,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(f309,plain,
    ( ~ spl0_32
    | spl0_6
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f301,f267,f190,f306]) ).

fof(f190,plain,
    ( spl0_6
  <=> member(unordered_pair(x,unordered_pair(y,y)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f267,plain,
    ( spl0_24
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f301,plain,
    ( ~ member(unordered_pair(x,unordered_pair(y,y)),universal_class)
    | spl0_6
    | ~ spl0_24 ),
    inference(resolution,[],[f268,f192]) ).

fof(f192,plain,
    ( ~ member(unordered_pair(x,unordered_pair(y,y)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))))
    | spl0_6 ),
    inference(avatar_component_clause,[],[f190]) ).

fof(f268,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f267]) ).

fof(f297,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f108,f295]) ).

fof(f295,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(f108,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(f293,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f88,f291]) ).

fof(f291,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(f289,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f35,f287]) ).

fof(f287,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(f285,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f32,f283]) ).

fof(f283,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(f281,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f22,f279]) ).

fof(f279,plain,
    ( spl0_27
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

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

fof(f277,plain,
    ( spl0_26
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f252,f237,f217,f275]) ).

fof(f275,plain,
    ( spl0_26
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f217,plain,
    ( spl0_12
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f237,plain,
    ( spl0_17
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f252,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(resolution,[],[f238,f218]) ).

fof(f218,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f217]) ).

fof(f238,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f237]) ).

fof(f273,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f21,f271]) ).

fof(f271,plain,
    ( spl0_25
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

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

fof(f269,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f10,f267]) ).

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(f265,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f9,f263]) ).

fof(f263,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(f261,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f3,f259]) ).

fof(f259,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(f257,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f2,f255]) ).

fof(f255,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(f251,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f66,f249]) ).

fof(f249,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(f247,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f62,f245]) ).

fof(f245,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(f243,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f57,f241]) ).

fof(f241,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(f239,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f24,f237]) ).

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

fof(f235,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f87,f233]) ).

fof(f233,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(f231,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f86,f229]) ).

fof(f229,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(f227,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f82,f225]) ).

fof(f225,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(f223,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f51,f221]) ).

fof(f221,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(f219,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f47,f217]) ).

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

fof(f215,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f44,f212]) ).

fof(f212,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(f210,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f18,f207]) ).

fof(f207,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(f205,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f11,f203]) ).

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

fof(f201,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f78,f199]) ).

fof(f199,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(f197,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f71,f195]) ).

fof(f195,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(f193,plain,
    ~ spl0_6,
    inference(avatar_split_clause,[],[f103,f190]) ).

fof(f103,plain,
    ~ member(unordered_pair(x,unordered_pair(y,y)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),
    inference(definition_unfolding,[],[f92,f12,f97]) ).

fof(f97,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f13,f12,f12]) ).

fof(f13,axiom,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).

fof(f92,axiom,
    ~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unordered_pair_member_of_ordered_pair_1) ).

fof(f188,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f142,f186]) ).

fof(f186,plain,
    ( spl0_5
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f142,plain,
    ! [X1] : subclass(X1,X1),
    inference(equality_resolution,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass1) ).

fof(f184,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f52,f181]) ).

fof(f181,plain,
    ( spl0_4
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

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

fof(f179,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f4,f177]) ).

fof(f177,plain,
    ( spl0_3
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

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

fof(f175,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f69,f172]) ).

fof(f172,plain,
    ( spl0_2
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

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

fof(f170,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f50,f167]) ).

fof(f167,plain,
    ( spl0_1
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SET102-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.04/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n008.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   : Tue Apr 30 01:13:13 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.36  % (28730)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (28734)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  % (28733)WARNING: value z3 for option sas not known
% 0.20/0.38  % (28731)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38  % (28732)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38  % (28733)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.38  % (28736)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)
% 0.20/0.38  % (28735)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)
% 0.20/0.38  % (28737)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)
% 0.20/0.39  % (28735)First to succeed.
% 0.20/0.39  % (28735)Refutation found. Thanks to Tanya!
% 0.20/0.39  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39  % (28735)------------------------------
% 0.20/0.39  % (28735)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.39  % (28735)Termination reason: Refutation
% 0.20/0.39  
% 0.20/0.39  % (28735)Memory used [KB]: 1027
% 0.20/0.39  % (28735)Time elapsed: 0.012 s
% 0.20/0.39  % (28735)Instructions burned: 19 (million)
% 0.20/0.39  % (28735)------------------------------
% 0.20/0.39  % (28735)------------------------------
% 0.20/0.39  % (28730)Success in time 0.031 s
%------------------------------------------------------------------------------