TSTP Solution File: SET079+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET079+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.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 15:05:29 EDT 2024

% Result   : Theorem 0.19s 0.36s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   80
% Syntax   : Number of formulae    :  239 (  69 unt;   0 def)
%            Number of atoms       :  643 (  67 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  610 ( 206   ~; 202   |; 115   &)
%                                         (  68 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   52 (  50 usr;  46 prp; 0-2 aty)
%            Number of functors    :   29 (  29 usr;   8 con; 0-3 aty)
%            Number of variables   :  326 ( 299   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f534,plain,
    $false,
    inference(avatar_sat_refutation,[],[f272,f277,f282,f287,f291,f295,f300,f304,f309,f314,f318,f322,f326,f332,f336,f340,f344,f348,f352,f356,f360,f365,f369,f373,f377,f381,f385,f400,f404,f409,f413,f417,f421,f425,f429,f433,f437,f441,f445,f474,f478,f482,f486,f490,f494,f533]) ).

fof(f533,plain,
    ( ~ spl7_5
    | ~ spl7_40 ),
    inference(avatar_contradiction_clause,[],[f531]) ).

fof(f531,plain,
    ( $false
    | ~ spl7_5
    | ~ spl7_40 ),
    inference(resolution,[],[f473,f290]) ).

fof(f290,plain,
    ( ! [X0] : ~ member(X0,null_class)
    | ~ spl7_5 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f289,plain,
    ( spl7_5
  <=> ! [X0] : ~ member(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).

fof(f473,plain,
    ( member(sK0,null_class)
    | ~ spl7_40 ),
    inference(avatar_component_clause,[],[f471]) ).

fof(f471,plain,
    ( spl7_40
  <=> member(sK0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_40])]) ).

fof(f494,plain,
    spl7_45,
    inference(avatar_split_clause,[],[f186,f492]) ).

fof(f492,plain,
    ( spl7_45
  <=> ! [X0,X1] :
        ( member(sK4(X0,X1),X1)
        | ~ member(X0,sum_class(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_45])]) ).

fof(f186,plain,
    ! [X0,X1] :
      ( member(sK4(X0,X1),X1)
      | ~ member(X0,sum_class(X1)) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ( member(X0,sum_class(X1))
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X0,X2) ) )
      & ( ( member(sK4(X0,X1),X1)
          & member(X0,sK4(X0,X1)) )
        | ~ member(X0,sum_class(X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f110,f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & member(X0,X3) )
     => ( member(sK4(X0,X1),X1)
        & member(X0,sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ( member(X0,sum_class(X1))
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X0,X2) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & member(X0,X3) )
        | ~ member(X0,sum_class(X1)) ) ),
    inference(rectify,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( member(X0,sum_class(X1))
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X0,X2) ) )
      & ( ? [X2] :
            ( member(X2,X1)
            & member(X0,X2) )
        | ~ member(X0,sum_class(X1)) ) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( member(X0,sum_class(X1))
    <=> ? [X2] :
          ( member(X2,X1)
          & member(X0,X2) ) ),
    inference(rectify,[],[f31]) ).

fof(f31,axiom,
    ! [X2,X0] :
      ( member(X2,sum_class(X0))
    <=> ? [X1] :
          ( member(X1,X0)
          & member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_defn) ).

fof(f490,plain,
    spl7_44,
    inference(avatar_split_clause,[],[f185,f488]) ).

fof(f488,plain,
    ( spl7_44
  <=> ! [X0,X1] :
        ( member(X0,sK4(X0,X1))
        | ~ member(X0,sum_class(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_44])]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( member(X0,sK4(X0,X1))
      | ~ member(X0,sum_class(X1)) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f486,plain,
    spl7_43,
    inference(avatar_split_clause,[],[f173,f484]) ).

fof(f484,plain,
    ( spl7_43
  <=> ! [X0,X1,X3] :
        ( member(X3,X1)
        | ~ member(X3,X0)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_43])]) ).

fof(f173,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subclass(X0,X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ( subclass(X0,X1)
        | ( ~ member(sK3(X0,X1),X1)
          & member(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subclass(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f100,f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ( subclass(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subclass(X0,X1) ) ),
    inference(rectify,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ( subclass(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subclass(X0,X1) ) ),
    inference(nnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).

fof(f482,plain,
    spl7_42,
    inference(avatar_split_clause,[],[f172,f480]) ).

fof(f480,plain,
    ( spl7_42
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | ~ member(X2,X0)
        | ~ disjoint(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_42])]) ).

fof(f172,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | ~ member(X2,X0)
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ member(X2,X1)
          | ~ member(X2,X0) )
      | ~ disjoint(X0,X1) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
     => ! [X2] :
          ~ ( member(X2,X1)
            & member(X2,X0) ) ),
    inference(unused_predicate_definition_removal,[],[f40]) ).

fof(f40,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
    <=> ! [X2] :
          ~ ( member(X2,X1)
            & member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).

fof(f478,plain,
    spl7_41,
    inference(avatar_split_clause,[],[f171,f476]) ).

fof(f476,plain,
    ( spl7_41
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ subclass(X1,X0)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_41])]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subclass(X1,X0)
      | ~ subclass(X0,X1) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subclass(X1,X0)
        | ~ subclass(X0,X1) )
      & ( ( subclass(X1,X0)
          & subclass(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subclass(X1,X0)
        | ~ subclass(X0,X1) )
      & ( ( subclass(X1,X0)
          & subclass(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subclass(X1,X0)
        & subclass(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).

fof(f474,plain,
    ( ~ spl7_1
    | spl7_40
    | ~ spl7_2
    | ~ spl7_38 ),
    inference(avatar_split_clause,[],[f467,f439,f274,f471,f269]) ).

fof(f269,plain,
    ( spl7_1
  <=> member(sK0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f274,plain,
    ( spl7_2
  <=> null_class = unordered_pair(sK0,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

fof(f439,plain,
    ( spl7_38
  <=> ! [X2,X1] :
        ( member(X2,unordered_pair(X1,X2))
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_38])]) ).

fof(f467,plain,
    ( member(sK0,null_class)
    | ~ member(sK0,universal_class)
    | ~ spl7_2
    | ~ spl7_38 ),
    inference(superposition,[],[f440,f276]) ).

fof(f276,plain,
    ( null_class = unordered_pair(sK0,sK0)
    | ~ spl7_2 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f440,plain,
    ( ! [X2,X1] :
        ( member(X2,unordered_pair(X1,X2))
        | ~ member(X2,universal_class) )
    | ~ spl7_38 ),
    inference(avatar_component_clause,[],[f439]) ).

fof(f445,plain,
    spl7_39,
    inference(avatar_split_clause,[],[f267,f443]) ).

fof(f443,plain,
    ( spl7_39
  <=> ! [X2,X1] :
        ( member(X1,unordered_pair(X1,X2))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_39])]) ).

fof(f267,plain,
    ! [X2,X1] :
      ( member(X1,unordered_pair(X1,X2))
      | ~ member(X1,universal_class) ),
    inference(equality_resolution,[],[f205]) ).

fof(f205,plain,
    ! [X2,X0,X1] :
      ( member(X0,unordered_pair(X1,X2))
      | X0 != X1
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 )
        | ~ member(X0,universal_class) )
      & ( ( ( X0 = X2
            | X0 = X1 )
          & member(X0,universal_class) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(flattening,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 )
        | ~ member(X0,universal_class) )
      & ( ( ( X0 = X2
            | X0 = X1 )
          & member(X0,universal_class) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X1,X2))
    <=> ( ( X0 = X2
          | X0 = X1 )
        & member(X0,universal_class) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,unordered_pair(X0,X1))
    <=> ( ( X1 = X2
          | X0 = X2 )
        & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).

fof(f441,plain,
    spl7_38,
    inference(avatar_split_clause,[],[f266,f439]) ).

fof(f266,plain,
    ! [X2,X1] :
      ( member(X2,unordered_pair(X1,X2))
      | ~ member(X2,universal_class) ),
    inference(equality_resolution,[],[f206]) ).

fof(f206,plain,
    ! [X2,X0,X1] :
      ( member(X0,unordered_pair(X1,X2))
      | X0 != X2
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f437,plain,
    spl7_37,
    inference(avatar_split_clause,[],[f203,f435]) ).

fof(f435,plain,
    ( spl7_37
  <=> ! [X2,X0,X1] :
        ( member(X0,universal_class)
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_37])]) ).

fof(f203,plain,
    ! [X2,X0,X1] :
      ( member(X0,universal_class)
      | ~ member(X0,unordered_pair(X1,X2)) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f433,plain,
    spl7_36,
    inference(avatar_split_clause,[],[f202,f431]) ).

fof(f431,plain,
    ( spl7_36
  <=> ! [X2,X0,X1] :
        ( member(X2,union(X0,X1))
        | ~ member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_36])]) ).

fof(f202,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f119]) ).

fof(f119,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,union(X0,X1))
    <=> ( member(X4,X1)
        | member(X4,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

fof(f429,plain,
    spl7_35,
    inference(avatar_split_clause,[],[f201,f427]) ).

fof(f427,plain,
    ( spl7_35
  <=> ! [X2,X0,X1] :
        ( member(X2,union(X0,X1))
        | ~ member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_35])]) ).

fof(f201,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f425,plain,
    spl7_34,
    inference(avatar_split_clause,[],[f198,f423]) ).

fof(f423,plain,
    ( spl7_34
  <=> ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_34])]) ).

fof(f198,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(flattening,[],[f117]) ).

fof(f117,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1,X4] :
      ( member(X4,intersection(X0,X1))
    <=> ( member(X4,X1)
        & member(X4,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).

fof(f421,plain,
    spl7_33,
    inference(avatar_split_clause,[],[f197,f419]) ).

fof(f419,plain,
    ( spl7_33
  <=> ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_33])]) ).

fof(f197,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f417,plain,
    spl7_32,
    inference(avatar_split_clause,[],[f175,f415]) ).

fof(f415,plain,
    ( spl7_32
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(sK3(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_32])]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f413,plain,
    spl7_31,
    inference(avatar_split_clause,[],[f174,f411]) ).

fof(f411,plain,
    ( spl7_31
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(sK3(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_31])]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f409,plain,
    ( ~ spl7_30
    | ~ spl7_5
    | ~ spl7_11 ),
    inference(avatar_split_clause,[],[f327,f316,f289,f406]) ).

fof(f406,plain,
    ( spl7_30
  <=> inductive(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_30])]) ).

fof(f316,plain,
    ( spl7_11
  <=> ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).

fof(f327,plain,
    ( ~ inductive(null_class)
    | ~ spl7_5
    | ~ spl7_11 ),
    inference(resolution,[],[f317,f290]) ).

fof(f317,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl7_11 ),
    inference(avatar_component_clause,[],[f316]) ).

fof(f404,plain,
    spl7_29,
    inference(avatar_split_clause,[],[f146,f402]) ).

fof(f402,plain,
    ( spl7_29
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_29])]) ).

fof(f146,plain,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip) ).

fof(f400,plain,
    spl7_28,
    inference(avatar_split_clause,[],[f145,f398]) ).

fof(f398,plain,
    ( spl7_28
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_28])]) ).

fof(f145,plain,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate) ).

fof(f385,plain,
    spl7_27,
    inference(avatar_split_clause,[],[f182,f383]) ).

fof(f383,plain,
    ( spl7_27
  <=> ! [X0,X1] :
        ( member(X1,universal_class)
        | ~ member(X1,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_27])]) ).

fof(f182,plain,
    ! [X0,X1] :
      ( member(X1,universal_class)
      | ~ member(X1,domain_of(X0)) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ( member(X1,domain_of(X0))
        | null_class = restrict(X0,singleton(X1),universal_class)
        | ~ member(X1,universal_class) )
      & ( ( null_class != restrict(X0,singleton(X1),universal_class)
          & member(X1,universal_class) )
        | ~ member(X1,domain_of(X0)) ) ),
    inference(flattening,[],[f107]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ( member(X1,domain_of(X0))
        | null_class = restrict(X0,singleton(X1),universal_class)
        | ~ member(X1,universal_class) )
      & ( ( null_class != restrict(X0,singleton(X1),universal_class)
          & member(X1,universal_class) )
        | ~ member(X1,domain_of(X0)) ) ),
    inference(nnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( member(X1,domain_of(X0))
    <=> ( null_class != restrict(X0,singleton(X1),universal_class)
        & member(X1,universal_class) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X4] :
      ( member(X4,domain_of(X0))
    <=> ( null_class != restrict(X0,singleton(X4),universal_class)
        & member(X4,universal_class) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of) ).

fof(f381,plain,
    spl7_26,
    inference(avatar_split_clause,[],[f180,f379]) ).

fof(f379,plain,
    ( spl7_26
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(X0,power_class(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_26])]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(X0,power_class(X1)) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ( member(X0,power_class(X1))
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class) )
      & ( ( subclass(X0,X1)
          & member(X0,universal_class) )
        | ~ member(X0,power_class(X1)) ) ),
    inference(flattening,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ( member(X0,power_class(X1))
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class) )
      & ( ( subclass(X0,X1)
          & member(X0,universal_class) )
        | ~ member(X0,power_class(X1)) ) ),
    inference(nnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( member(X0,power_class(X1))
    <=> ( subclass(X0,X1)
        & member(X0,universal_class) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,axiom,
    ! [X2,X0] :
      ( member(X2,power_class(X0))
    <=> ( subclass(X2,X0)
        & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_defn) ).

fof(f377,plain,
    spl7_25,
    inference(avatar_split_clause,[],[f179,f375]) ).

fof(f375,plain,
    ( spl7_25
  <=> ! [X0,X1] :
        ( member(X0,universal_class)
        | ~ member(X0,power_class(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_25])]) ).

fof(f179,plain,
    ! [X0,X1] :
      ( member(X0,universal_class)
      | ~ member(X0,power_class(X1)) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f373,plain,
    spl7_24,
    inference(avatar_split_clause,[],[f177,f371]) ).

fof(f371,plain,
    ( spl7_24
  <=> ! [X0,X1] :
        ( ~ member(X1,X0)
        | ~ member(X1,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_24])]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( ~ member(X1,X0)
      | ~ member(X1,complement(X0)) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ( member(X1,complement(X0))
        | member(X1,X0)
        | ~ member(X1,universal_class) )
      & ( ( ~ member(X1,X0)
          & member(X1,universal_class) )
        | ~ member(X1,complement(X0)) ) ),
    inference(flattening,[],[f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ( member(X1,complement(X0))
        | member(X1,X0)
        | ~ member(X1,universal_class) )
      & ( ( ~ member(X1,X0)
          & member(X1,universal_class) )
        | ~ member(X1,complement(X0)) ) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( member(X1,complement(X0))
    <=> ( ~ member(X1,X0)
        & member(X1,universal_class) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X4] :
      ( member(X4,complement(X0))
    <=> ( ~ member(X4,X0)
        & member(X4,universal_class) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).

fof(f369,plain,
    spl7_23,
    inference(avatar_split_clause,[],[f176,f367]) ).

fof(f367,plain,
    ( spl7_23
  <=> ! [X0,X1] :
        ( member(X1,universal_class)
        | ~ member(X1,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_23])]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( member(X1,universal_class)
      | ~ member(X1,complement(X0)) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f365,plain,
    ( spl7_22
    | ~ spl7_2
    | ~ spl7_12 ),
    inference(avatar_split_clause,[],[f328,f320,f274,f362]) ).

fof(f362,plain,
    ( spl7_22
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_22])]) ).

fof(f320,plain,
    ( spl7_12
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).

fof(f328,plain,
    ( member(null_class,universal_class)
    | ~ spl7_2
    | ~ spl7_12 ),
    inference(superposition,[],[f321,f276]) ).

fof(f321,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl7_12 ),
    inference(avatar_component_clause,[],[f320]) ).

fof(f360,plain,
    spl7_21,
    inference(avatar_split_clause,[],[f162,f358]) ).

fof(f358,plain,
    ( spl7_21
  <=> ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_21])]) ).

fof(f162,plain,
    ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
    inference(rectify,[],[f35]) ).

fof(f35,axiom,
    ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn1) ).

fof(f356,plain,
    spl7_20,
    inference(avatar_split_clause,[],[f158,f354]) ).

fof(f354,plain,
    ( spl7_20
  <=> ! [X0] :
        ( member(sK2(X0),universal_class)
        | ~ member(X0,identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_20])]) ).

fof(f158,plain,
    ! [X0] :
      ( member(sK2(X0),universal_class)
      | ~ member(X0,identity_relation) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0] :
      ( ( member(X0,identity_relation)
        | ! [X1] :
            ( ordered_pair(X1,X1) != X0
            | ~ member(X1,universal_class) ) )
      & ( ( ordered_pair(sK2(X0),sK2(X0)) = X0
          & member(sK2(X0),universal_class) )
        | ~ member(X0,identity_relation) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f94,f95]) ).

fof(f95,plain,
    ! [X0] :
      ( ? [X2] :
          ( ordered_pair(X2,X2) = X0
          & member(X2,universal_class) )
     => ( ordered_pair(sK2(X0),sK2(X0)) = X0
        & member(sK2(X0),universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ! [X0] :
      ( ( member(X0,identity_relation)
        | ! [X1] :
            ( ordered_pair(X1,X1) != X0
            | ~ member(X1,universal_class) ) )
      & ( ? [X2] :
            ( ordered_pair(X2,X2) = X0
            & member(X2,universal_class) )
        | ~ member(X0,identity_relation) ) ),
    inference(rectify,[],[f93]) ).

fof(f93,plain,
    ! [X0] :
      ( ( member(X0,identity_relation)
        | ! [X1] :
            ( ordered_pair(X1,X1) != X0
            | ~ member(X1,universal_class) ) )
      & ( ? [X1] :
            ( ordered_pair(X1,X1) = X0
            & member(X1,universal_class) )
        | ~ member(X0,identity_relation) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( member(X0,identity_relation)
    <=> ? [X1] :
          ( ordered_pair(X1,X1) = X0
          & member(X1,universal_class) ) ),
    inference(rectify,[],[f37]) ).

fof(f37,axiom,
    ! [X4] :
      ( member(X4,identity_relation)
    <=> ? [X0] :
          ( ordered_pair(X0,X0) = X4
          & member(X0,universal_class) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).

fof(f352,plain,
    spl7_19,
    inference(avatar_split_clause,[],[f155,f350]) ).

fof(f350,plain,
    ( spl7_19
  <=> ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_19])]) ).

fof(f155,plain,
    ! [X0] :
      ( subclass(X0,cross_product(universal_class,universal_class))
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ( function(X0)
        | ~ subclass(compose(X0,inverse(X0)),identity_relation)
        | ~ subclass(X0,cross_product(universal_class,universal_class)) )
      & ( ( subclass(compose(X0,inverse(X0)),identity_relation)
          & subclass(X0,cross_product(universal_class,universal_class)) )
        | ~ function(X0) ) ),
    inference(flattening,[],[f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ( function(X0)
        | ~ subclass(compose(X0,inverse(X0)),identity_relation)
        | ~ subclass(X0,cross_product(universal_class,universal_class)) )
      & ( ( subclass(compose(X0,inverse(X0)),identity_relation)
          & subclass(X0,cross_product(universal_class,universal_class)) )
        | ~ function(X0) ) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( function(X0)
    <=> ( subclass(compose(X0,inverse(X0)),identity_relation)
        & subclass(X0,cross_product(universal_class,universal_class)) ) ),
    inference(rectify,[],[f38]) ).

fof(f38,axiom,
    ! [X8] :
      ( function(X8)
    <=> ( subclass(compose(X8,inverse(X8)),identity_relation)
        & subclass(X8,cross_product(universal_class,universal_class)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',function_defn) ).

fof(f348,plain,
    spl7_18,
    inference(avatar_split_clause,[],[f151,f346]) ).

fof(f346,plain,
    ( spl7_18
  <=> ! [X0] :
        ( member(sum_class(X0),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_18])]) ).

fof(f151,plain,
    ! [X0] :
      ( member(sum_class(X0),universal_class)
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( member(sum_class(X0),universal_class)
      | ~ member(X0,universal_class) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0] :
      ( member(X0,universal_class)
     => member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class) ).

fof(f344,plain,
    spl7_17,
    inference(avatar_split_clause,[],[f150,f342]) ).

fof(f342,plain,
    ( spl7_17
  <=> ! [X0] :
        ( member(power_class(X0),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_17])]) ).

fof(f150,plain,
    ! [X0] :
      ( member(power_class(X0),universal_class)
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( member(power_class(X0),universal_class)
      | ~ member(X0,universal_class) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( member(X0,universal_class)
     => member(power_class(X0),universal_class) ),
    inference(rectify,[],[f34]) ).

fof(f34,axiom,
    ! [X2] :
      ( member(X2,universal_class)
     => member(power_class(X2),universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class) ).

fof(f340,plain,
    spl7_16,
    inference(avatar_split_clause,[],[f149,f338]) ).

fof(f338,plain,
    ( spl7_16
  <=> ! [X0] :
        ( disjoint(sK1(X0),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_16])]) ).

fof(f149,plain,
    ! [X0] :
      ( disjoint(sK1(X0),X0)
      | null_class = X0 ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ( disjoint(sK1(X0),X0)
        & member(sK1(X0),X0)
        & member(sK1(X0),universal_class) )
      | null_class = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f72,f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ? [X1] :
          ( disjoint(X1,X0)
          & member(X1,X0)
          & member(X1,universal_class) )
     => ( disjoint(sK1(X0),X0)
        & member(sK1(X0),X0)
        & member(sK1(X0),universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0] :
      ( ? [X1] :
          ( disjoint(X1,X0)
          & member(X1,X0)
          & member(X1,universal_class) )
      | null_class = X0 ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( null_class != X0
     => ? [X1] :
          ( disjoint(X1,X0)
          & member(X1,X0)
          & member(X1,universal_class) ) ),
    inference(rectify,[],[f41]) ).

fof(f41,axiom,
    ! [X0] :
      ( null_class != X0
     => ? [X2] :
          ( disjoint(X2,X0)
          & member(X2,X0)
          & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity) ).

fof(f336,plain,
    spl7_15,
    inference(avatar_split_clause,[],[f148,f334]) ).

fof(f334,plain,
    ( spl7_15
  <=> ! [X0] :
        ( member(sK1(X0),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_15])]) ).

fof(f148,plain,
    ! [X0] :
      ( member(sK1(X0),X0)
      | null_class = X0 ),
    inference(cnf_transformation,[],[f88]) ).

fof(f332,plain,
    spl7_14,
    inference(avatar_split_clause,[],[f147,f330]) ).

fof(f330,plain,
    ( spl7_14
  <=> ! [X0] :
        ( member(sK1(X0),universal_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_14])]) ).

fof(f147,plain,
    ! [X0] :
      ( member(sK1(X0),universal_class)
      | null_class = X0 ),
    inference(cnf_transformation,[],[f88]) ).

fof(f326,plain,
    spl7_13,
    inference(avatar_split_clause,[],[f223,f324]) ).

fof(f324,plain,
    ( spl7_13
  <=> ! [X1] :
        ( subclass(sK6,X1)
        | ~ inductive(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_13])]) ).

fof(f223,plain,
    ! [X1] :
      ( subclass(sK6,X1)
      | ~ inductive(X1) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ( ! [X1] :
        ( subclass(sK6,X1)
        | ~ inductive(X1) )
    & inductive(sK6)
    & member(sK6,universal_class) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f84,f133]) ).

fof(f133,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( subclass(X0,X1)
            | ~ inductive(X1) )
        & inductive(X0)
        & member(X0,universal_class) )
   => ( ! [X1] :
          ( subclass(sK6,X1)
          | ~ inductive(X1) )
      & inductive(sK6)
      & member(sK6,universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ? [X0] :
      ( ! [X1] :
          ( subclass(X0,X1)
          | ~ inductive(X1) )
      & inductive(X0)
      & member(X0,universal_class) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ? [X0] :
      ( ! [X1] :
          ( inductive(X1)
         => subclass(X0,X1) )
      & inductive(X0)
      & member(X0,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity) ).

fof(f322,plain,
    spl7_12,
    inference(avatar_split_clause,[],[f161,f320]) ).

fof(f161,plain,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).

fof(f318,plain,
    spl7_11,
    inference(avatar_split_clause,[],[f152,f316]) ).

fof(f152,plain,
    ! [X0] :
      ( member(null_class,X0)
      | ~ inductive(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0] :
      ( ( inductive(X0)
        | ~ subclass(image(successor_relation,X0),X0)
        | ~ member(null_class,X0) )
      & ( ( subclass(image(successor_relation,X0),X0)
          & member(null_class,X0) )
        | ~ inductive(X0) ) ),
    inference(flattening,[],[f89]) ).

fof(f89,plain,
    ! [X0] :
      ( ( inductive(X0)
        | ~ subclass(image(successor_relation,X0),X0)
        | ~ member(null_class,X0) )
      & ( ( subclass(image(successor_relation,X0),X0)
          & member(null_class,X0) )
        | ~ inductive(X0) ) ),
    inference(nnf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0] :
      ( inductive(X0)
    <=> ( subclass(image(successor_relation,X0),X0)
        & member(null_class,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive_defn) ).

fof(f314,plain,
    spl7_10,
    inference(avatar_split_clause,[],[f138,f311]) ).

fof(f311,plain,
    ( spl7_10
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_10])]) ).

fof(f138,plain,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn1) ).

fof(f309,plain,
    spl7_9,
    inference(avatar_split_clause,[],[f137,f306]) ).

fof(f306,plain,
    ( spl7_9
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_9])]) ).

fof(f137,plain,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation) ).

fof(f304,plain,
    spl7_8,
    inference(avatar_split_clause,[],[f263,f302]) ).

fof(f302,plain,
    ( spl7_8
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).

fof(f263,plain,
    ! [X1] : subclass(X1,X1),
    inference(equality_resolution,[],[f170]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( subclass(X1,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f98]) ).

fof(f300,plain,
    spl7_7,
    inference(avatar_split_clause,[],[f221,f297]) ).

fof(f297,plain,
    ( spl7_7
  <=> member(sK6,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).

fof(f221,plain,
    member(sK6,universal_class),
    inference(cnf_transformation,[],[f134]) ).

fof(f295,plain,
    spl7_6,
    inference(avatar_split_clause,[],[f140,f293]) ).

fof(f293,plain,
    ( spl7_6
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).

fof(f140,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f291,plain,
    spl7_5,
    inference(avatar_split_clause,[],[f139,f289]) ).

fof(f139,plain,
    ! [X0] : ~ member(X0,null_class),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] : ~ member(X0,null_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).

fof(f287,plain,
    spl7_4,
    inference(avatar_split_clause,[],[f222,f284]) ).

fof(f284,plain,
    ( spl7_4
  <=> inductive(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).

fof(f222,plain,
    inductive(sK6),
    inference(cnf_transformation,[],[f134]) ).

fof(f282,plain,
    spl7_3,
    inference(avatar_split_clause,[],[f219,f279]) ).

fof(f279,plain,
    ( spl7_3
  <=> function(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).

fof(f219,plain,
    function(sK5),
    inference(cnf_transformation,[],[f132]) ).

fof(f132,plain,
    ( ! [X1] :
        ( member(apply(sK5,X1),X1)
        | null_class = X1
        | ~ member(X1,universal_class) )
    & function(sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f83,f131]) ).

fof(f131,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( member(apply(X0,X1),X1)
            | null_class = X1
            | ~ member(X1,universal_class) )
        & function(X0) )
   => ( ! [X1] :
          ( member(apply(sK5,X1),X1)
          | null_class = X1
          | ~ member(X1,universal_class) )
      & function(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ? [X0] :
      ( ! [X1] :
          ( member(apply(X0,X1),X1)
          | null_class = X1
          | ~ member(X1,universal_class) )
      & function(X0) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ? [X0] :
      ( ! [X1] :
          ( member(apply(X0,X1),X1)
          | null_class = X1
          | ~ member(X1,universal_class) )
      & function(X0) ),
    inference(ennf_transformation,[],[f69]) ).

fof(f69,plain,
    ? [X0] :
      ( ! [X1] :
          ( member(X1,universal_class)
         => ( member(apply(X0,X1),X1)
            | null_class = X1 ) )
      & function(X0) ),
    inference(rectify,[],[f43]) ).

fof(f43,axiom,
    ? [X8] :
      ( ! [X1] :
          ( member(X1,universal_class)
         => ( member(apply(X8,X1),X1)
            | null_class = X1 ) )
      & function(X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice) ).

fof(f277,plain,
    spl7_2,
    inference(avatar_split_clause,[],[f229,f274]) ).

fof(f229,plain,
    null_class = unordered_pair(sK0,sK0),
    inference(definition_unfolding,[],[f136,f142]) ).

fof(f142,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).

fof(f136,plain,
    null_class = singleton(sK0),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ( null_class = singleton(sK0)
    & member(sK0,universal_class) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f71,f85]) ).

fof(f85,plain,
    ( ? [X0] :
        ( singleton(X0) = null_class
        & member(X0,universal_class) )
   => ( null_class = singleton(sK0)
      & member(sK0,universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ? [X0] :
      ( singleton(X0) = null_class
      & member(X0,universal_class) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0] :
        ( member(X0,universal_class)
       => singleton(X0) != null_class ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0] :
      ( member(X0,universal_class)
     => singleton(X0) != null_class ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).

fof(f272,plain,
    spl7_1,
    inference(avatar_split_clause,[],[f135,f269]) ).

fof(f135,plain,
    member(sK0,universal_class),
    inference(cnf_transformation,[],[f86]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET079+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n011.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Apr 30 01:21:16 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.34  % (14458)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (14463)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)
% 0.14/0.36  % (14461)WARNING: value z3 for option sas not known
% 0.14/0.36  % (14463)First to succeed.
% 0.14/0.36  % (14459)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36  % (14461)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)
% 0.14/0.36  % (14462)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36  % (14460)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.36  % (14464)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)
% 0.14/0.36  % (14465)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)
% 0.19/0.36  % (14463)Refutation found. Thanks to Tanya!
% 0.19/0.36  % SZS status Theorem for theBenchmark
% 0.19/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.37  % (14463)------------------------------
% 0.19/0.37  % (14463)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.37  % (14463)Termination reason: Refutation
% 0.19/0.37  
% 0.19/0.37  % (14463)Memory used [KB]: 1036
% 0.19/0.37  % (14463)Time elapsed: 0.009 s
% 0.19/0.37  % (14463)Instructions burned: 20 (million)
% 0.19/0.37  % (14463)------------------------------
% 0.19/0.37  % (14463)------------------------------
% 0.19/0.37  % (14458)Success in time 0.02 s
%------------------------------------------------------------------------------