TSTP Solution File: SEU040+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU040+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n007.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 03:52:48 EDT 2024

% Result   : Theorem 0.23s 0.40s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  105
% Syntax   : Number of formulae    :  273 (  86 unt;   0 def)
%            Number of atoms       :  592 (   8 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  511 ( 192   ~; 154   |;  77   &)
%                                         (  57 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   66 (  64 usr;  57 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  11 con; 0-2 aty)
%            Number of variables   :  227 ( 197   !;  30   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f471,plain,
    $false,
    inference(avatar_sat_refutation,[],[f160,f165,f170,f175,f180,f185,f190,f195,f200,f205,f210,f215,f220,f225,f230,f235,f240,f245,f250,f255,f259,f263,f267,f276,f280,f284,f288,f302,f307,f311,f315,f319,f323,f327,f331,f335,f351,f359,f363,f367,f372,f377,f381,f385,f389,f393,f397,f404,f424,f428,f432,f442,f446,f450,f462,f469,f470]) ).

fof(f470,plain,
    ( ~ spl13_1
    | spl13_25
    | ~ spl13_54 ),
    inference(avatar_split_clause,[],[f452,f444,f273,f157]) ).

fof(f157,plain,
    ( spl13_1
  <=> relation(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).

fof(f273,plain,
    ( spl13_25
  <=> subset(relation_rng(relation_dom_restriction(sK1,sK0)),relation_rng(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).

fof(f444,plain,
    ( spl13_54
  <=> ! [X0,X1] :
        ( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_54])]) ).

fof(f452,plain,
    ( ~ relation(sK1)
    | spl13_25
    | ~ spl13_54 ),
    inference(resolution,[],[f445,f275]) ).

fof(f275,plain,
    ( ~ subset(relation_rng(relation_dom_restriction(sK1,sK0)),relation_rng(sK1))
    | spl13_25 ),
    inference(avatar_component_clause,[],[f273]) ).

fof(f445,plain,
    ( ! [X0,X1] :
        ( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
        | ~ relation(X1) )
    | ~ spl13_54 ),
    inference(avatar_component_clause,[],[f444]) ).

fof(f469,plain,
    ( ~ spl13_1
    | spl13_24
    | ~ spl13_53 ),
    inference(avatar_split_clause,[],[f451,f440,f269,f157]) ).

fof(f269,plain,
    ( spl13_24
  <=> subset(relation_dom(relation_dom_restriction(sK1,sK0)),relation_dom(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).

fof(f440,plain,
    ( spl13_53
  <=> ! [X0,X1] :
        ( subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1))
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_53])]) ).

fof(f451,plain,
    ( ~ relation(sK1)
    | spl13_24
    | ~ spl13_53 ),
    inference(resolution,[],[f441,f271]) ).

fof(f271,plain,
    ( ~ subset(relation_dom(relation_dom_restriction(sK1,sK0)),relation_dom(sK1))
    | spl13_24 ),
    inference(avatar_component_clause,[],[f269]) ).

fof(f441,plain,
    ( ! [X0,X1] :
        ( subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1))
        | ~ relation(X1) )
    | ~ spl13_53 ),
    inference(avatar_component_clause,[],[f440]) ).

fof(f462,plain,
    spl13_56,
    inference(avatar_split_clause,[],[f139,f460]) ).

fof(f460,plain,
    ( spl13_56
  <=> ! [X2,X0,X1] :
        ( element(X0,X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_56])]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

fof(f450,plain,
    spl13_55,
    inference(avatar_split_clause,[],[f140,f448]) ).

fof(f448,plain,
    ( spl13_55
  <=> ! [X2,X0,X1] :
        ( ~ empty(X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_55])]) ).

fof(f140,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

fof(f446,plain,
    spl13_54,
    inference(avatar_split_clause,[],[f127,f444]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1] :
      ( relation(X1)
     => subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).

fof(f442,plain,
    spl13_53,
    inference(avatar_split_clause,[],[f126,f440]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1))
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1))
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0,X1] :
      ( relation(X1)
     => subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_relat_1) ).

fof(f432,plain,
    spl13_52,
    inference(avatar_split_clause,[],[f134,f430]) ).

fof(f430,plain,
    ( spl13_52
  <=> ! [X0,X1] :
        ( function(relation_dom_restriction(X0,X1))
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_52])]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( function(relation_dom_restriction(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0,X1] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(f428,plain,
    spl13_51,
    inference(avatar_split_clause,[],[f132,f426]) ).

fof(f426,plain,
    ( spl13_51
  <=> ! [X0,X1] :
        ( relation_empty_yielding(relation_dom_restriction(X0,X1))
        | ~ relation_empty_yielding(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_51])]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( relation_empty_yielding(relation_dom_restriction(X0,X1))
      | ~ relation_empty_yielding(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ relation_empty_yielding(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ relation_empty_yielding(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ( relation_empty_yielding(X0)
        & relation(X0) )
     => ( relation_empty_yielding(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).

fof(f424,plain,
    spl13_50,
    inference(avatar_split_clause,[],[f130,f422]) ).

fof(f422,plain,
    ( spl13_50
  <=> ! [X0,X1] :
        ( in(X0,X1)
        | empty(X1)
        | ~ element(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_50])]) ).

fof(f130,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f404,plain,
    ( spl13_49
    | ~ spl13_7
    | ~ spl13_27 ),
    inference(avatar_split_clause,[],[f296,f282,f187,f401]) ).

fof(f401,plain,
    ( spl13_49
  <=> relation(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_49])]) ).

fof(f187,plain,
    ( spl13_7
  <=> empty(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).

fof(f282,plain,
    ( spl13_27
  <=> ! [X0] :
        ( relation(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).

fof(f296,plain,
    ( relation(sK6)
    | ~ spl13_7
    | ~ spl13_27 ),
    inference(resolution,[],[f283,f189]) ).

fof(f189,plain,
    ( empty(sK6)
    | ~ spl13_7 ),
    inference(avatar_component_clause,[],[f187]) ).

fof(f283,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation(X0) )
    | ~ spl13_27 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f397,plain,
    spl13_48,
    inference(avatar_split_clause,[],[f137,f395]) ).

fof(f395,plain,
    ( spl13_48
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_48])]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

fof(f393,plain,
    spl13_47,
    inference(avatar_split_clause,[],[f136,f391]) ).

fof(f391,plain,
    ( spl13_47
  <=> ! [X0,X1] :
        ( element(X0,powerset(X1))
        | ~ subset(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_47])]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

fof(f389,plain,
    spl13_46,
    inference(avatar_split_clause,[],[f135,f387]) ).

fof(f387,plain,
    ( spl13_46
  <=> ! [X0,X1] :
        ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_46])]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f385,plain,
    spl13_45,
    inference(avatar_split_clause,[],[f118,f383]) ).

fof(f383,plain,
    ( spl13_45
  <=> ! [X0] :
        ( ~ empty(relation_rng(X0))
        | ~ relation(X0)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_45])]) ).

fof(f118,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_rng(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).

fof(f381,plain,
    spl13_44,
    inference(avatar_split_clause,[],[f117,f379]) ).

fof(f379,plain,
    ( spl13_44
  <=> ! [X0] :
        ( ~ empty(relation_dom(X0))
        | ~ relation(X0)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_44])]) ).

fof(f117,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_dom(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).

fof(f377,plain,
    spl13_43,
    inference(avatar_split_clause,[],[f108,f375]) ).

fof(f375,plain,
    ( spl13_43
  <=> ! [X0] :
        ( element(sK2(X0),powerset(X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_43])]) ).

fof(f108,plain,
    ! [X0] :
      ( element(sK2(X0),powerset(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0] :
      ( ( ~ empty(sK2(X0))
        & element(sK2(X0),powerset(X0)) )
      | empty(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f45,f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
     => ( ~ empty(sK2(X0))
        & element(sK2(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
      | empty(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ~ empty(X0)
     => ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).

fof(f372,plain,
    ( spl13_42
    | ~ spl13_10
    | ~ spl13_26 ),
    inference(avatar_split_clause,[],[f292,f278,f202,f369]) ).

fof(f369,plain,
    ( spl13_42
  <=> function(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_42])]) ).

fof(f202,plain,
    ( spl13_10
  <=> empty(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).

fof(f278,plain,
    ( spl13_26
  <=> ! [X0] :
        ( function(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).

fof(f292,plain,
    ( function(sK8)
    | ~ spl13_10
    | ~ spl13_26 ),
    inference(resolution,[],[f279,f204]) ).

fof(f204,plain,
    ( empty(sK8)
    | ~ spl13_10 ),
    inference(avatar_component_clause,[],[f202]) ).

fof(f279,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(X0) )
    | ~ spl13_26 ),
    inference(avatar_component_clause,[],[f278]) ).

fof(f367,plain,
    spl13_41,
    inference(avatar_split_clause,[],[f129,f365]) ).

fof(f365,plain,
    ( spl13_41
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

fof(f363,plain,
    spl13_40,
    inference(avatar_split_clause,[],[f128,f361]) ).

fof(f361,plain,
    ( spl13_40
  <=> ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f359,plain,
    spl13_39,
    inference(avatar_split_clause,[],[f125,f357]) ).

fof(f357,plain,
    ( spl13_39
  <=> ! [X0,X1] :
        ( relation(relation_dom_restriction(X0,X1))
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( relation(X0)
     => relation(relation_dom_restriction(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).

fof(f351,plain,
    ( spl13_38
    | ~ spl13_7
    | ~ spl13_26 ),
    inference(avatar_split_clause,[],[f291,f278,f187,f348]) ).

fof(f348,plain,
    ( spl13_38
  <=> function(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).

fof(f291,plain,
    ( function(sK6)
    | ~ spl13_7
    | ~ spl13_26 ),
    inference(resolution,[],[f279,f189]) ).

fof(f335,plain,
    spl13_37,
    inference(avatar_split_clause,[],[f138,f333]) ).

fof(f333,plain,
    ( spl13_37
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(f331,plain,
    spl13_36,
    inference(avatar_split_clause,[],[f122,f329]) ).

fof(f329,plain,
    ( spl13_36
  <=> ! [X0] : element(sK4(X0),powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).

fof(f122,plain,
    ! [X0] : element(sK4(X0),powerset(X0)),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0] :
      ( empty(sK4(X0))
      & element(sK4(X0),powerset(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f29,f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ? [X1] :
          ( empty(X1)
          & element(X1,powerset(X0)) )
     => ( empty(sK4(X0))
        & element(sK4(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,axiom,
    ! [X0] :
    ? [X1] :
      ( empty(X1)
      & element(X1,powerset(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

fof(f327,plain,
    spl13_35,
    inference(avatar_split_clause,[],[f116,f325]) ).

fof(f325,plain,
    ( spl13_35
  <=> ! [X0] :
        ( relation(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).

fof(f116,plain,
    ! [X0] :
      ( relation(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).

fof(f323,plain,
    spl13_34,
    inference(avatar_split_clause,[],[f115,f321]) ).

fof(f321,plain,
    ( spl13_34
  <=> ! [X0] :
        ( empty(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).

fof(f115,plain,
    ! [X0] :
      ( empty(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f319,plain,
    spl13_33,
    inference(avatar_split_clause,[],[f114,f317]) ).

fof(f317,plain,
    ( spl13_33
  <=> ! [X0] :
        ( relation(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).

fof(f114,plain,
    ! [X0] :
      ( relation(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).

fof(f315,plain,
    spl13_32,
    inference(avatar_split_clause,[],[f113,f313]) ).

fof(f313,plain,
    ( spl13_32
  <=> ! [X0] :
        ( empty(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_32])]) ).

fof(f113,plain,
    ! [X0] :
      ( empty(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f311,plain,
    spl13_31,
    inference(avatar_split_clause,[],[f112,f309]) ).

fof(f309,plain,
    ( spl13_31
  <=> ! [X0] :
        ( empty_set = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_31])]) ).

fof(f112,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(f307,plain,
    ( spl13_30
    | ~ spl13_3
    | ~ spl13_26 ),
    inference(avatar_split_clause,[],[f289,f278,f167,f304]) ).

fof(f304,plain,
    ( spl13_30
  <=> function(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_30])]) ).

fof(f167,plain,
    ( spl13_3
  <=> empty(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).

fof(f289,plain,
    ( function(empty_set)
    | ~ spl13_3
    | ~ spl13_26 ),
    inference(resolution,[],[f279,f169]) ).

fof(f169,plain,
    ( empty(empty_set)
    | ~ spl13_3 ),
    inference(avatar_component_clause,[],[f167]) ).

fof(f302,plain,
    spl13_29,
    inference(avatar_split_clause,[],[f109,f300]) ).

fof(f300,plain,
    ( spl13_29
  <=> ! [X0] :
        ( ~ empty(sK2(X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).

fof(f109,plain,
    ! [X0] :
      ( ~ empty(sK2(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f288,plain,
    spl13_28,
    inference(avatar_split_clause,[],[f121,f286]) ).

fof(f286,plain,
    ( spl13_28
  <=> ! [X0] : element(sK3(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).

fof(f121,plain,
    ! [X0] : element(sK3(X0),X0),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0] : element(sK3(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f9,f77]) ).

fof(f77,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK3(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f9,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f284,plain,
    spl13_27,
    inference(avatar_split_clause,[],[f111,f282]) ).

fof(f111,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( empty(X0)
     => relation(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).

fof(f280,plain,
    spl13_26,
    inference(avatar_split_clause,[],[f110,f278]) ).

fof(f110,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( empty(X0)
     => function(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).

fof(f276,plain,
    ( ~ spl13_24
    | ~ spl13_25 ),
    inference(avatar_split_clause,[],[f100,f273,f269]) ).

fof(f100,plain,
    ( ~ subset(relation_rng(relation_dom_restriction(sK1,sK0)),relation_rng(sK1))
    | ~ subset(relation_dom(relation_dom_restriction(sK1,sK0)),relation_dom(sK1)) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ( ( ~ subset(relation_rng(relation_dom_restriction(sK1,sK0)),relation_rng(sK1))
      | ~ subset(relation_dom(relation_dom_restriction(sK1,sK0)),relation_dom(sK1)) )
    & function(sK1)
    & relation(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f44,f73]) ).

fof(f73,plain,
    ( ? [X0,X1] :
        ( ( ~ subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
          | ~ subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1)) )
        & function(X1)
        & relation(X1) )
   => ( ( ~ subset(relation_rng(relation_dom_restriction(sK1,sK0)),relation_rng(sK1))
        | ~ subset(relation_dom(relation_dom_restriction(sK1,sK0)),relation_dom(sK1)) )
      & function(sK1)
      & relation(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ? [X0,X1] :
      ( ( ~ subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
        | ~ subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1)) )
      & function(X1)
      & relation(X1) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ? [X0,X1] :
      ( ( ~ subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
        | ~ subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1)) )
      & function(X1)
      & relation(X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( function(X1)
          & relation(X1) )
       => ( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
          & subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1)) ) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
        & subset(relation_dom(relation_dom_restriction(X1,X0)),relation_dom(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funct_1) ).

fof(f267,plain,
    spl13_23,
    inference(avatar_split_clause,[],[f124,f265]) ).

fof(f265,plain,
    ( spl13_23
  <=> ! [X0] : subset(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).

fof(f124,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f263,plain,
    spl13_22,
    inference(avatar_split_clause,[],[f123,f261]) ).

fof(f261,plain,
    ( spl13_22
  <=> ! [X0] : empty(sK4(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).

fof(f123,plain,
    ! [X0] : empty(sK4(X0)),
    inference(cnf_transformation,[],[f80]) ).

fof(f259,plain,
    spl13_21,
    inference(avatar_split_clause,[],[f107,f257]) ).

fof(f257,plain,
    ( spl13_21
  <=> ! [X0] : ~ empty(powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).

fof(f107,plain,
    ! [X0] : ~ empty(powerset(X0)),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] : ~ empty(powerset(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

fof(f255,plain,
    spl13_20,
    inference(avatar_split_clause,[],[f155,f252]) ).

fof(f252,plain,
    ( spl13_20
  <=> function(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).

fof(f155,plain,
    function(sK12),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ( function(sK12)
    & empty(sK12)
    & relation(sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f26,f96]) ).

fof(f96,plain,
    ( ? [X0] :
        ( function(X0)
        & empty(X0)
        & relation(X0) )
   => ( function(sK12)
      & empty(sK12)
      & relation(sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,axiom,
    ? [X0] :
      ( function(X0)
      & empty(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

fof(f250,plain,
    spl13_19,
    inference(avatar_split_clause,[],[f154,f247]) ).

fof(f247,plain,
    ( spl13_19
  <=> empty(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).

fof(f154,plain,
    empty(sK12),
    inference(cnf_transformation,[],[f97]) ).

fof(f245,plain,
    spl13_18,
    inference(avatar_split_clause,[],[f153,f242]) ).

fof(f242,plain,
    ( spl13_18
  <=> relation(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).

fof(f153,plain,
    relation(sK12),
    inference(cnf_transformation,[],[f97]) ).

fof(f240,plain,
    spl13_17,
    inference(avatar_split_clause,[],[f152,f237]) ).

fof(f237,plain,
    ( spl13_17
  <=> function(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).

fof(f152,plain,
    function(sK11),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ( function(sK11)
    & relation(sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f42,f94]) ).

fof(f94,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK11)
      & relation(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    inference(pure_predicate_removal,[],[f27]) ).

fof(f27,axiom,
    ? [X0] :
      ( one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).

fof(f235,plain,
    spl13_16,
    inference(avatar_split_clause,[],[f151,f232]) ).

fof(f232,plain,
    ( spl13_16
  <=> relation(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).

fof(f151,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f95]) ).

fof(f230,plain,
    spl13_15,
    inference(avatar_split_clause,[],[f150,f227]) ).

fof(f227,plain,
    ( spl13_15
  <=> function(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).

fof(f150,plain,
    function(sK10),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ( function(sK10)
    & relation(sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f25,f92]) ).

fof(f92,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK10)
      & relation(sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,axiom,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

fof(f225,plain,
    spl13_14,
    inference(avatar_split_clause,[],[f149,f222]) ).

fof(f222,plain,
    ( spl13_14
  <=> relation(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).

fof(f149,plain,
    relation(sK10),
    inference(cnf_transformation,[],[f93]) ).

fof(f220,plain,
    spl13_13,
    inference(avatar_split_clause,[],[f148,f217]) ).

fof(f217,plain,
    ( spl13_13
  <=> relation_empty_yielding(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).

fof(f148,plain,
    relation_empty_yielding(sK9),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ( relation_empty_yielding(sK9)
    & relation(sK9) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f32,f90]) ).

fof(f90,plain,
    ( ? [X0] :
        ( relation_empty_yielding(X0)
        & relation(X0) )
   => ( relation_empty_yielding(sK9)
      & relation(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,axiom,
    ? [X0] :
      ( relation_empty_yielding(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).

fof(f215,plain,
    spl13_12,
    inference(avatar_split_clause,[],[f147,f212]) ).

fof(f212,plain,
    ( spl13_12
  <=> relation(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).

fof(f147,plain,
    relation(sK9),
    inference(cnf_transformation,[],[f91]) ).

fof(f210,plain,
    spl13_11,
    inference(avatar_split_clause,[],[f146,f207]) ).

fof(f207,plain,
    ( spl13_11
  <=> relation(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).

fof(f146,plain,
    relation(sK8),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ( relation(sK8)
    & empty(sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f30,f88]) ).

fof(f88,plain,
    ( ? [X0] :
        ( relation(X0)
        & empty(X0) )
   => ( relation(sK8)
      & empty(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,axiom,
    ? [X0] :
      ( relation(X0)
      & empty(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

fof(f205,plain,
    spl13_10,
    inference(avatar_split_clause,[],[f145,f202]) ).

fof(f145,plain,
    empty(sK8),
    inference(cnf_transformation,[],[f89]) ).

fof(f200,plain,
    spl13_9,
    inference(avatar_split_clause,[],[f144,f197]) ).

fof(f197,plain,
    ( spl13_9
  <=> relation(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).

fof(f144,plain,
    relation(sK7),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ( relation(sK7)
    & ~ empty(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f31,f86]) ).

fof(f86,plain,
    ( ? [X0] :
        ( relation(X0)
        & ~ empty(X0) )
   => ( relation(sK7)
      & ~ empty(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,axiom,
    ? [X0] :
      ( relation(X0)
      & ~ empty(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).

fof(f195,plain,
    ~ spl13_8,
    inference(avatar_split_clause,[],[f143,f192]) ).

fof(f192,plain,
    ( spl13_8
  <=> empty(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).

fof(f143,plain,
    ~ empty(sK7),
    inference(cnf_transformation,[],[f87]) ).

fof(f190,plain,
    spl13_7,
    inference(avatar_split_clause,[],[f142,f187]) ).

fof(f142,plain,
    empty(sK6),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    empty(sK6),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f33,f84]) ).

fof(f84,plain,
    ( ? [X0] : empty(X0)
   => empty(sK6) ),
    introduced(choice_axiom,[]) ).

fof(f33,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f185,plain,
    ~ spl13_6,
    inference(avatar_split_clause,[],[f141,f182]) ).

fof(f182,plain,
    ( spl13_6
  <=> empty(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).

fof(f141,plain,
    ~ empty(sK5),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ~ empty(sK5),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f34,f82]) ).

fof(f82,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK5) ),
    introduced(choice_axiom,[]) ).

fof(f34,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f180,plain,
    spl13_5,
    inference(avatar_split_clause,[],[f106,f177]) ).

fof(f177,plain,
    ( spl13_5
  <=> relation_empty_yielding(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).

fof(f106,plain,
    relation_empty_yielding(empty_set),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ( relation_empty_yielding(empty_set)
    & relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).

fof(f175,plain,
    spl13_4,
    inference(avatar_split_clause,[],[f103,f172]) ).

fof(f172,plain,
    ( spl13_4
  <=> relation(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).

fof(f103,plain,
    relation(empty_set),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f170,plain,
    spl13_3,
    inference(avatar_split_clause,[],[f101,f167]) ).

fof(f101,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f165,plain,
    spl13_2,
    inference(avatar_split_clause,[],[f99,f162]) ).

fof(f162,plain,
    ( spl13_2
  <=> function(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).

fof(f99,plain,
    function(sK1),
    inference(cnf_transformation,[],[f74]) ).

fof(f160,plain,
    spl13_1,
    inference(avatar_split_clause,[],[f98,f157]) ).

fof(f98,plain,
    relation(sK1),
    inference(cnf_transformation,[],[f74]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU040+1 : TPTP v8.2.0. Released v3.2.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n007.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Sun May 19 15:31:38 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (10713)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.39  % (10716)WARNING: value z3 for option sas not known
% 0.23/0.39  % (10714)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.39  % (10715)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.39  % (10717)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.39  % (10716)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)
% 0.23/0.39  % (10720)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)
% 0.23/0.39  % (10719)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)
% 0.23/0.39  % (10718)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)
% 0.23/0.39  TRYING [1]
% 0.23/0.39  TRYING [2]
% 0.23/0.39  TRYING [3]
% 0.23/0.39  % (10718)First to succeed.
% 0.23/0.39  TRYING [1]
% 0.23/0.39  TRYING [4]
% 0.23/0.39  TRYING [1]
% 0.23/0.39  TRYING [2]
% 0.23/0.39  TRYING [2]
% 0.23/0.39  TRYING [3]
% 0.23/0.40  % (10718)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10713"
% 0.23/0.40  TRYING [4]
% 0.23/0.40  % (10719)Also succeeded, but the first one will report.
% 0.23/0.40  % (10718)Refutation found. Thanks to Tanya!
% 0.23/0.40  % SZS status Theorem for theBenchmark
% 0.23/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.40  % (10718)------------------------------
% 0.23/0.40  % (10718)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.23/0.40  % (10718)Termination reason: Refutation
% 0.23/0.40  
% 0.23/0.40  % (10718)Memory used [KB]: 972
% 0.23/0.40  % (10718)Time elapsed: 0.010 s
% 0.23/0.40  % (10718)Instructions burned: 13 (million)
% 0.23/0.40  % (10713)Success in time 0.029 s
%------------------------------------------------------------------------------