TSTP Solution File: SEU174+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU174+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 : Sun May  5 09:28:02 EDT 2024

% Result   : Theorem 1.61s 0.60s
% Output   : Refutation 1.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   50
% Syntax   : Number of formulae    :  207 (  31 unt;   0 def)
%            Number of atoms       :  583 (  86 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  611 ( 235   ~; 222   |;  94   &)
%                                         (  38 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   26 (  24 usr;  17 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   3 con; 0-3 aty)
%            Number of variables   :  312 ( 284   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9761,plain,
    $false,
    inference(avatar_sat_refutation,[],[f1029,f3769,f4434,f4927,f6202,f6217,f8031,f8040,f9218,f9739,f9755,f9756,f9758,f9760]) ).

fof(f9760,plain,
    ( spl39_1
    | ~ spl39_2 ),
    inference(avatar_contradiction_clause,[],[f9759]) ).

fof(f9759,plain,
    ( $false
    | spl39_1
    | ~ spl39_2 ),
    inference(subsumption_resolution,[],[f9747,f1031]) ).

fof(f1031,plain,
    ( ~ empty(sK9)
    | spl39_1 ),
    inference(resolution,[],[f1025,f900]) ).

fof(f900,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | ~ empty(X0) ),
    inference(resolution,[],[f354,f497]) ).

fof(f497,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f203]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f114]) ).

fof(f114,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(f354,plain,
    ! [X0,X1] :
      ( in(sK12(X0,X1),X0)
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f230]) ).

fof(f230,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X1)
            | ~ in(X2,X0) ) )
      & ( ( in(sK12(X0,X1),X1)
          & in(sK12(X0,X1),X0) )
        | disjoint(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f143,f229]) ).

fof(f229,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X1)
          & in(X3,X0) )
     => ( in(sK12(X0,X1),X1)
        & in(sK12(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] :
            ( ~ in(X2,X1)
            | ~ in(X2,X0) ) )
      & ( ? [X3] :
            ( in(X3,X1)
            & in(X3,X0) )
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f126]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] :
              ( in(X2,X1)
              & in(X2,X0) ) )
      & ~ ( ! [X3] :
              ~ ( in(X3,X1)
                & in(X3,X0) )
          & ~ disjoint(X0,X1) ) ),
    inference(rectify,[],[f93]) ).

fof(f93,axiom,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] :
              ( in(X2,X1)
              & in(X2,X0) ) )
      & ~ ( ! [X2] :
              ~ ( in(X2,X1)
                & in(X2,X0) )
          & ~ disjoint(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).

fof(f1025,plain,
    ( ~ disjoint(sK9,powerset(sK8))
    | spl39_1 ),
    inference(avatar_component_clause,[],[f1023]) ).

fof(f1023,plain,
    ( spl39_1
  <=> disjoint(sK9,powerset(sK8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_1])]) ).

fof(f9747,plain,
    ( empty(sK9)
    | ~ spl39_2 ),
    inference(resolution,[],[f1028,f1813]) ).

fof(f1813,plain,
    ! [X0] :
      ( in(sK16(X0),X0)
      | empty(X0) ),
    inference(resolution,[],[f443,f427]) ).

fof(f427,plain,
    ! [X0] : element(sK16(X0),X0),
    inference(cnf_transformation,[],[f257]) ).

fof(f257,plain,
    ! [X0] : element(sK16(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f36,f256]) ).

fof(f256,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK16(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f36,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f443,plain,
    ! [X0,X1] :
      ( ~ element(X1,X0)
      | in(X1,X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f264,plain,
    ! [X0,X1] :
      ( ( ( ( element(X1,X0)
            | ~ empty(X1) )
          & ( empty(X1)
            | ~ element(X1,X0) ) )
        | ~ empty(X0) )
      & ( ( ( element(X1,X0)
            | ~ in(X1,X0) )
          & ( in(X1,X0)
            | ~ element(X1,X0) ) )
        | empty(X0) ) ),
    inference(nnf_transformation,[],[f183]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( ( ( element(X1,X0)
        <=> empty(X1) )
        | ~ empty(X0) )
      & ( ( element(X1,X0)
        <=> in(X1,X0) )
        | empty(X0) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ( empty(X0)
       => ( element(X1,X0)
        <=> empty(X1) ) )
      & ( ~ empty(X0)
       => ( element(X1,X0)
        <=> in(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).

fof(f1028,plain,
    ( ! [X0] : ~ in(X0,sK9)
    | ~ spl39_2 ),
    inference(avatar_component_clause,[],[f1027]) ).

fof(f1027,plain,
    ( spl39_2
  <=> ! [X0] : ~ in(X0,sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_2])]) ).

fof(f9758,plain,
    ~ spl39_2,
    inference(avatar_contradiction_clause,[],[f9757]) ).

fof(f9757,plain,
    ( $false
    | ~ spl39_2 ),
    inference(subsumption_resolution,[],[f9746,f334]) ).

fof(f334,plain,
    empty_set != sK9,
    inference(cnf_transformation,[],[f223]) ).

fof(f223,plain,
    ( empty_set = complements_of_subsets(sK8,sK9)
    & empty_set != sK9
    & element(sK9,powerset(powerset(sK8))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f136,f222]) ).

fof(f222,plain,
    ( ? [X0,X1] :
        ( empty_set = complements_of_subsets(X0,X1)
        & empty_set != X1
        & element(X1,powerset(powerset(X0))) )
   => ( empty_set = complements_of_subsets(sK8,sK9)
      & empty_set != sK9
      & element(sK9,powerset(powerset(sK8))) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ? [X0,X1] :
      ( empty_set = complements_of_subsets(X0,X1)
      & empty_set != X1
      & element(X1,powerset(powerset(X0))) ),
    inference(flattening,[],[f135]) ).

fof(f135,plain,
    ? [X0,X1] :
      ( empty_set = complements_of_subsets(X0,X1)
      & empty_set != X1
      & element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f99]) ).

fof(f99,negated_conjecture,
    ~ ! [X0,X1] :
        ( element(X1,powerset(powerset(X0)))
       => ~ ( empty_set = complements_of_subsets(X0,X1)
            & empty_set != X1 ) ),
    inference(negated_conjecture,[],[f98]) ).

fof(f98,conjecture,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => ~ ( empty_set = complements_of_subsets(X0,X1)
          & empty_set != X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).

fof(f9746,plain,
    ( empty_set = sK9
    | ~ spl39_2 ),
    inference(resolution,[],[f1028,f426]) ).

fof(f426,plain,
    ! [X0] :
      ( in(sK15(X0),X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f255]) ).

fof(f255,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK15(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f253,f254]) ).

fof(f254,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK15(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f252]) ).

fof(f252,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f9756,plain,
    ( spl39_1
    | ~ spl39_2 ),
    inference(avatar_contradiction_clause,[],[f9741]) ).

fof(f9741,plain,
    ( $false
    | spl39_1
    | ~ spl39_2 ),
    inference(resolution,[],[f1028,f4504]) ).

fof(f4504,plain,
    ( in(sK11(sK9,powerset(sK8)),sK9)
    | spl39_1 ),
    inference(subsumption_resolution,[],[f4497,f1025]) ).

fof(f4497,plain,
    ( in(sK11(sK9,powerset(sK8)),sK9)
    | disjoint(sK9,powerset(sK8)) ),
    inference(superposition,[],[f352,f1011]) ).

fof(f1011,plain,
    sK9 = set_intersection2(sK9,powerset(sK8)),
    inference(resolution,[],[f358,f765]) ).

fof(f765,plain,
    subset(sK9,powerset(sK8)),
    inference(resolution,[],[f494,f333]) ).

fof(f333,plain,
    element(sK9,powerset(powerset(sK8))),
    inference(cnf_transformation,[],[f223]) ).

fof(f494,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(X1))
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f297]) ).

fof(f297,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f92]) ).

fof(f92,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

fof(f358,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_intersection2(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f78,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f352,plain,
    ! [X0,X1] :
      ( in(sK11(X0,X1),set_intersection2(X0,X1))
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f228]) ).

fof(f228,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
      & ( in(sK11(X0,X1),set_intersection2(X0,X1))
        | disjoint(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f142,f227]) ).

fof(f227,plain,
    ! [X0,X1] :
      ( ? [X3] : in(X3,set_intersection2(X0,X1))
     => in(sK11(X0,X1),set_intersection2(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
      & ( ? [X3] : in(X3,set_intersection2(X0,X1))
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f125]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    inference(rectify,[],[f104]) ).

fof(f104,axiom,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).

fof(f9755,plain,
    ( spl39_1
    | ~ spl39_2 ),
    inference(avatar_contradiction_clause,[],[f9742]) ).

fof(f9742,plain,
    ( $false
    | spl39_1
    | ~ spl39_2 ),
    inference(resolution,[],[f1028,f4503]) ).

fof(f4503,plain,
    ( in(sK11(powerset(sK8),sK9),sK9)
    | spl39_1 ),
    inference(subsumption_resolution,[],[f4496,f2052]) ).

fof(f2052,plain,
    ( ~ disjoint(powerset(sK8),sK9)
    | spl39_1 ),
    inference(subsumption_resolution,[],[f2051,f1031]) ).

fof(f2051,plain,
    ( empty(sK9)
    | ~ disjoint(powerset(sK8),sK9) ),
    inference(superposition,[],[f1867,f1011]) ).

fof(f1867,plain,
    ! [X0,X1] :
      ( empty(set_intersection2(X1,X0))
      | ~ disjoint(X0,X1) ),
    inference(superposition,[],[f1832,f440]) ).

fof(f440,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f1832,plain,
    ! [X0,X1] :
      ( empty(set_intersection2(X0,X1))
      | ~ disjoint(X0,X1) ),
    inference(resolution,[],[f1813,f353]) ).

fof(f353,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,set_intersection2(X0,X1))
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f228]) ).

fof(f4496,plain,
    ( in(sK11(powerset(sK8),sK9),sK9)
    | disjoint(powerset(sK8),sK9) ),
    inference(superposition,[],[f352,f4074]) ).

fof(f4074,plain,
    sK9 = set_intersection2(powerset(sK8),sK9),
    inference(resolution,[],[f524,f1019]) ).

fof(f1019,plain,
    sP5(sK9,powerset(sK8),sK9),
    inference(superposition,[],[f654,f1011]) ).

fof(f654,plain,
    ! [X0,X1] : sP5(X1,X0,set_intersection2(X1,X0)),
    inference(superposition,[],[f563,f440]) ).

fof(f563,plain,
    ! [X0,X1] : sP5(X1,X0,set_intersection2(X0,X1)),
    inference(equality_resolution,[],[f523]) ).

fof(f523,plain,
    ! [X2,X0,X1] :
      ( sP5(X1,X0,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f316]) ).

fof(f316,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ~ sP5(X1,X0,X2) )
      & ( sP5(X1,X0,X2)
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f217]) ).

fof(f217,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> sP5(X1,X0,X2) ),
    inference(definition_folding,[],[f15,f216]) ).

fof(f216,plain,
    ! [X1,X0,X2] :
      ( sP5(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f15,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f524,plain,
    ! [X2,X0,X1] :
      ( ~ sP5(X1,X0,X2)
      | set_intersection2(X0,X1) = X2 ),
    inference(cnf_transformation,[],[f316]) ).

fof(f9739,plain,
    ( spl39_2
    | ~ spl39_16 ),
    inference(avatar_split_clause,[],[f9738,f8037,f1027]) ).

fof(f8037,plain,
    ( spl39_16
  <=> sP0(empty_set,sK8,sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_16])]) ).

fof(f9738,plain,
    ( ! [X0] : ~ in(X0,sK9)
    | ~ spl39_16 ),
    inference(subsumption_resolution,[],[f9737,f5476]) ).

fof(f5476,plain,
    ! [X0] :
      ( element(X0,powerset(sK8))
      | ~ in(X0,sK9) ),
    inference(resolution,[],[f498,f333]) ).

fof(f498,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X2))
      | element(X0,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f205,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f204]) ).

fof(f204,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f103]) ).

fof(f103,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

fof(f9737,plain,
    ( ! [X0] :
        ( ~ in(X0,sK9)
        | ~ element(X0,powerset(sK8)) )
    | ~ spl39_16 ),
    inference(subsumption_resolution,[],[f9736,f548]) ).

fof(f548,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f425]) ).

fof(f425,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f255]) ).

fof(f9736,plain,
    ( ! [X0] :
        ( ~ in(X0,sK9)
        | ~ element(X0,powerset(sK8))
        | in(subset_complement(sK8,X0),empty_set) )
    | ~ spl39_16 ),
    inference(resolution,[],[f461,f8039]) ).

fof(f8039,plain,
    ( sP0(empty_set,sK8,sK9)
    | ~ spl39_16 ),
    inference(avatar_component_clause,[],[f8037]) ).

fof(f461,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP0(X0,X1,X2)
      | ~ in(X4,X2)
      | ~ element(X4,powerset(X1))
      | in(subset_complement(X1,X4),X0) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f271,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ~ in(subset_complement(X1,sK20(X0,X1,X2)),X0)
            | ~ in(sK20(X0,X1,X2),X2) )
          & ( in(subset_complement(X1,sK20(X0,X1,X2)),X0)
            | in(sK20(X0,X1,X2),X2) )
          & element(sK20(X0,X1,X2),powerset(X1)) ) )
      & ( ! [X4] :
            ( ( ( in(X4,X2)
                | ~ in(subset_complement(X1,X4),X0) )
              & ( in(subset_complement(X1,X4),X0)
                | ~ in(X4,X2) ) )
            | ~ element(X4,powerset(X1)) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f269,f270]) ).

fof(f270,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(subset_complement(X1,X3),X0)
            | ~ in(X3,X2) )
          & ( in(subset_complement(X1,X3),X0)
            | in(X3,X2) )
          & element(X3,powerset(X1)) )
     => ( ( ~ in(subset_complement(X1,sK20(X0,X1,X2)),X0)
          | ~ in(sK20(X0,X1,X2),X2) )
        & ( in(subset_complement(X1,sK20(X0,X1,X2)),X0)
          | in(sK20(X0,X1,X2),X2) )
        & element(sK20(X0,X1,X2),powerset(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f269,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ( ~ in(subset_complement(X1,X3),X0)
              | ~ in(X3,X2) )
            & ( in(subset_complement(X1,X3),X0)
              | in(X3,X2) )
            & element(X3,powerset(X1)) ) )
      & ( ! [X4] :
            ( ( ( in(X4,X2)
                | ~ in(subset_complement(X1,X4),X0) )
              & ( in(subset_complement(X1,X4),X0)
                | ~ in(X4,X2) ) )
            | ~ element(X4,powerset(X1)) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f268]) ).

fof(f268,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ~ in(subset_complement(X0,X3),X1)
              | ~ in(X3,X2) )
            & ( in(subset_complement(X0,X3),X1)
              | in(X3,X2) )
            & element(X3,powerset(X0)) ) )
      & ( ! [X3] :
            ( ( ( in(X3,X2)
                | ~ in(subset_complement(X0,X3),X1) )
              & ( in(subset_complement(X0,X3),X1)
                | ~ in(X3,X2) ) )
            | ~ element(X3,powerset(X0)) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(flattening,[],[f267]) ).

fof(f267,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ~ in(subset_complement(X0,X3),X1)
              | ~ in(X3,X2) )
            & ( in(subset_complement(X0,X3),X1)
              | in(X3,X2) )
            & element(X3,powerset(X0)) ) )
      & ( ! [X3] :
            ( ( ( in(X3,X2)
                | ~ in(subset_complement(X0,X3),X1) )
              & ( in(subset_complement(X0,X3),X1)
                | ~ in(X3,X2) ) )
            | ~ element(X3,powerset(X0)) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f207]) ).

fof(f207,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ! [X3] :
          ( ( in(X3,X2)
          <=> in(subset_complement(X0,X3),X1) )
          | ~ element(X3,powerset(X0)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f9218,plain,
    spl39_15,
    inference(avatar_contradiction_clause,[],[f9217]) ).

fof(f9217,plain,
    ( $false
    | spl39_15 ),
    inference(subsumption_resolution,[],[f9209,f8035]) ).

fof(f8035,plain,
    ( ~ sP1(sK9,sK8,empty_set)
    | spl39_15 ),
    inference(avatar_component_clause,[],[f8033]) ).

fof(f8033,plain,
    ( spl39_15
  <=> sP1(sK9,sK8,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_15])]) ).

fof(f9209,plain,
    sP1(sK9,sK8,empty_set),
    inference(resolution,[],[f9140,f582]) ).

fof(f582,plain,
    ! [X0] : element(empty_set,powerset(X0)),
    inference(forward_demodulation,[],[f432,f579]) ).

fof(f579,plain,
    ! [X0] : empty_set = sK19(X0),
    inference(resolution,[],[f424,f433]) ).

fof(f433,plain,
    ! [X0] : empty(sK19(X0)),
    inference(cnf_transformation,[],[f263]) ).

fof(f263,plain,
    ! [X0] :
      ( empty(sK19(X0))
      & element(sK19(X0),powerset(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f61,f262]) ).

fof(f262,plain,
    ! [X0] :
      ( ? [X1] :
          ( empty(X1)
          & element(X1,powerset(X0)) )
     => ( empty(sK19(X0))
        & element(sK19(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,axiom,
    ! [X0] :
    ? [X1] :
      ( empty(X1)
      & element(X1,powerset(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

fof(f424,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f180]) ).

fof(f180,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f112]) ).

fof(f112,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(f432,plain,
    ! [X0] : element(sK19(X0),powerset(X0)),
    inference(cnf_transformation,[],[f263]) ).

fof(f9140,plain,
    ! [X0] :
      ( ~ element(X0,powerset(powerset(sK8)))
      | sP1(sK9,sK8,X0) ),
    inference(resolution,[],[f466,f333]) ).

fof(f466,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,powerset(powerset(X0)))
      | sP1(X2,X0,X1)
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(cnf_transformation,[],[f209]) ).

fof(f209,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sP1(X2,X0,X1)
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(definition_folding,[],[f197,f208,f207]) ).

fof(f208,plain,
    ! [X2,X0,X1] :
      ( ( complements_of_subsets(X0,X1) = X2
      <=> sP0(X1,X0,X2) )
      | ~ sP1(X2,X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( complements_of_subsets(X0,X1) = X2
          <=> ! [X3] :
                ( ( in(X3,X2)
                <=> in(subset_complement(X0,X3),X1) )
                | ~ element(X3,powerset(X0)) ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => ! [X2] :
          ( element(X2,powerset(powerset(X0)))
         => ( complements_of_subsets(X0,X1) = X2
          <=> ! [X3] :
                ( element(X3,powerset(X0))
               => ( in(X3,X2)
                <=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).

fof(f8040,plain,
    ( ~ spl39_15
    | spl39_16 ),
    inference(avatar_split_clause,[],[f8022,f8037,f8033]) ).

fof(f8022,plain,
    ( sP0(empty_set,sK8,sK9)
    | ~ sP1(sK9,sK8,empty_set) ),
    inference(forward_demodulation,[],[f8020,f7737]) ).

fof(f7737,plain,
    sK9 = complements_of_subsets(sK8,empty_set),
    inference(forward_demodulation,[],[f7732,f335]) ).

fof(f335,plain,
    empty_set = complements_of_subsets(sK8,sK9),
    inference(cnf_transformation,[],[f223]) ).

fof(f7732,plain,
    sK9 = complements_of_subsets(sK8,complements_of_subsets(sK8,sK9)),
    inference(resolution,[],[f457,f333]) ).

fof(f457,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(powerset(X0)))
      | complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f195]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).

fof(f8020,plain,
    ( ~ sP1(sK9,sK8,empty_set)
    | sP0(empty_set,sK8,complements_of_subsets(sK8,empty_set)) ),
    inference(superposition,[],[f549,f7737]) ).

fof(f549,plain,
    ! [X2,X1] :
      ( ~ sP1(complements_of_subsets(X1,X2),X1,X2)
      | sP0(X2,X1,complements_of_subsets(X1,X2)) ),
    inference(equality_resolution,[],[f459]) ).

fof(f459,plain,
    ! [X2,X0,X1] :
      ( sP0(X2,X1,X0)
      | complements_of_subsets(X1,X2) != X0
      | ~ sP1(X0,X1,X2) ),
    inference(cnf_transformation,[],[f266]) ).

fof(f266,plain,
    ! [X0,X1,X2] :
      ( ( ( complements_of_subsets(X1,X2) = X0
          | ~ sP0(X2,X1,X0) )
        & ( sP0(X2,X1,X0)
          | complements_of_subsets(X1,X2) != X0 ) )
      | ~ sP1(X0,X1,X2) ),
    inference(rectify,[],[f265]) ).

fof(f265,plain,
    ! [X2,X0,X1] :
      ( ( ( complements_of_subsets(X0,X1) = X2
          | ~ sP0(X1,X0,X2) )
        & ( sP0(X1,X0,X2)
          | complements_of_subsets(X0,X1) != X2 ) )
      | ~ sP1(X2,X0,X1) ),
    inference(nnf_transformation,[],[f208]) ).

fof(f8031,plain,
    ( ~ spl39_13
    | spl39_14 ),
    inference(avatar_split_clause,[],[f8021,f8028,f8024]) ).

fof(f8024,plain,
    ( spl39_13
  <=> sP1(empty_set,sK8,sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_13])]) ).

fof(f8028,plain,
    ( spl39_14
  <=> sP0(sK9,sK8,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_14])]) ).

fof(f8021,plain,
    ( sP0(sK9,sK8,empty_set)
    | ~ sP1(empty_set,sK8,sK9) ),
    inference(forward_demodulation,[],[f8019,f335]) ).

fof(f8019,plain,
    ( ~ sP1(empty_set,sK8,sK9)
    | sP0(sK9,sK8,complements_of_subsets(sK8,sK9)) ),
    inference(superposition,[],[f549,f335]) ).

fof(f6217,plain,
    ( ~ spl39_11
    | spl39_12
    | spl39_1 ),
    inference(avatar_split_clause,[],[f4686,f1023,f6214,f6210]) ).

fof(f6210,plain,
    ( spl39_11
  <=> subset(sK8,sK16(sK9)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_11])]) ).

fof(f6214,plain,
    ( spl39_12
  <=> sK8 = sK16(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_12])]) ).

fof(f4686,plain,
    ( sK8 = sK16(sK9)
    | ~ subset(sK8,sK16(sK9))
    | spl39_1 ),
    inference(resolution,[],[f4661,f471]) ).

fof(f471,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f276]) ).

fof(f276,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f275]) ).

fof(f275,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(f4661,plain,
    ( subset(sK16(sK9),sK8)
    | spl39_1 ),
    inference(superposition,[],[f656,f4373]) ).

fof(f4373,plain,
    ( sK16(sK9) = set_intersection2(sK16(sK9),sK8)
    | spl39_1 ),
    inference(subsumption_resolution,[],[f4367,f1031]) ).

fof(f4367,plain,
    ( sK16(sK9) = set_intersection2(sK16(sK9),sK8)
    | empty(sK9) ),
    inference(resolution,[],[f3854,f1813]) ).

fof(f3854,plain,
    ! [X0] :
      ( ~ in(X0,sK9)
      | set_intersection2(X0,sK8) = X0 ),
    inference(resolution,[],[f3787,f358]) ).

fof(f3787,plain,
    ! [X0] :
      ( subset(X0,sK8)
      | ~ in(X0,sK9) ),
    inference(resolution,[],[f3783,f557]) ).

fof(f557,plain,
    ! [X3,X0] :
      ( ~ in(X3,powerset(X0))
      | subset(X3,X0) ),
    inference(equality_resolution,[],[f490]) ).

fof(f490,plain,
    ! [X3,X0,X1] :
      ( subset(X3,X0)
      | ~ in(X3,X1)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f296]) ).

fof(f296,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ( ( ~ subset(sK27(X0,X1),X0)
            | ~ in(sK27(X0,X1),X1) )
          & ( subset(sK27(X0,X1),X0)
            | in(sK27(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f294,f295]) ).

fof(f295,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK27(X0,X1),X0)
          | ~ in(sK27(X0,X1),X1) )
        & ( subset(sK27(X0,X1),X0)
          | in(sK27(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f294,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(rectify,[],[f293]) ).

fof(f293,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ subset(X2,X0) )
            & ( subset(X2,X0)
              | ~ in(X2,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(f3783,plain,
    ! [X0] :
      ( in(X0,powerset(sK8))
      | ~ in(X0,sK9) ),
    inference(resolution,[],[f3697,f380]) ).

fof(f380,plain,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f239]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( ( subset(singleton(X0),X1)
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ~ subset(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f51,axiom,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).

fof(f3697,plain,
    ! [X0] :
      ( ~ subset(singleton(X0),sK9)
      | in(X0,powerset(sK8)) ),
    inference(resolution,[],[f3681,f379]) ).

fof(f379,plain,
    ! [X0,X1] :
      ( ~ subset(singleton(X0),X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f239]) ).

fof(f3681,plain,
    ! [X0] :
      ( subset(X0,powerset(sK8))
      | ~ subset(X0,sK9) ),
    inference(resolution,[],[f400,f765]) ).

fof(f400,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X2)
      | subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f170]) ).

fof(f170,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X2)
      | ~ subset(X1,X2)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f169]) ).

fof(f169,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X2)
      | ~ subset(X1,X2)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X1,X2)
        & subset(X0,X1) )
     => subset(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(f656,plain,
    ! [X0,X1] : subset(set_intersection2(X1,X0),X0),
    inference(superposition,[],[f347,f440]) ).

fof(f347,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,axiom,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).

fof(f6202,plain,
    ( ~ spl39_9
    | spl39_10 ),
    inference(avatar_split_clause,[],[f4423,f6199,f6195]) ).

fof(f6195,plain,
    ( spl39_9
  <=> subset(sK8,sK15(sK9)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_9])]) ).

fof(f6199,plain,
    ( spl39_10
  <=> sK8 = sK15(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_10])]) ).

fof(f4423,plain,
    ( sK8 = sK15(sK9)
    | ~ subset(sK8,sK15(sK9)) ),
    inference(resolution,[],[f4386,f471]) ).

fof(f4386,plain,
    subset(sK15(sK9),sK8),
    inference(superposition,[],[f656,f4372]) ).

fof(f4372,plain,
    sK15(sK9) = set_intersection2(sK15(sK9),sK8),
    inference(subsumption_resolution,[],[f4366,f334]) ).

fof(f4366,plain,
    ( sK15(sK9) = set_intersection2(sK15(sK9),sK8)
    | empty_set = sK9 ),
    inference(resolution,[],[f3854,f426]) ).

fof(f4927,plain,
    ( ~ spl39_7
    | spl39_8
    | spl39_1 ),
    inference(avatar_split_clause,[],[f4677,f1023,f4924,f4920]) ).

fof(f4920,plain,
    ( spl39_7
  <=> disjoint(sK16(sK9),sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_7])]) ).

fof(f4924,plain,
    ( spl39_8
  <=> empty(sK16(sK9)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_8])]) ).

fof(f4677,plain,
    ( empty(sK16(sK9))
    | ~ disjoint(sK16(sK9),sK8)
    | spl39_1 ),
    inference(superposition,[],[f1832,f4373]) ).

fof(f4434,plain,
    ( ~ spl39_5
    | spl39_6 ),
    inference(avatar_split_clause,[],[f4394,f4431,f4427]) ).

fof(f4427,plain,
    ( spl39_5
  <=> empty(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_5])]) ).

fof(f4431,plain,
    ( spl39_6
  <=> empty(sK15(sK9)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_6])]) ).

fof(f4394,plain,
    ( empty(sK15(sK9))
    | ~ empty(sK8) ),
    inference(superposition,[],[f1126,f4372]) ).

fof(f1126,plain,
    ! [X0,X1] :
      ( empty(set_intersection2(X1,X0))
      | ~ empty(X0) ),
    inference(superposition,[],[f1106,f440]) ).

fof(f1106,plain,
    ! [X0,X1] :
      ( empty(set_intersection2(X0,X1))
      | ~ empty(X0) ),
    inference(superposition,[],[f448,f1060]) ).

fof(f1060,plain,
    ! [X0,X1] : set_union2(set_intersection2(X0,X1),X0) = X0,
    inference(resolution,[],[f359,f347]) ).

fof(f359,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_union2(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( set_union2(X0,X1) = X1
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f69]) ).

fof(f69,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_union2(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(f448,plain,
    ! [X0,X1] :
      ( ~ empty(set_union2(X0,X1))
      | empty(X0) ),
    inference(cnf_transformation,[],[f185]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( ~ empty(set_union2(X0,X1))
      | empty(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,axiom,
    ! [X0,X1] :
      ( ~ empty(X0)
     => ~ empty(set_union2(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).

fof(f3769,plain,
    ( ~ spl39_3
    | spl39_4 ),
    inference(avatar_split_clause,[],[f3757,f3766,f3762]) ).

fof(f3762,plain,
    ( spl39_3
  <=> subset(powerset(sK8),sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_3])]) ).

fof(f3766,plain,
    ( spl39_4
  <=> sK9 = powerset(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl39_4])]) ).

fof(f3757,plain,
    ( sK9 = powerset(sK8)
    | ~ subset(powerset(sK8),sK9) ),
    inference(resolution,[],[f471,f765]) ).

fof(f1029,plain,
    ( ~ spl39_1
    | spl39_2 ),
    inference(avatar_split_clause,[],[f1016,f1027,f1023]) ).

fof(f1016,plain,
    ! [X0] :
      ( ~ in(X0,sK9)
      | ~ disjoint(sK9,powerset(sK8)) ),
    inference(superposition,[],[f353,f1011]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SEU174+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n020.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 11:30:01 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.22/0.36  % (14014)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (14022)WARNING: value z3 for option sas not known
% 0.22/0.38  % (14019)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38  % (14021)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38  % (14026)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)
% 0.22/0.38  % (14024)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)
% 0.22/0.38  % (14022)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)
% 0.22/0.38  % (14025)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)
% 0.22/0.38  % (14023)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.40  TRYING [1]
% 0.22/0.40  TRYING [2]
% 0.22/0.41  TRYING [3]
% 0.22/0.45  TRYING [1]
% 0.22/0.47  TRYING [2]
% 0.22/0.49  TRYING [4]
% 0.22/0.51  TRYING [1]
% 0.22/0.51  TRYING [2]
% 0.22/0.51  TRYING [3]
% 0.22/0.53  TRYING [3]
% 0.22/0.53  TRYING [4]
% 1.61/0.60  % (14022)First to succeed.
% 1.61/0.60  % (14022)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14014"
% 1.61/0.60  % (14022)Refutation found. Thanks to Tanya!
% 1.61/0.60  % SZS status Theorem for theBenchmark
% 1.61/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.61/0.60  % (14022)------------------------------
% 1.61/0.60  % (14022)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.61/0.60  % (14022)Termination reason: Refutation
% 1.61/0.60  
% 1.61/0.60  % (14022)Memory used [KB]: 4241
% 1.61/0.60  % (14022)Time elapsed: 0.221 s
% 1.61/0.60  % (14022)Instructions burned: 485 (million)
% 1.61/0.60  % (14014)Success in time 0.23 s
%------------------------------------------------------------------------------