TSTP Solution File: SEU179+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU179+1 : 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 : 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 Apr 30 15:23:15 EDT 2024

% Result   : Theorem 0.12s 0.30s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  118 (  12 unt;   0 def)
%            Number of atoms       :  365 (  24 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  415 ( 168   ~; 142   |;  58   &)
%                                         (  26 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   23 (  21 usr;  17 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   3 con; 0-2 aty)
%            Number of variables   :  207 ( 168   !;  39   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f870,plain,
    $false,
    inference(avatar_sat_refutation,[],[f163,f213,f228,f501,f571,f585,f599,f659,f859,f869]) ).

fof(f869,plain,
    spl15_2,
    inference(avatar_contradiction_clause,[],[f868]) ).

fof(f868,plain,
    ( $false
    | spl15_2 ),
    inference(subsumption_resolution,[],[f867,f162]) ).

fof(f162,plain,
    ( ~ subset(relation_rng(sK0),relation_rng(sK1))
    | spl15_2 ),
    inference(avatar_component_clause,[],[f160]) ).

fof(f160,plain,
    ( spl15_2
  <=> subset(relation_rng(sK0),relation_rng(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).

fof(f867,plain,
    subset(relation_rng(sK0),relation_rng(sK1)),
    inference(duplicate_literal_removal,[],[f866]) ).

fof(f866,plain,
    ( subset(relation_rng(sK0),relation_rng(sK1))
    | subset(relation_rng(sK0),relation_rng(sK1)) ),
    inference(resolution,[],[f563,f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( in(sK11(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK11(X0,X1),X1)
          & in(sK11(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f76,f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK11(X0,X1),X1)
        & in(sK11(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f563,plain,
    ! [X0] :
      ( ~ in(sK11(X0,relation_rng(sK1)),relation_rng(sK0))
      | subset(X0,relation_rng(sK1)) ),
    inference(resolution,[],[f523,f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ~ in(sK11(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f523,plain,
    ! [X0] :
      ( in(X0,relation_rng(sK1))
      | ~ in(X0,relation_rng(sK0)) ),
    inference(subsumption_resolution,[],[f504,f86]) ).

fof(f86,plain,
    relation(sK0),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ( ( ~ subset(relation_rng(sK0),relation_rng(sK1))
      | ~ subset(relation_dom(sK0),relation_dom(sK1)) )
    & subset(sK0,sK1)
    & relation(sK1)
    & relation(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f39,f55,f54]) ).

fof(f54,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ( ~ subset(relation_rng(X0),relation_rng(X1))
              | ~ subset(relation_dom(X0),relation_dom(X1)) )
            & subset(X0,X1)
            & relation(X1) )
        & relation(X0) )
   => ( ? [X1] :
          ( ( ~ subset(relation_rng(sK0),relation_rng(X1))
            | ~ subset(relation_dom(sK0),relation_dom(X1)) )
          & subset(sK0,X1)
          & relation(X1) )
      & relation(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ( ? [X1] :
        ( ( ~ subset(relation_rng(sK0),relation_rng(X1))
          | ~ subset(relation_dom(sK0),relation_dom(X1)) )
        & subset(sK0,X1)
        & relation(X1) )
   => ( ( ~ subset(relation_rng(sK0),relation_rng(sK1))
        | ~ subset(relation_dom(sK0),relation_dom(sK1)) )
      & subset(sK0,sK1)
      & relation(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ subset(relation_rng(X0),relation_rng(X1))
            | ~ subset(relation_dom(X0),relation_dom(X1)) )
          & subset(X0,X1)
          & relation(X1) )
      & relation(X0) ),
    inference(flattening,[],[f38]) ).

fof(f38,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ subset(relation_rng(X0),relation_rng(X1))
            | ~ subset(relation_dom(X0),relation_dom(X1)) )
          & subset(X0,X1)
          & relation(X1) )
      & relation(X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X0] :
        ( relation(X0)
       => ! [X1] :
            ( relation(X1)
           => ( subset(X0,X1)
             => ( subset(relation_rng(X0),relation_rng(X1))
                & subset(relation_dom(X0),relation_dom(X1)) ) ) ) ),
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation(X1)
         => ( subset(X0,X1)
           => ( subset(relation_rng(X0),relation_rng(X1))
              & subset(relation_dom(X0),relation_dom(X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).

fof(f504,plain,
    ! [X0] :
      ( ~ in(X0,relation_rng(sK0))
      | ~ relation(sK0)
      | in(X0,relation_rng(sK1)) ),
    inference(resolution,[],[f131,f389]) ).

fof(f389,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X1,X0),sK0)
      | in(X0,relation_rng(sK1)) ),
    inference(subsumption_resolution,[],[f388,f87]) ).

fof(f87,plain,
    relation(sK1),
    inference(cnf_transformation,[],[f56]) ).

fof(f388,plain,
    ! [X0,X1] :
      ( in(X0,relation_rng(sK1))
      | ~ relation(sK1)
      | ~ in(ordered_pair(X1,X0),sK0) ),
    inference(resolution,[],[f130,f199]) ).

fof(f199,plain,
    ! [X0] :
      ( in(X0,sK1)
      | ~ in(X0,sK0) ),
    inference(resolution,[],[f115,f88]) ).

fof(f88,plain,
    subset(sK0,sK1),
    inference(cnf_transformation,[],[f56]) ).

fof(f115,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f130,plain,
    ! [X0,X6,X5] :
      ( ~ in(ordered_pair(X6,X5),X0)
      | in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X6,X5),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(X3,sK6(X0,X1)),X0)
                | ~ in(sK6(X0,X1),X1) )
              & ( in(ordered_pair(sK7(X0,X1),sK6(X0,X1)),X0)
                | in(sK6(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(ordered_pair(sK8(X0,X5),X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f66,f69,f68,f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X4,X2),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(X3,sK6(X0,X1)),X0)
          | ~ in(sK6(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(X4,sK6(X0,X1)),X0)
          | in(sK6(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(X4,sK6(X0,X1)),X0)
     => in(ordered_pair(sK7(X0,X1),sK6(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X7,X5),X0)
     => in(ordered_pair(sK8(X0,X5),X5),X0) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X4,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( ? [X7] : in(ordered_pair(X7,X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f131,plain,
    ! [X0,X5] :
      ( in(ordered_pair(sK8(X0,X5),X5),X0)
      | ~ in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(sK8(X0,X5),X5),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f859,plain,
    spl15_1,
    inference(avatar_contradiction_clause,[],[f858]) ).

fof(f858,plain,
    ( $false
    | spl15_1 ),
    inference(subsumption_resolution,[],[f857,f158]) ).

fof(f158,plain,
    ( ~ subset(relation_dom(sK0),relation_dom(sK1))
    | spl15_1 ),
    inference(avatar_component_clause,[],[f156]) ).

fof(f156,plain,
    ( spl15_1
  <=> subset(relation_dom(sK0),relation_dom(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).

fof(f857,plain,
    subset(relation_dom(sK0),relation_dom(sK1)),
    inference(duplicate_literal_removal,[],[f856]) ).

fof(f856,plain,
    ( subset(relation_dom(sK0),relation_dom(sK1))
    | subset(relation_dom(sK0),relation_dom(sK1)) ),
    inference(resolution,[],[f493,f116]) ).

fof(f493,plain,
    ! [X0] :
      ( ~ in(sK11(X0,relation_dom(sK1)),relation_dom(sK0))
      | subset(X0,relation_dom(sK1)) ),
    inference(resolution,[],[f465,f117]) ).

fof(f465,plain,
    ! [X0] :
      ( in(X0,relation_dom(sK1))
      | ~ in(X0,relation_dom(sK0)) ),
    inference(subsumption_resolution,[],[f447,f86]) ).

fof(f447,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sK0))
      | ~ relation(sK0)
      | in(X0,relation_dom(sK1)) ),
    inference(resolution,[],[f129,f345]) ).

fof(f345,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),sK0)
      | in(X0,relation_dom(sK1)) ),
    inference(subsumption_resolution,[],[f344,f87]) ).

fof(f344,plain,
    ! [X0,X1] :
      ( in(X0,relation_dom(sK1))
      | ~ relation(sK1)
      | ~ in(ordered_pair(X0,X1),sK0) ),
    inference(resolution,[],[f128,f199]) ).

fof(f128,plain,
    ! [X0,X6,X5] :
      ( ~ in(ordered_pair(X5,X6),X0)
      | in(X5,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X5,X6),X0)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0)
                | ~ in(sK3(X0,X1),X1) )
              & ( in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
                | in(sK3(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( in(ordered_pair(X5,sK5(X0,X5)),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f60,f63,f62,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X2,X4),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0)
          | ~ in(sK3(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(sK3(X0,X1),X4),X0)
          | in(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(sK3(X0,X1),X4),X0)
     => in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X5,X7),X0)
     => in(ordered_pair(X5,sK5(X0,X5)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X2,X4),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( ? [X7] : in(ordered_pair(X5,X7),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).

fof(f129,plain,
    ! [X0,X5] :
      ( in(ordered_pair(X5,sK5(X0,X5)),X0)
      | ~ in(X5,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(X5,sK5(X0,X5)),X0)
      | ~ in(X5,X1)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f659,plain,
    ( ~ spl15_15
    | ~ spl15_16 ),
    inference(avatar_split_clause,[],[f573,f656,f652]) ).

fof(f652,plain,
    ( spl15_15
  <=> in(relation_dom(sK1),relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).

fof(f656,plain,
    ( spl15_16
  <=> in(relation_rng(sK1),relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).

fof(f573,plain,
    ( ~ in(relation_rng(sK1),relation_dom(sK0))
    | ~ in(relation_dom(sK1),relation_rng(sK0)) ),
    inference(resolution,[],[f487,f523]) ).

fof(f487,plain,
    ! [X0] :
      ( ~ in(relation_dom(sK1),X0)
      | ~ in(X0,relation_dom(sK0)) ),
    inference(resolution,[],[f465,f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,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/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f599,plain,
    ( ~ spl15_13
    | ~ spl15_14 ),
    inference(avatar_split_clause,[],[f562,f596,f592]) ).

fof(f592,plain,
    ( spl15_13
  <=> in(relation_rng(sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).

fof(f596,plain,
    ( spl15_14
  <=> in(sK1,relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).

fof(f562,plain,
    ( ~ in(sK1,relation_rng(sK0))
    | ~ in(relation_rng(sK1),sK0) ),
    inference(resolution,[],[f523,f202]) ).

fof(f202,plain,
    ! [X0] :
      ( ~ in(sK1,X0)
      | ~ in(X0,sK0) ),
    inference(resolution,[],[f199,f112]) ).

fof(f585,plain,
    ( ~ spl15_11
    | ~ spl15_12 ),
    inference(avatar_split_clause,[],[f492,f582,f578]) ).

fof(f578,plain,
    ( spl15_11
  <=> in(relation_dom(sK1),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).

fof(f582,plain,
    ( spl15_12
  <=> in(sK1,relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).

fof(f492,plain,
    ( ~ in(sK1,relation_dom(sK0))
    | ~ in(relation_dom(sK1),sK0) ),
    inference(resolution,[],[f465,f202]) ).

fof(f571,plain,
    ( ~ spl15_9
    | spl15_10 ),
    inference(avatar_split_clause,[],[f557,f569,f565]) ).

fof(f565,plain,
    ( spl15_9
  <=> empty(relation_rng(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).

fof(f569,plain,
    ( spl15_10
  <=> ! [X0] : ~ in(X0,relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).

fof(f557,plain,
    ! [X0] :
      ( ~ in(X0,relation_rng(sK0))
      | ~ empty(relation_rng(sK1)) ),
    inference(resolution,[],[f523,f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f501,plain,
    ( ~ spl15_7
    | spl15_8 ),
    inference(avatar_split_clause,[],[f488,f499,f495]) ).

fof(f495,plain,
    ( spl15_7
  <=> empty(relation_dom(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).

fof(f499,plain,
    ( spl15_8
  <=> ! [X0] : ~ in(X0,relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).

fof(f488,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sK0))
      | ~ empty(relation_dom(sK1)) ),
    inference(resolution,[],[f465,f121]) ).

fof(f228,plain,
    ( spl15_5
    | spl15_6 ),
    inference(avatar_split_clause,[],[f219,f226,f223]) ).

fof(f223,plain,
    ( spl15_5
  <=> ! [X1] : ~ in(X1,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).

fof(f226,plain,
    ( spl15_6
  <=> ! [X0] : ~ empty(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).

fof(f219,plain,
    ! [X0,X1] :
      ( ~ empty(X0)
      | ~ in(X1,empty_set) ),
    inference(resolution,[],[f123,f140]) ).

fof(f140,plain,
    ! [X0] : element(empty_set,powerset(X0)),
    inference(forward_demodulation,[],[f105,f133]) ).

fof(f133,plain,
    ! [X0] : empty_set = sK10(X0),
    inference(resolution,[],[f103,f106]) ).

fof(f106,plain,
    ! [X0] : empty(sK10(X0)),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( empty(sK10(X0))
      & element(sK10(X0),powerset(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f24,f73]) ).

fof(f73,plain,
    ! [X0] :
      ( ? [X1] :
          ( empty(X1)
          & element(X1,powerset(X0)) )
     => ( empty(sK10(X0))
        & element(sK10(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,axiom,
    ! [X0] :
    ? [X1] :
      ( empty(X1)
      & element(X1,powerset(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

fof(f103,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f105,plain,
    ! [X0] : element(sK10(X0),powerset(X0)),
    inference(cnf_transformation,[],[f74]) ).

fof(f123,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X2))
      | ~ empty(X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(f213,plain,
    ( ~ spl15_3
    | spl15_4 ),
    inference(avatar_split_clause,[],[f203,f211,f207]) ).

fof(f207,plain,
    ( spl15_3
  <=> empty(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).

fof(f211,plain,
    ( spl15_4
  <=> ! [X0] : ~ in(X0,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).

fof(f203,plain,
    ! [X0] :
      ( ~ in(X0,sK0)
      | ~ empty(sK1) ),
    inference(resolution,[],[f199,f121]) ).

fof(f163,plain,
    ( ~ spl15_1
    | ~ spl15_2 ),
    inference(avatar_split_clause,[],[f89,f160,f156]) ).

fof(f89,plain,
    ( ~ subset(relation_rng(sK0),relation_rng(sK1))
    | ~ subset(relation_dom(sK0),relation_dom(sK1)) ),
    inference(cnf_transformation,[],[f56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem    : SEU179+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.09  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.27  % Computer : n007.cluster.edu
% 0.08/0.27  % Model    : x86_64 x86_64
% 0.08/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27  % Memory   : 8042.1875MB
% 0.08/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27  % CPULimit   : 300
% 0.08/0.27  % WCLimit    : 300
% 0.08/0.27  % DateTime   : Mon Apr 29 20:13:32 EDT 2024
% 0.08/0.27  % CPUTime    : 
% 0.08/0.28  % (23231)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.28  % (23234)WARNING: value z3 for option sas not known
% 0.12/0.28  % (23235)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.28  % (23232)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.29  % (23234)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)
% 0.12/0.29  % (23233)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.29  % (23236)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)
% 0.12/0.29  % (23237)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)
% 0.12/0.29  % (23238)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)
% 0.12/0.29  TRYING [1]
% 0.12/0.29  TRYING [2]
% 0.12/0.29  TRYING [3]
% 0.12/0.29  TRYING [1]
% 0.12/0.29  TRYING [2]
% 0.12/0.29  TRYING [4]
% 0.12/0.30  % (23234)First to succeed.
% 0.12/0.30  % (23234)Refutation found. Thanks to Tanya!
% 0.12/0.30  % SZS status Theorem for theBenchmark
% 0.12/0.30  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.30  % (23234)------------------------------
% 0.12/0.30  % (23234)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.12/0.30  % (23234)Termination reason: Refutation
% 0.12/0.30  
% 0.12/0.30  % (23234)Memory used [KB]: 1150
% 0.12/0.30  % (23234)Time elapsed: 0.017 s
% 0.12/0.30  % (23234)Instructions burned: 43 (million)
% 0.12/0.30  % (23234)------------------------------
% 0.12/0.30  % (23234)------------------------------
% 0.12/0.30  % (23231)Success in time 0.025 s
%------------------------------------------------------------------------------