TSTP Solution File: NUM557+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM557+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.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 14:33:24 EDT 2024

% Result   : Theorem 0.11s 0.37s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  104 (  36 unt;   0 def)
%            Number of atoms       :  549 ( 100 equ)
%            Maximal formula atoms :   43 (   5 avg)
%            Number of connectives :  651 ( 206   ~; 170   |; 233   &)
%                                         (   5 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  12 con; 0-2 aty)
%            Number of variables   :  126 ( 106   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f453,plain,
    $false,
    inference(global_subsumption,[],[f253,f252,f251,f250,f254,f255,f256,f257,f259,f258,f262,f261,f260,f267,f266,f265,f264,f263,f270,f269,f268,f281,f431,f279,f278,f277,f276,f275,f432,f273,f272,f271,f308,f307,f306,f305,f304,f303,f302,f301,f300,f299,f298,f297,f296,f295,f294,f293,f292,f291,f290,f289,f288,f287,f286,f285,f284,f283,f282,f314,f433,f312,f311,f310,f309,f317,f316]) ).

fof(f316,plain,
    aSubsetOf0(xP,xS),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ( xk = sbrdtbr0(xP)
    & aSubsetOf0(xP,xS)
    & ! [X0] :
        ( aElementOf0(X0,xS)
        | ~ aElementOf0(X0,xP) ) ),
    inference(ennf_transformation,[],[f72]) ).

fof(f72,axiom,
    ( xk = sbrdtbr0(xP)
    & aSubsetOf0(xP,xS)
    & ! [X0] :
        ( aElementOf0(X0,xP)
       => aElementOf0(X0,xS) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2431) ).

fof(f317,plain,
    xk = sbrdtbr0(xP),
    inference(cnf_transformation,[],[f88]) ).

fof(f309,plain,
    ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(cnf_transformation,[],[f191]) ).

fof(f191,plain,
    ( ! [X0] :
        ( ( aElementOf0(X0,sdtmndt0(xQ,xy))
          | xy = X0
          | ~ aElementOf0(X0,xQ)
          | ~ aElement0(X0) )
        & ( ( xy != X0
            & aElementOf0(X0,xQ)
            & aElement0(X0) )
          | ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
    & aSet0(sdtmndt0(xQ,xy))
    & ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
    inference(flattening,[],[f190]) ).

fof(f190,plain,
    ( ! [X0] :
        ( ( aElementOf0(X0,sdtmndt0(xQ,xy))
          | xy = X0
          | ~ aElementOf0(X0,xQ)
          | ~ aElement0(X0) )
        & ( ( xy != X0
            & aElementOf0(X0,xQ)
            & aElement0(X0) )
          | ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
    & aSet0(sdtmndt0(xQ,xy))
    & ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f71,axiom,
    ( ! [X0] :
        ( aElementOf0(X0,sdtmndt0(xQ,xy))
      <=> ( xy != X0
          & aElementOf0(X0,xQ)
          & aElement0(X0) ) )
    & aSet0(sdtmndt0(xQ,xy))
    & ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2411) ).

fof(f310,plain,
    aSet0(sdtmndt0(xQ,xy)),
    inference(cnf_transformation,[],[f191]) ).

fof(f311,plain,
    ! [X0] :
      ( aElement0(X0)
      | ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f312,plain,
    ! [X0] :
      ( aElementOf0(X0,xQ)
      | ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f433,plain,
    ~ aElementOf0(xy,sdtmndt0(xQ,xy)),
    inference(equality_resolution,[],[f313]) ).

fof(f313,plain,
    ! [X0] :
      ( xy != X0
      | ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f314,plain,
    ! [X0] :
      ( aElementOf0(X0,sdtmndt0(xQ,xy))
      | xy = X0
      | ~ aElementOf0(X0,xQ)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f282,plain,
    aSet0(slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[],[f189]) ).

fof(f189,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & aElementOf0(sK7,slbdtsldtrb0(xS,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X1) != xk
          | ( ~ aSubsetOf0(X1,xS)
            & ( ( ~ aElementOf0(sK8(X1),xS)
                & aElementOf0(sK8(X1),X1) )
              | ~ aSet0(X1) ) ) )
        & ( ( sbrdtbr0(X1) = xk
            & aSubsetOf0(X1,xS)
            & ! [X3] :
                ( aElementOf0(X3,xS)
                | ~ aElementOf0(X3,X1) )
            & aSet0(X1) )
          | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ( ~ aElementOf0(sK9(X5),xT)
                & aElementOf0(sK9(X5),X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ( ~ aElementOf0(sK10(X8),xS)
                & aElementOf0(sK10(X8),X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f184,f188,f187,f186,f185]) ).

fof(f185,plain,
    ( ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
   => aElementOf0(sK7,slbdtsldtrb0(xS,xk)) ),
    introduced(choice_axiom,[]) ).

fof(f186,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,xS)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK8(X1),xS)
        & aElementOf0(sK8(X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f187,plain,
    ! [X5] :
      ( ? [X6] :
          ( ~ aElementOf0(X6,xT)
          & aElementOf0(X6,X5) )
     => ( ~ aElementOf0(sK9(X5),xT)
        & aElementOf0(sK9(X5),X5) ) ),
    introduced(choice_axiom,[]) ).

fof(f188,plain,
    ! [X8] :
      ( ? [X9] :
          ( ~ aElementOf0(X9,xS)
          & aElementOf0(X9,X8) )
     => ( ~ aElementOf0(sK10(X8),xS)
        & aElementOf0(sK10(X8),X8) ) ),
    introduced(choice_axiom,[]) ).

fof(f184,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X1) != xk
          | ( ~ aSubsetOf0(X1,xS)
            & ( ? [X2] :
                  ( ~ aElementOf0(X2,xS)
                  & aElementOf0(X2,X1) )
              | ~ aSet0(X1) ) ) )
        & ( ( sbrdtbr0(X1) = xk
            & aSubsetOf0(X1,xS)
            & ! [X3] :
                ( aElementOf0(X3,xS)
                | ~ aElementOf0(X3,X1) )
            & aSet0(X1) )
          | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,xT)
                  & aElementOf0(X6,X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ? [X9] :
                  ( ~ aElementOf0(X9,xS)
                  & aElementOf0(X9,X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(rectify,[],[f87]) ).

fof(f87,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk))
    & ! [X0] :
        ( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X0) != xk
          | ( ~ aSubsetOf0(X0,xS)
            & ( ? [X1] :
                  ( ~ aElementOf0(X1,xS)
                  & aElementOf0(X1,X0) )
              | ~ aSet0(X0) ) ) )
        & ( ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xS)
            & ! [X2] :
                ( aElementOf0(X2,xS)
                | ~ aElementOf0(X2,X0) )
            & aSet0(X0) )
          | ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,xT)
                  & aElementOf0(X6,X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ? [X9] :
                  ( ~ aElementOf0(X9,xS)
                  & aElementOf0(X9,X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(flattening,[],[f86]) ).

fof(f86,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk))
    & ! [X0] :
        ( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X0) != xk
          | ( ~ aSubsetOf0(X0,xS)
            & ( ? [X1] :
                  ( ~ aElementOf0(X1,xS)
                  & aElementOf0(X1,X0) )
              | ~ aSet0(X0) ) ) )
        & ( ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xS)
            & ! [X2] :
                ( aElementOf0(X2,xS)
                | ~ aElementOf0(X2,X0) )
            & aSet0(X0) )
          | ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,xT)
                  & aElementOf0(X6,X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ? [X9] :
                  ( ~ aElementOf0(X9,xS)
                  & aElementOf0(X9,X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f76,plain,
    ( ~ ( ! [X0] :
            ( ( ( sbrdtbr0(X0) = xk
                & ( aSubsetOf0(X0,xS)
                  | ( ! [X1] :
                        ( aElementOf0(X1,X0)
                       => aElementOf0(X1,xS) )
                    & aSet0(X0) ) ) )
             => aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
            & ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
             => ( sbrdtbr0(X0) = xk
                & aSubsetOf0(X0,xS)
                & ! [X2] :
                    ( aElementOf0(X2,X0)
                   => aElementOf0(X2,xS) )
                & aSet0(X0) ) ) )
       => ( slcrc0 = slbdtsldtrb0(xS,xk)
          | ~ ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xS,xk))
       => aElementOf0(X4,slbdtsldtrb0(xT,xk)) )
    & ! [X5] :
        ( ( ( xk = sbrdtbr0(X5)
            & ( aSubsetOf0(X5,xT)
              | ( ! [X6] :
                    ( aElementOf0(X6,X5)
                   => aElementOf0(X6,xT) )
                & aSet0(X5) ) ) )
         => aElementOf0(X5,slbdtsldtrb0(xT,xk)) )
        & ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
         => ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,X5)
               => aElementOf0(X7,xT) )
            & aSet0(X5) ) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( ( xk = sbrdtbr0(X8)
            & ( aSubsetOf0(X8,xS)
              | ( ! [X9] :
                    ( aElementOf0(X9,X8)
                   => aElementOf0(X9,xS) )
                & aSet0(X8) ) ) )
         => aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
        & ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
         => ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,X8)
               => aElementOf0(X10,xS) )
            & aSet0(X8) ) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(rectify,[],[f63]) ).

fof(f63,axiom,
    ( ~ ( ! [X0] :
            ( ( ( sbrdtbr0(X0) = xk
                & ( aSubsetOf0(X0,xS)
                  | ( ! [X1] :
                        ( aElementOf0(X1,X0)
                       => aElementOf0(X1,xS) )
                    & aSet0(X0) ) ) )
             => aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
            & ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
             => ( sbrdtbr0(X0) = xk
                & aSubsetOf0(X0,xS)
                & ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xS) )
                & aSet0(X0) ) ) )
       => ( slcrc0 = slbdtsldtrb0(xS,xk)
          | ~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X0] :
        ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
       => aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
    & ! [X0] :
        ( ( ( sbrdtbr0(X0) = xk
            & ( aSubsetOf0(X0,xT)
              | ( ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xT) )
                & aSet0(X0) ) ) )
         => aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
        & ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
         => ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xT)
            & ! [X1] :
                ( aElementOf0(X1,X0)
               => aElementOf0(X1,xT) )
            & aSet0(X0) ) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X0] :
        ( ( ( sbrdtbr0(X0) = xk
            & ( aSubsetOf0(X0,xS)
              | ( ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xS) )
                & aSet0(X0) ) ) )
         => aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
        & ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
         => ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xS)
            & ! [X1] :
                ( aElementOf0(X1,X0)
               => aElementOf0(X1,xS) )
            & aSet0(X0) ) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).

fof(f283,plain,
    ! [X8] :
      ( aSet0(X8)
      | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f284,plain,
    ! [X10,X8] :
      ( aElementOf0(X10,xS)
      | ~ aElementOf0(X10,X8)
      | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f285,plain,
    ! [X8] :
      ( aSubsetOf0(X8,xS)
      | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f286,plain,
    ! [X8] :
      ( xk = sbrdtbr0(X8)
      | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f287,plain,
    ! [X8] :
      ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
      | xk != sbrdtbr0(X8)
      | aElementOf0(sK10(X8),X8)
      | ~ aSet0(X8) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f288,plain,
    ! [X8] :
      ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
      | xk != sbrdtbr0(X8)
      | ~ aElementOf0(sK10(X8),xS)
      | ~ aSet0(X8) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f289,plain,
    ! [X8] :
      ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
      | xk != sbrdtbr0(X8)
      | ~ aSubsetOf0(X8,xS) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f290,plain,
    aSet0(slbdtsldtrb0(xT,xk)),
    inference(cnf_transformation,[],[f189]) ).

fof(f291,plain,
    ! [X5] :
      ( aSet0(X5)
      | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f292,plain,
    ! [X7,X5] :
      ( aElementOf0(X7,xT)
      | ~ aElementOf0(X7,X5)
      | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f293,plain,
    ! [X5] :
      ( aSubsetOf0(X5,xT)
      | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f294,plain,
    ! [X5] :
      ( xk = sbrdtbr0(X5)
      | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f295,plain,
    ! [X5] :
      ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
      | xk != sbrdtbr0(X5)
      | aElementOf0(sK9(X5),X5)
      | ~ aSet0(X5) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f296,plain,
    ! [X5] :
      ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
      | xk != sbrdtbr0(X5)
      | ~ aElementOf0(sK9(X5),xT)
      | ~ aSet0(X5) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f297,plain,
    ! [X5] :
      ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
      | xk != sbrdtbr0(X5)
      | ~ aSubsetOf0(X5,xT) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f298,plain,
    ! [X4] :
      ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
      | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f299,plain,
    aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
    inference(cnf_transformation,[],[f189]) ).

fof(f300,plain,
    ! [X1] :
      ( aSet0(X1)
      | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f301,plain,
    ! [X3,X1] :
      ( aElementOf0(X3,xS)
      | ~ aElementOf0(X3,X1)
      | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f302,plain,
    ! [X1] :
      ( aSubsetOf0(X1,xS)
      | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f303,plain,
    ! [X1] :
      ( sbrdtbr0(X1) = xk
      | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f304,plain,
    ! [X1] :
      ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
      | sbrdtbr0(X1) != xk
      | aElementOf0(sK8(X1),X1)
      | ~ aSet0(X1) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f305,plain,
    ! [X1] :
      ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
      | sbrdtbr0(X1) != xk
      | ~ aElementOf0(sK8(X1),xS)
      | ~ aSet0(X1) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f306,plain,
    ! [X1] :
      ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
      | sbrdtbr0(X1) != xk
      | ~ aSubsetOf0(X1,xS) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f307,plain,
    aElementOf0(sK7,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[],[f189]) ).

fof(f308,plain,
    slcrc0 != slbdtsldtrb0(xS,xk),
    inference(cnf_transformation,[],[f189]) ).

fof(f271,plain,
    aSet0(sdtmndt0(xQ,xy)),
    inference(cnf_transformation,[],[f183]) ).

fof(f183,plain,
    ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
    & ! [X0] :
        ( ( aElementOf0(X0,xP)
          | ( xx != X0
            & ~ aElementOf0(X0,sdtmndt0(xQ,xy)) )
          | ~ aElement0(X0) )
        & ( ( ( xx = X0
              | aElementOf0(X0,sdtmndt0(xQ,xy)) )
            & aElement0(X0) )
          | ~ aElementOf0(X0,xP) ) )
    & aSet0(xP)
    & ! [X1] :
        ( ( aElementOf0(X1,sdtmndt0(xQ,xy))
          | xy = X1
          | ~ aElementOf0(X1,xQ)
          | ~ aElement0(X1) )
        & ( ( xy != X1
            & aElementOf0(X1,xQ)
            & aElement0(X1) )
          | ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ) )
    & aSet0(sdtmndt0(xQ,xy)) ),
    inference(flattening,[],[f182]) ).

fof(f182,plain,
    ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
    & ! [X0] :
        ( ( aElementOf0(X0,xP)
          | ( xx != X0
            & ~ aElementOf0(X0,sdtmndt0(xQ,xy)) )
          | ~ aElement0(X0) )
        & ( ( ( xx = X0
              | aElementOf0(X0,sdtmndt0(xQ,xy)) )
            & aElement0(X0) )
          | ~ aElementOf0(X0,xP) ) )
    & aSet0(xP)
    & ! [X1] :
        ( ( aElementOf0(X1,sdtmndt0(xQ,xy))
          | xy = X1
          | ~ aElementOf0(X1,xQ)
          | ~ aElement0(X1) )
        & ( ( xy != X1
            & aElementOf0(X1,xQ)
            & aElement0(X1) )
          | ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ) )
    & aSet0(sdtmndt0(xQ,xy)) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
    & ! [X0] :
        ( aElementOf0(X0,xP)
      <=> ( ( xx = X0
            | aElementOf0(X0,sdtmndt0(xQ,xy)) )
          & aElement0(X0) ) )
    & aSet0(xP)
    & ! [X1] :
        ( aElementOf0(X1,sdtmndt0(xQ,xy))
      <=> ( xy != X1
          & aElementOf0(X1,xQ)
          & aElement0(X1) ) )
    & aSet0(sdtmndt0(xQ,xy)) ),
    inference(rectify,[],[f70]) ).

fof(f70,axiom,
    ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
    & ! [X0] :
        ( aElementOf0(X0,xP)
      <=> ( ( xx = X0
            | aElementOf0(X0,sdtmndt0(xQ,xy)) )
          & aElement0(X0) ) )
    & aSet0(xP)
    & ! [X0] :
        ( aElementOf0(X0,sdtmndt0(xQ,xy))
      <=> ( xy != X0
          & aElementOf0(X0,xQ)
          & aElement0(X0) ) )
    & aSet0(sdtmndt0(xQ,xy)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).

fof(f272,plain,
    ! [X1] :
      ( aElement0(X1)
      | ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f273,plain,
    ! [X1] :
      ( aElementOf0(X1,xQ)
      | ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f432,plain,
    ~ aElementOf0(xy,sdtmndt0(xQ,xy)),
    inference(equality_resolution,[],[f274]) ).

fof(f274,plain,
    ! [X1] :
      ( xy != X1
      | ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f275,plain,
    ! [X1] :
      ( aElementOf0(X1,sdtmndt0(xQ,xy))
      | xy = X1
      | ~ aElementOf0(X1,xQ)
      | ~ aElement0(X1) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f276,plain,
    aSet0(xP),
    inference(cnf_transformation,[],[f183]) ).

fof(f277,plain,
    ! [X0] :
      ( aElement0(X0)
      | ~ aElementOf0(X0,xP) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f278,plain,
    ! [X0] :
      ( xx = X0
      | aElementOf0(X0,sdtmndt0(xQ,xy))
      | ~ aElementOf0(X0,xP) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f279,plain,
    ! [X0] :
      ( aElementOf0(X0,xP)
      | ~ aElementOf0(X0,sdtmndt0(xQ,xy))
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f431,plain,
    ( aElementOf0(xx,xP)
    | ~ aElement0(xx) ),
    inference(equality_resolution,[],[f280]) ).

fof(f280,plain,
    ! [X0] :
      ( aElementOf0(X0,xP)
      | xx != X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f281,plain,
    xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
    inference(cnf_transformation,[],[f183]) ).

fof(f268,plain,
    aSet0(xS),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    ( sz00 != xk
    & aSet0(xT)
    & aSet0(xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).

fof(f269,plain,
    aSet0(xT),
    inference(cnf_transformation,[],[f62]) ).

fof(f270,plain,
    sz00 != xk,
    inference(cnf_transformation,[],[f62]) ).

fof(f263,plain,
    aSet0(xQ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
    & xk = sbrdtbr0(xQ)
    & aSubsetOf0(xQ,xS)
    & ! [X0] :
        ( aElementOf0(X0,xS)
        | ~ aElementOf0(X0,xQ) )
    & aSet0(xQ) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,axiom,
    ( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
    & xk = sbrdtbr0(xQ)
    & aSubsetOf0(xQ,xS)
    & ! [X0] :
        ( aElementOf0(X0,xQ)
       => aElementOf0(X0,xS) )
    & aSet0(xQ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).

fof(f264,plain,
    ! [X0] :
      ( aElementOf0(X0,xS)
      | ~ aElementOf0(X0,xQ) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f265,plain,
    aSubsetOf0(xQ,xS),
    inference(cnf_transformation,[],[f85]) ).

fof(f266,plain,
    xk = sbrdtbr0(xQ),
    inference(cnf_transformation,[],[f85]) ).

fof(f267,plain,
    aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[],[f85]) ).

fof(f260,plain,
    aSet0(xQ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    ( xk = sbrdtbr0(xQ)
    & isFinite0(xQ)
    & aSet0(xQ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).

fof(f261,plain,
    isFinite0(xQ),
    inference(cnf_transformation,[],[f66]) ).

fof(f262,plain,
    xk = sbrdtbr0(xQ),
    inference(cnf_transformation,[],[f66]) ).

fof(f258,plain,
    aElement0(xy),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,axiom,
    ( aElementOf0(xy,xQ)
    & aElement0(xy) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).

fof(f259,plain,
    aElementOf0(xy,xQ),
    inference(cnf_transformation,[],[f67]) ).

fof(f257,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,axiom,
    aElementOf0(xk,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).

fof(f256,plain,
    aElementOf0(xx,xS),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).

fof(f255,plain,
    ~ aElementOf0(xx,xQ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,axiom,
    ~ aElementOf0(xx,xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2338) ).

fof(f254,plain,
    ~ aElementOf0(xx,xQ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,axiom,
    ~ aElementOf0(xx,xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2323) ).

fof(f250,plain,
    ( xk != sbrdtbr0(xP)
    | aElementOf0(sK6,xP) ),
    inference(cnf_transformation,[],[f181]) ).

fof(f181,plain,
    ( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
    & ( xk != sbrdtbr0(xP)
      | ( ~ aSubsetOf0(xP,xS)
        & ~ aElementOf0(sK6,xS)
        & aElementOf0(sK6,xP) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f84,f180]) ).

fof(f180,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,xS)
        & aElementOf0(X0,xP) )
   => ( ~ aElementOf0(sK6,xS)
      & aElementOf0(sK6,xP) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ( ~ aElementOf0(xP,slbdtsldtrb0(xS,xk))
    & ( xk != sbrdtbr0(xP)
      | ( ~ aSubsetOf0(xP,xS)
        & ? [X0] :
            ( ~ aElementOf0(X0,xS)
            & aElementOf0(X0,xP) ) ) ) ),
    inference(ennf_transformation,[],[f74]) ).

fof(f74,negated_conjecture,
    ~ ( aElementOf0(xP,slbdtsldtrb0(xS,xk))
      | ( xk = sbrdtbr0(xP)
        & ( aSubsetOf0(xP,xS)
          | ! [X0] :
              ( aElementOf0(X0,xP)
             => aElementOf0(X0,xS) ) ) ) ),
    inference(negated_conjecture,[],[f73]) ).

fof(f73,conjecture,
    ( aElementOf0(xP,slbdtsldtrb0(xS,xk))
    | ( xk = sbrdtbr0(xP)
      & ( aSubsetOf0(xP,xS)
        | ! [X0] :
            ( aElementOf0(X0,xP)
           => aElementOf0(X0,xS) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f251,plain,
    ( xk != sbrdtbr0(xP)
    | ~ aElementOf0(sK6,xS) ),
    inference(cnf_transformation,[],[f181]) ).

fof(f252,plain,
    ( xk != sbrdtbr0(xP)
    | ~ aSubsetOf0(xP,xS) ),
    inference(cnf_transformation,[],[f181]) ).

fof(f253,plain,
    ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[],[f181]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem    : NUM557+3 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33  % Computer : n021.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Mon Apr 29 23:56:25 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.34  % (2713)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.36  % (2716)WARNING: value z3 for option sas not known
% 0.11/0.36  % (2716)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)
% 0.11/0.37  % (2716)First to succeed.
% 0.11/0.37  % (2716)Refutation found. Thanks to Tanya!
% 0.11/0.37  % SZS status Theorem for theBenchmark
% 0.11/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.37  % (2716)------------------------------
% 0.11/0.37  % (2716)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.37  % (2716)Termination reason: Refutation
% 0.11/0.37  
% 0.11/0.37  % (2716)Memory used [KB]: 1011
% 0.11/0.37  % (2716)Time elapsed: 0.009 s
% 0.11/0.37  % (2716)Instructions burned: 15 (million)
% 0.11/0.37  % (2716)------------------------------
% 0.11/0.37  % (2716)------------------------------
% 0.11/0.37  % (2713)Success in time 0.034 s
%------------------------------------------------------------------------------