TSTP Solution File: NUM566+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM566+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 02:09:24 EDT 2024

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   88 (  16 unt;   0 def)
%            Number of atoms       :  486 (  91 equ)
%            Maximal formula atoms :   24 (   5 avg)
%            Number of connectives :  583 ( 185   ~; 154   |; 205   &)
%                                         (   8 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   7 con; 0-2 aty)
%            Number of variables   :  165 ( 131   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2437,plain,
    $false,
    inference(resolution,[],[f2432,f638]) ).

fof(f638,plain,
    aElementOf0(slcrc0,szDzozmdt0(xc)),
    inference(forward_demodulation,[],[f401,f633]) ).

fof(f633,plain,
    szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00),
    inference(forward_demodulation,[],[f384,f374]) ).

fof(f374,plain,
    sz00 = xK,
    inference(cnf_transformation,[],[f78]) ).

fof(f78,axiom,
    sz00 = xK,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).

fof(f384,plain,
    szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
    inference(cnf_transformation,[],[f245]) ).

fof(f245,plain,
    ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
    & ! [X0] :
        ( aElementOf0(X0,xT)
        | ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
    & ! [X1] :
        ( ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
          | ! [X2] :
              ( sdtlpdtrp0(xc,X2) != X1
              | ~ aElementOf0(X2,szDzozmdt0(xc)) ) )
        & ( ( sdtlpdtrp0(xc,sK24(X1)) = X1
            & aElementOf0(sK24(X1),szDzozmdt0(xc)) )
          | ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
    & aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & ! [X4] :
        ( ( aElementOf0(X4,szDzozmdt0(xc))
          | xK != sbrdtbr0(X4)
          | ( ~ aSubsetOf0(X4,xS)
            & ( ( ~ aElementOf0(sK25(X4),xS)
                & aElementOf0(sK25(X4),X4) )
              | ~ aSet0(X4) ) ) )
        & ( ( xK = sbrdtbr0(X4)
            & aSubsetOf0(X4,xS)
            & ! [X6] :
                ( aElementOf0(X6,xS)
                | ~ aElementOf0(X6,X4) )
            & aSet0(X4) )
          | ~ aElementOf0(X4,szDzozmdt0(xc)) ) )
    & aFunction0(xc) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f242,f244,f243]) ).

fof(f243,plain,
    ! [X1] :
      ( ? [X3] :
          ( sdtlpdtrp0(xc,X3) = X1
          & aElementOf0(X3,szDzozmdt0(xc)) )
     => ( sdtlpdtrp0(xc,sK24(X1)) = X1
        & aElementOf0(sK24(X1),szDzozmdt0(xc)) ) ),
    introduced(choice_axiom,[]) ).

fof(f244,plain,
    ! [X4] :
      ( ? [X5] :
          ( ~ aElementOf0(X5,xS)
          & aElementOf0(X5,X4) )
     => ( ~ aElementOf0(sK25(X4),xS)
        & aElementOf0(sK25(X4),X4) ) ),
    introduced(choice_axiom,[]) ).

fof(f242,plain,
    ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
    & ! [X0] :
        ( aElementOf0(X0,xT)
        | ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
    & ! [X1] :
        ( ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
          | ! [X2] :
              ( sdtlpdtrp0(xc,X2) != X1
              | ~ aElementOf0(X2,szDzozmdt0(xc)) ) )
        & ( ? [X3] :
              ( sdtlpdtrp0(xc,X3) = X1
              & aElementOf0(X3,szDzozmdt0(xc)) )
          | ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
    & aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & ! [X4] :
        ( ( aElementOf0(X4,szDzozmdt0(xc))
          | xK != sbrdtbr0(X4)
          | ( ~ aSubsetOf0(X4,xS)
            & ( ? [X5] :
                  ( ~ aElementOf0(X5,xS)
                  & aElementOf0(X5,X4) )
              | ~ aSet0(X4) ) ) )
        & ( ( xK = sbrdtbr0(X4)
            & aSubsetOf0(X4,xS)
            & ! [X6] :
                ( aElementOf0(X6,xS)
                | ~ aElementOf0(X6,X4) )
            & aSet0(X4) )
          | ~ aElementOf0(X4,szDzozmdt0(xc)) ) )
    & aFunction0(xc) ),
    inference(rectify,[],[f241]) ).

fof(f241,plain,
    ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
    & ! [X0] :
        ( aElementOf0(X0,xT)
        | ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
    & ! [X1] :
        ( ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
          | ! [X2] :
              ( sdtlpdtrp0(xc,X2) != X1
              | ~ aElementOf0(X2,szDzozmdt0(xc)) ) )
        & ( ? [X2] :
              ( sdtlpdtrp0(xc,X2) = X1
              & aElementOf0(X2,szDzozmdt0(xc)) )
          | ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
    & aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & ! [X3] :
        ( ( aElementOf0(X3,szDzozmdt0(xc))
          | sbrdtbr0(X3) != xK
          | ( ~ aSubsetOf0(X3,xS)
            & ( ? [X4] :
                  ( ~ aElementOf0(X4,xS)
                  & aElementOf0(X4,X3) )
              | ~ aSet0(X3) ) ) )
        & ( ( sbrdtbr0(X3) = xK
            & aSubsetOf0(X3,xS)
            & ! [X5] :
                ( aElementOf0(X5,xS)
                | ~ aElementOf0(X5,X3) )
            & aSet0(X3) )
          | ~ aElementOf0(X3,szDzozmdt0(xc)) ) )
    & aFunction0(xc) ),
    inference(nnf_transformation,[],[f98]) ).

fof(f98,plain,
    ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
    & ! [X0] :
        ( aElementOf0(X0,xT)
        | ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
    & ! [X1] :
        ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
      <=> ? [X2] :
            ( sdtlpdtrp0(xc,X2) = X1
            & aElementOf0(X2,szDzozmdt0(xc)) ) )
    & aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & ! [X3] :
        ( ( aElementOf0(X3,szDzozmdt0(xc))
          | sbrdtbr0(X3) != xK
          | ( ~ aSubsetOf0(X3,xS)
            & ( ? [X4] :
                  ( ~ aElementOf0(X4,xS)
                  & aElementOf0(X4,X3) )
              | ~ aSet0(X3) ) ) )
        & ( ( sbrdtbr0(X3) = xK
            & aSubsetOf0(X3,xS)
            & ! [X5] :
                ( aElementOf0(X5,xS)
                | ~ aElementOf0(X5,X3) )
            & aSet0(X3) )
          | ~ aElementOf0(X3,szDzozmdt0(xc)) ) )
    & aFunction0(xc) ),
    inference(flattening,[],[f97]) ).

fof(f97,plain,
    ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
    & ! [X0] :
        ( aElementOf0(X0,xT)
        | ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
    & ! [X1] :
        ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
      <=> ? [X2] :
            ( sdtlpdtrp0(xc,X2) = X1
            & aElementOf0(X2,szDzozmdt0(xc)) ) )
    & aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & ! [X3] :
        ( ( aElementOf0(X3,szDzozmdt0(xc))
          | sbrdtbr0(X3) != xK
          | ( ~ aSubsetOf0(X3,xS)
            & ( ? [X4] :
                  ( ~ aElementOf0(X4,xS)
                  & aElementOf0(X4,X3) )
              | ~ aSet0(X3) ) ) )
        & ( ( sbrdtbr0(X3) = xK
            & aSubsetOf0(X3,xS)
            & ! [X5] :
                ( aElementOf0(X5,xS)
                | ~ aElementOf0(X5,X3) )
            & aSet0(X3) )
          | ~ aElementOf0(X3,szDzozmdt0(xc)) ) )
    & aFunction0(xc) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,plain,
    ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
    & ! [X0] :
        ( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
       => aElementOf0(X0,xT) )
    & ! [X1] :
        ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
      <=> ? [X2] :
            ( sdtlpdtrp0(xc,X2) = X1
            & aElementOf0(X2,szDzozmdt0(xc)) ) )
    & aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & ! [X3] :
        ( ( ( sbrdtbr0(X3) = xK
            & ( aSubsetOf0(X3,xS)
              | ( ! [X4] :
                    ( aElementOf0(X4,X3)
                   => aElementOf0(X4,xS) )
                & aSet0(X3) ) ) )
         => aElementOf0(X3,szDzozmdt0(xc)) )
        & ( aElementOf0(X3,szDzozmdt0(xc))
         => ( sbrdtbr0(X3) = xK
            & aSubsetOf0(X3,xS)
            & ! [X5] :
                ( aElementOf0(X5,X3)
               => aElementOf0(X5,xS) )
            & aSet0(X3) ) ) )
    & aFunction0(xc) ),
    inference(rectify,[],[f76]) ).

fof(f76,axiom,
    ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
    & ! [X0] :
        ( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
       => aElementOf0(X0,xT) )
    & ! [X0] :
        ( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
      <=> ? [X1] :
            ( sdtlpdtrp0(xc,X1) = X0
            & aElementOf0(X1,szDzozmdt0(xc)) ) )
    & aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & ! [X0] :
        ( ( ( sbrdtbr0(X0) = xK
            & ( aSubsetOf0(X0,xS)
              | ( ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xS) )
                & aSet0(X0) ) ) )
         => aElementOf0(X0,szDzozmdt0(xc)) )
        & ( aElementOf0(X0,szDzozmdt0(xc))
         => ( sbrdtbr0(X0) = xK
            & aSubsetOf0(X0,xS)
            & ! [X1] :
                ( aElementOf0(X1,X0)
               => aElementOf0(X1,xS) )
            & aSet0(X0) ) ) )
    & aFunction0(xc) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).

fof(f401,plain,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
    & aSubsetOf0(slcrc0,xS)
    & ! [X0] :
        ( aElementOf0(X0,xS)
        | ~ aElementOf0(X0,slcrc0) )
    & ! [X1] : ~ aElementOf0(X1,slcrc0)
    & aSet0(slcrc0) ),
    inference(ennf_transformation,[],[f85]) ).

fof(f85,plain,
    ( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
    & aSubsetOf0(slcrc0,xS)
    & ! [X0] :
        ( aElementOf0(X0,slcrc0)
       => aElementOf0(X0,xS) )
    & ~ ? [X1] : aElementOf0(X1,slcrc0)
    & aSet0(slcrc0) ),
    inference(rectify,[],[f79]) ).

fof(f79,axiom,
    ( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
    & aSubsetOf0(slcrc0,xS)
    & ! [X0] :
        ( aElementOf0(X0,slcrc0)
       => aElementOf0(X0,xS) )
    & ~ ? [X0] : aElementOf0(X0,slcrc0)
    & aSet0(slcrc0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3476) ).

fof(f2432,plain,
    ~ aElementOf0(slcrc0,szDzozmdt0(xc)),
    inference(resolution,[],[f2430,f1363]) ).

fof(f1363,plain,
    ! [X0] :
      ( aElementOf0(sdtlpdtrp0(xc,X0),xT)
      | ~ aElementOf0(X0,szDzozmdt0(xc)) ),
    inference(resolution,[],[f599,f389]) ).

fof(f389,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
      | aElementOf0(X0,xT) ),
    inference(cnf_transformation,[],[f245]) ).

fof(f599,plain,
    ! [X2] :
      ( aElementOf0(sdtlpdtrp0(xc,X2),sdtlcdtrc0(xc,szDzozmdt0(xc)))
      | ~ aElementOf0(X2,szDzozmdt0(xc)) ),
    inference(equality_resolution,[],[f388]) ).

fof(f388,plain,
    ! [X2,X1] :
      ( aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc)))
      | sdtlpdtrp0(xc,X2) != X1
      | ~ aElementOf0(X2,szDzozmdt0(xc)) ),
    inference(cnf_transformation,[],[f245]) ).

fof(f2430,plain,
    ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
    inference(resolution,[],[f2427,f393]) ).

fof(f393,plain,
    aSet0(xS),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ( isCountable0(xS)
    & aSubsetOf0(xS,szNzAzT0)
    & ! [X0] :
        ( aElementOf0(X0,szNzAzT0)
        | ~ aElementOf0(X0,xS) )
    & aSet0(xS) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,axiom,
    ( isCountable0(xS)
    & aSubsetOf0(xS,szNzAzT0)
    & ! [X0] :
        ( aElementOf0(X0,xS)
       => aElementOf0(X0,szNzAzT0) )
    & aSet0(xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).

fof(f2427,plain,
    ( ~ aSet0(xS)
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(resolution,[],[f2425,f480]) ).

fof(f480,plain,
    ! [X0] :
      ( aSubsetOf0(X0,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0] :
      ( aSubsetOf0(X0,X0)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( aSet0(X0)
     => aSubsetOf0(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).

fof(f2425,plain,
    ( ~ aSubsetOf0(xS,xS)
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(resolution,[],[f2325,f396]) ).

fof(f396,plain,
    isCountable0(xS),
    inference(cnf_transformation,[],[f99]) ).

fof(f2325,plain,
    ( ~ isCountable0(xS)
    | ~ aSubsetOf0(xS,xS)
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(resolution,[],[f2322,f373]) ).

fof(f373,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | ~ isCountable0(X1)
      | ~ aSubsetOf0(X1,xS)
      | ~ aElementOf0(X0,xT) ),
    inference(cnf_transformation,[],[f240]) ).

fof(f240,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP0(X0,X1)
          | ~ isCountable0(X1)
          | ( ~ aSubsetOf0(X1,xS)
            & ( ( ~ aElementOf0(sK23(X1),xS)
                & aElementOf0(sK23(X1),X1) )
              | ~ aSet0(X1) ) ) )
      | ~ aElementOf0(X0,xT) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f238,f239]) ).

fof(f239,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,xS)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK23(X1),xS)
        & aElementOf0(sK23(X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f238,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP0(X0,X1)
          | ~ isCountable0(X1)
          | ( ~ aSubsetOf0(X1,xS)
            & ( ? [X2] :
                  ( ~ aElementOf0(X2,xS)
                  & aElementOf0(X2,X1) )
              | ~ aSet0(X1) ) ) )
      | ~ aElementOf0(X0,xT) ),
    inference(rectify,[],[f204]) ).

fof(f204,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP0(X0,X1)
          | ~ isCountable0(X1)
          | ( ~ aSubsetOf0(X1,xS)
            & ( ? [X4] :
                  ( ~ aElementOf0(X4,xS)
                  & aElementOf0(X4,X1) )
              | ~ aSet0(X1) ) ) )
      | ~ aElementOf0(X0,xT) ),
    inference(definition_folding,[],[f96,f203]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtlpdtrp0(xc,X2) != X0
          & aElementOf0(X2,slbdtsldtrb0(X1,xK))
          & sbrdtbr0(X2) = xK
          & aSubsetOf0(X2,X1)
          & ! [X3] :
              ( aElementOf0(X3,X1)
              | ~ aElementOf0(X3,X2) )
          & aSet0(X2) )
      | ~ sP0(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f96,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( sdtlpdtrp0(xc,X2) != X0
              & aElementOf0(X2,slbdtsldtrb0(X1,xK))
              & sbrdtbr0(X2) = xK
              & aSubsetOf0(X2,X1)
              & ! [X3] :
                  ( aElementOf0(X3,X1)
                  | ~ aElementOf0(X3,X2) )
              & aSet0(X2) )
          | ~ isCountable0(X1)
          | ( ~ aSubsetOf0(X1,xS)
            & ( ? [X4] :
                  ( ~ aElementOf0(X4,xS)
                  & aElementOf0(X4,X1) )
              | ~ aSet0(X1) ) ) )
      | ~ aElementOf0(X0,xT) ),
    inference(flattening,[],[f95]) ).

fof(f95,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( sdtlpdtrp0(xc,X2) != X0
              & aElementOf0(X2,slbdtsldtrb0(X1,xK))
              & sbrdtbr0(X2) = xK
              & aSubsetOf0(X2,X1)
              & ! [X3] :
                  ( aElementOf0(X3,X1)
                  | ~ aElementOf0(X3,X2) )
              & aSet0(X2) )
          | ~ isCountable0(X1)
          | ( ~ aSubsetOf0(X1,xS)
            & ( ? [X4] :
                  ( ~ aElementOf0(X4,xS)
                  & aElementOf0(X4,X1) )
              | ~ aSet0(X1) ) ) )
      | ~ aElementOf0(X0,xT) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,plain,
    ~ ? [X0] :
        ( ? [X1] :
            ( ! [X2] :
                ( ( aElementOf0(X2,slbdtsldtrb0(X1,xK))
                  & sbrdtbr0(X2) = xK
                  & aSubsetOf0(X2,X1)
                  & ! [X3] :
                      ( aElementOf0(X3,X2)
                     => aElementOf0(X3,X1) )
                  & aSet0(X2) )
               => sdtlpdtrp0(xc,X2) = X0 )
            & isCountable0(X1)
            & ( aSubsetOf0(X1,xS)
              | ( ! [X4] :
                    ( aElementOf0(X4,X1)
                   => aElementOf0(X4,xS) )
                & aSet0(X1) ) ) )
        & aElementOf0(X0,xT) ),
    inference(rectify,[],[f82]) ).

fof(f82,negated_conjecture,
    ~ ? [X0] :
        ( ? [X1] :
            ( ! [X2] :
                ( ( aElementOf0(X2,slbdtsldtrb0(X1,xK))
                  & sbrdtbr0(X2) = xK
                  & aSubsetOf0(X2,X1)
                  & ! [X3] :
                      ( aElementOf0(X3,X2)
                     => aElementOf0(X3,X1) )
                  & aSet0(X2) )
               => sdtlpdtrp0(xc,X2) = X0 )
            & isCountable0(X1)
            & ( aSubsetOf0(X1,xS)
              | ( ! [X2] :
                    ( aElementOf0(X2,X1)
                   => aElementOf0(X2,xS) )
                & aSet0(X1) ) ) )
        & aElementOf0(X0,xT) ),
    inference(negated_conjecture,[],[f81]) ).

fof(f81,conjecture,
    ? [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( ( aElementOf0(X2,slbdtsldtrb0(X1,xK))
                & sbrdtbr0(X2) = xK
                & aSubsetOf0(X2,X1)
                & ! [X3] :
                    ( aElementOf0(X3,X2)
                   => aElementOf0(X3,X1) )
                & aSet0(X2) )
             => sdtlpdtrp0(xc,X2) = X0 )
          & isCountable0(X1)
          & ( aSubsetOf0(X1,xS)
            | ( ! [X2] :
                  ( aElementOf0(X2,X1)
                 => aElementOf0(X2,xS) )
              & aSet0(X1) ) ) )
      & aElementOf0(X0,xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f2322,plain,
    ~ sP0(sdtlpdtrp0(xc,slcrc0),xS),
    inference(trivial_inequality_removal,[],[f2318]) ).

fof(f2318,plain,
    ( sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,slcrc0)
    | ~ sP0(sdtlpdtrp0(xc,slcrc0),xS) ),
    inference(superposition,[],[f370,f2257]) ).

fof(f2257,plain,
    slcrc0 = sK22(sdtlpdtrp0(xc,slcrc0),xS),
    inference(resolution,[],[f2253,f638]) ).

fof(f2253,plain,
    ( ~ aElementOf0(slcrc0,szDzozmdt0(xc))
    | slcrc0 = sK22(sdtlpdtrp0(xc,slcrc0),xS) ),
    inference(resolution,[],[f2251,f1363]) ).

fof(f2251,plain,
    ( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
    | slcrc0 = sK22(sdtlpdtrp0(xc,slcrc0),xS) ),
    inference(resolution,[],[f2248,f393]) ).

fof(f2248,plain,
    ( ~ aSet0(xS)
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
    | slcrc0 = sK22(sdtlpdtrp0(xc,slcrc0),xS) ),
    inference(resolution,[],[f2207,f480]) ).

fof(f2207,plain,
    ( ~ aSubsetOf0(xS,xS)
    | slcrc0 = sK22(sdtlpdtrp0(xc,slcrc0),xS)
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(resolution,[],[f1431,f396]) ).

fof(f1431,plain,
    ( ~ isCountable0(xS)
    | slcrc0 = sK22(sdtlpdtrp0(xc,slcrc0),xS)
    | ~ aSubsetOf0(xS,xS)
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(resolution,[],[f1427,f373]) ).

fof(f1427,plain,
    ( ~ sP0(sdtlpdtrp0(xc,slcrc0),xS)
    | slcrc0 = sK22(sdtlpdtrp0(xc,slcrc0),xS) ),
    inference(resolution,[],[f1406,f365]) ).

fof(f365,plain,
    ! [X0,X1] :
      ( aSet0(sK22(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f237]) ).

fof(f237,plain,
    ! [X0,X1] :
      ( ( sdtlpdtrp0(xc,sK22(X0,X1)) != X0
        & aElementOf0(sK22(X0,X1),slbdtsldtrb0(X1,xK))
        & xK = sbrdtbr0(sK22(X0,X1))
        & aSubsetOf0(sK22(X0,X1),X1)
        & ! [X3] :
            ( aElementOf0(X3,X1)
            | ~ aElementOf0(X3,sK22(X0,X1)) )
        & aSet0(sK22(X0,X1)) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f235,f236]) ).

fof(f236,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtlpdtrp0(xc,X2) != X0
          & aElementOf0(X2,slbdtsldtrb0(X1,xK))
          & sbrdtbr0(X2) = xK
          & aSubsetOf0(X2,X1)
          & ! [X3] :
              ( aElementOf0(X3,X1)
              | ~ aElementOf0(X3,X2) )
          & aSet0(X2) )
     => ( sdtlpdtrp0(xc,sK22(X0,X1)) != X0
        & aElementOf0(sK22(X0,X1),slbdtsldtrb0(X1,xK))
        & xK = sbrdtbr0(sK22(X0,X1))
        & aSubsetOf0(sK22(X0,X1),X1)
        & ! [X3] :
            ( aElementOf0(X3,X1)
            | ~ aElementOf0(X3,sK22(X0,X1)) )
        & aSet0(sK22(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f235,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtlpdtrp0(xc,X2) != X0
          & aElementOf0(X2,slbdtsldtrb0(X1,xK))
          & sbrdtbr0(X2) = xK
          & aSubsetOf0(X2,X1)
          & ! [X3] :
              ( aElementOf0(X3,X1)
              | ~ aElementOf0(X3,X2) )
          & aSet0(X2) )
      | ~ sP0(X0,X1) ),
    inference(nnf_transformation,[],[f203]) ).

fof(f1406,plain,
    ( ~ aSet0(sK22(sdtlpdtrp0(xc,slcrc0),xS))
    | slcrc0 = sK22(sdtlpdtrp0(xc,slcrc0),xS) ),
    inference(trivial_inequality_removal,[],[f1401]) ).

fof(f1401,plain,
    ( sz00 != sz00
    | slcrc0 = sK22(sdtlpdtrp0(xc,slcrc0),xS)
    | ~ aSet0(sK22(sdtlpdtrp0(xc,slcrc0),xS)) ),
    inference(superposition,[],[f481,f1392]) ).

fof(f1392,plain,
    sz00 = sbrdtbr0(sK22(sdtlpdtrp0(xc,slcrc0),xS)),
    inference(resolution,[],[f1361,f638]) ).

fof(f1361,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szDzozmdt0(xc))
      | sz00 = sbrdtbr0(sK22(sdtlpdtrp0(xc,X0),xS)) ),
    inference(resolution,[],[f599,f1126]) ).

fof(f1126,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
      | sz00 = sbrdtbr0(sK22(X0,xS)) ),
    inference(resolution,[],[f1123,f391]) ).

fof(f391,plain,
    aSet0(xT),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,axiom,
    ( isFinite0(xT)
    & aSet0(xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).

fof(f1123,plain,
    ! [X0] :
      ( ~ aSet0(xT)
      | ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
      | sz00 = sbrdtbr0(sK22(X0,xS)) ),
    inference(resolution,[],[f1087,f390]) ).

fof(f390,plain,
    aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
    inference(cnf_transformation,[],[f245]) ).

fof(f1087,plain,
    ! [X0,X1] :
      ( ~ aSubsetOf0(X1,xT)
      | ~ aElementOf0(X0,X1)
      | ~ aSet0(xT)
      | sz00 = sbrdtbr0(sK22(X0,xS)) ),
    inference(resolution,[],[f490,f695]) ).

fof(f695,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xT)
      | sz00 = sbrdtbr0(sK22(X0,xS)) ),
    inference(resolution,[],[f694,f393]) ).

fof(f694,plain,
    ! [X0] :
      ( ~ aSet0(xS)
      | ~ aElementOf0(X0,xT)
      | sz00 = sbrdtbr0(sK22(X0,xS)) ),
    inference(resolution,[],[f691,f480]) ).

fof(f691,plain,
    ! [X0] :
      ( ~ aSubsetOf0(xS,xS)
      | sz00 = sbrdtbr0(sK22(X0,xS))
      | ~ aElementOf0(X0,xT) ),
    inference(resolution,[],[f690,f396]) ).

fof(f690,plain,
    ! [X0,X1] :
      ( ~ isCountable0(X1)
      | sz00 = sbrdtbr0(sK22(X0,X1))
      | ~ aSubsetOf0(X1,xS)
      | ~ aElementOf0(X0,xT) ),
    inference(resolution,[],[f631,f373]) ).

fof(f631,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | sz00 = sbrdtbr0(sK22(X0,X1)) ),
    inference(forward_demodulation,[],[f368,f374]) ).

fof(f368,plain,
    ! [X0,X1] :
      ( xK = sbrdtbr0(sK22(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f237]) ).

fof(f490,plain,
    ! [X3,X0,X1] :
      ( aElementOf0(X3,X0)
      | ~ aElementOf0(X3,X1)
      | ~ aSubsetOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f305]) ).

fof(f305,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ( ~ aElementOf0(sK41(X0,X1),X0)
              & aElementOf0(sK41(X0,X1),X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f303,f304]) ).

fof(f304,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK41(X0,X1),X0)
        & aElementOf0(sK41(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f303,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(rectify,[],[f302]) ).

fof(f302,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(flattening,[],[f301]) ).

fof(f301,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f131]) ).

fof(f131,plain,
    ! [X0] :
      ( ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X0)
                | ~ aElementOf0(X2,X1) )
            & aSet0(X1) ) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,X0) )
            & aSet0(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).

fof(f481,plain,
    ! [X0] :
      ( sz00 != sbrdtbr0(X0)
      | slcrc0 = X0
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f299]) ).

fof(f299,plain,
    ! [X0] :
      ( ( ( sz00 = sbrdtbr0(X0)
          | slcrc0 != X0 )
        & ( slcrc0 = X0
          | sz00 != sbrdtbr0(X0) ) )
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X0] :
      ( ( sz00 = sbrdtbr0(X0)
      <=> slcrc0 = X0 )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ( sz00 = sbrdtbr0(X0)
      <=> slcrc0 = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).

fof(f370,plain,
    ! [X0,X1] :
      ( sdtlpdtrp0(xc,sK22(X0,X1)) != X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f237]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM566+3 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 07:04:22 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (22103)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (22106)WARNING: value z3 for option sas not known
% 0.13/0.37  % (22107)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (22108)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)
% 0.13/0.37  % (22109)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)
% 0.13/0.37  % (22104)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (22110)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)
% 0.13/0.37  % (22105)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (22106)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)
% 0.13/0.40  TRYING [1]
% 0.13/0.40  TRYING [2]
% 0.19/0.43  TRYING [3]
% 0.19/0.48  % (22109)First to succeed.
% 0.19/0.48  % (22109)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22103"
% 0.19/0.49  % (22109)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (22109)------------------------------
% 0.19/0.49  % (22109)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.49  % (22109)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (22109)Memory used [KB]: 2778
% 0.19/0.49  % (22109)Time elapsed: 0.118 s
% 0.19/0.49  % (22109)Instructions burned: 233 (million)
% 0.19/0.49  % (22103)Success in time 0.128 s
%------------------------------------------------------------------------------