TSTP Solution File: NUM558+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n011.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 : Thu Aug 31 11:31:26 EDT 2023

% Result   : Theorem 3.72s 1.14s
% Output   : CNFRefutation 3.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   47 (  17 unt;   0 def)
%            Number of atoms       :  395 (  62 equ)
%            Maximal formula atoms :   43 (   8 avg)
%            Number of connectives :  480 ( 132   ~; 109   |; 200   &)
%                                         (   4 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;  10 con; 0-2 aty)
%            Number of variables   :   95 (   0 sgn;  71   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aElementOf0(X1,X0)
         => aElement0(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).

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

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

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(f71,axiom,
    ( 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__2378) ).

fof(f72,conjecture,
    aElementOf0(xx,xT),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f73,negated_conjecture,
    ~ aElementOf0(xx,xT),
    inference(negated_conjecture,[],[f72]) ).

fof(f80,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(f81,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(f82,plain,
    ~ aElementOf0(xx,xT),
    inference(flattening,[],[f73]) ).

fof(f84,plain,
    ! [X0] :
      ( ! [X1] :
          ( aElement0(X1)
          | ~ aElementOf0(X1,X0) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f165,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,[],[f80]) ).

fof(f166,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,[],[f165]) ).

fof(f168,plain,
    ( aElementOf0(xP,slbdtsldtrb0(xS,xk))
    & xk = sbrdtbr0(xP)
    & aSubsetOf0(xP,xS)
    & ! [X0] :
        ( aElementOf0(X0,xS)
        | ~ aElementOf0(X0,xP) ) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f229,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,[],[f166]) ).

fof(f230,plain,
    ( ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
   => aElementOf0(sK15,slbdtsldtrb0(xS,xk)) ),
    introduced(choice_axiom,[]) ).

fof(f231,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,xS)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK16(X1),xS)
        & aElementOf0(sK16(X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f232,plain,
    ! [X5] :
      ( ? [X6] :
          ( ~ aElementOf0(X6,xT)
          & aElementOf0(X6,X5) )
     => ( ~ aElementOf0(sK17(X5),xT)
        & aElementOf0(sK17(X5),X5) ) ),
    introduced(choice_axiom,[]) ).

fof(f233,plain,
    ! [X8] :
      ( ? [X9] :
          ( ~ aElementOf0(X9,xS)
          & aElementOf0(X9,X8) )
     => ( ~ aElementOf0(sK18(X8),xS)
        & aElementOf0(sK18(X8),X8) ) ),
    introduced(choice_axiom,[]) ).

fof(f234,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & aElementOf0(sK15,slbdtsldtrb0(xS,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X1) != xk
          | ( ~ aSubsetOf0(X1,xS)
            & ( ( ~ aElementOf0(sK16(X1),xS)
                & aElementOf0(sK16(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(sK17(X5),xT)
                & aElementOf0(sK17(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(sK18(X8),xS)
                & aElementOf0(sK18(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,[sK15,sK16,sK17,sK18])],[f229,f233,f232,f231,f230]) ).

fof(f235,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,[],[f81]) ).

fof(f236,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,[],[f235]) ).

fof(f237,plain,
    ! [X0,X1] :
      ( aElement0(X1)
      | ~ aElementOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f347,plain,
    aSet0(xS),
    inference(cnf_transformation,[],[f62]) ).

fof(f360,plain,
    ! [X7,X5] :
      ( aElementOf0(X7,xT)
      | ~ aElementOf0(X7,X5)
      | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
    inference(cnf_transformation,[],[f234]) ).

fof(f366,plain,
    ! [X4] :
      ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
      | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f234]) ).

fof(f377,plain,
    aElementOf0(xx,xS),
    inference(cnf_transformation,[],[f64]) ).

fof(f399,plain,
    ! [X0] :
      ( aElementOf0(X0,xP)
      | xx != X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f236]) ).

fof(f404,plain,
    aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[],[f168]) ).

fof(f405,plain,
    ~ aElementOf0(xx,xT),
    inference(cnf_transformation,[],[f82]) ).

fof(f428,plain,
    ( aElementOf0(xx,xP)
    | ~ aElement0(xx) ),
    inference(equality_resolution,[],[f399]) ).

cnf(c_49,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ aSet0(X1)
    | aElement0(X0) ),
    inference(cnf_transformation,[],[f237]) ).

cnf(c_161,plain,
    aSet0(xS),
    inference(cnf_transformation,[],[f347]) ).

cnf(c_172,plain,
    ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
    | aElementOf0(X0,slbdtsldtrb0(xT,xk)) ),
    inference(cnf_transformation,[],[f366]) ).

cnf(c_178,plain,
    ( ~ aElementOf0(X0,slbdtsldtrb0(xT,xk))
    | ~ aElementOf0(X1,X0)
    | aElementOf0(X1,xT) ),
    inference(cnf_transformation,[],[f360]) ).

cnf(c_189,plain,
    aElementOf0(xx,xS),
    inference(cnf_transformation,[],[f377]) ).

cnf(c_203,plain,
    ( ~ aElement0(xx)
    | aElementOf0(xx,xP) ),
    inference(cnf_transformation,[],[f428]) ).

cnf(c_213,plain,
    aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[],[f404]) ).

cnf(c_217,negated_conjecture,
    ~ aElementOf0(xx,xT),
    inference(cnf_transformation,[],[f405]) ).

cnf(c_13511,plain,
    ( ~ aSet0(xS)
    | aElement0(xx) ),
    inference(superposition,[status(thm)],[c_189,c_49]) ).

cnf(c_13517,plain,
    aElement0(xx),
    inference(forward_subsumption_resolution,[status(thm)],[c_13511,c_161]) ).

cnf(c_13528,plain,
    aElementOf0(xx,xP),
    inference(backward_subsumption_resolution,[status(thm)],[c_203,c_13517]) ).

cnf(c_14037,plain,
    aElementOf0(xP,slbdtsldtrb0(xT,xk)),
    inference(superposition,[status(thm)],[c_213,c_172]) ).

cnf(c_14885,plain,
    ( ~ aElementOf0(X0,xP)
    | aElementOf0(X0,xT) ),
    inference(superposition,[status(thm)],[c_14037,c_178]) ).

cnf(c_14978,plain,
    aElementOf0(xx,xT),
    inference(superposition,[status(thm)],[c_13528,c_14885]) ).

cnf(c_14980,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_14978,c_217]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n011.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 : Fri Aug 25 17:54:23 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  Running first-order theorem proving
% 0.20/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.72/1.14  % SZS status Started for theBenchmark.p
% 3.72/1.14  % SZS status Theorem for theBenchmark.p
% 3.72/1.14  
% 3.72/1.14  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.72/1.14  
% 3.72/1.14  ------  iProver source info
% 3.72/1.14  
% 3.72/1.14  git: date: 2023-05-31 18:12:56 +0000
% 3.72/1.14  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.72/1.14  git: non_committed_changes: false
% 3.72/1.14  git: last_make_outside_of_git: false
% 3.72/1.14  
% 3.72/1.14  ------ Parsing...
% 3.72/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.72/1.14  
% 3.72/1.14  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.72/1.14  
% 3.72/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.72/1.14  
% 3.72/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.72/1.14  ------ Proving...
% 3.72/1.14  ------ Problem Properties 
% 3.72/1.14  
% 3.72/1.14  
% 3.72/1.14  clauses                                 159
% 3.72/1.14  conjectures                             1
% 3.72/1.14  EPR                                     47
% 3.72/1.14  Horn                                    124
% 3.72/1.14  unary                                   35
% 3.72/1.14  binary                                  30
% 3.72/1.14  lits                                    474
% 3.72/1.14  lits eq                                 72
% 3.72/1.14  fd_pure                                 0
% 3.72/1.14  fd_pseudo                               0
% 3.72/1.14  fd_cond                                 11
% 3.72/1.14  fd_pseudo_cond                          18
% 3.72/1.14  AC symbols                              0
% 3.72/1.14  
% 3.72/1.14  ------ Schedule dynamic 5 is on 
% 3.72/1.14  
% 3.72/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.72/1.14  
% 3.72/1.14  
% 3.72/1.14  ------ 
% 3.72/1.14  Current options:
% 3.72/1.14  ------ 
% 3.72/1.14  
% 3.72/1.14  
% 3.72/1.14  
% 3.72/1.14  
% 3.72/1.14  ------ Proving...
% 3.72/1.14  
% 3.72/1.14  
% 3.72/1.14  % SZS status Theorem for theBenchmark.p
% 3.72/1.14  
% 3.72/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.72/1.14  
% 3.72/1.15  
%------------------------------------------------------------------------------