TSTP Solution File: RNG108+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : RNG108+4 : 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 : n004.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 14:52:37 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   58 (  12 unt;   0 def)
%            Number of atoms       :  318 (  83 equ)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives :  393 ( 133   ~; 119   |; 121   &)
%                                         (   9 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :  113 (  77   !;  36   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f502,plain,
    $false,
    inference(resolution,[],[f500,f254]) ).

fof(f254,plain,
    aElement0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    aElement0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).

fof(f500,plain,
    ~ aElement0(sz00),
    inference(resolution,[],[f499,f253]) ).

fof(f253,plain,
    aElement0(sz10),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    aElement0(sz10),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).

fof(f499,plain,
    ( ~ aElement0(sz10)
    | ~ aElement0(sz00) ),
    inference(duplicate_literal_removal,[],[f498]) ).

fof(f498,plain,
    ( ~ aElement0(sz10)
    | ~ aElement0(sz00)
    | ~ aElement0(sz00) ),
    inference(resolution,[],[f497,f454]) ).

fof(f454,plain,
    ( aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElement0(sz00) ),
    inference(superposition,[],[f353,f370]) ).

fof(f370,plain,
    sz00 = sdtasdt0(xb,sz00),
    inference(resolution,[],[f259,f251]) ).

fof(f251,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ( aElement0(xb)
    & aElement0(xa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).

fof(f259,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sz00 = sdtasdt0(X0,sz00) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).

fof(f353,plain,
    ! [X6] :
      ( aElementOf0(sdtasdt0(xb,X6),slsdtgt0(xb))
      | ~ aElement0(X6) ),
    inference(equality_resolution,[],[f224]) ).

fof(f224,plain,
    ! [X6,X5] :
      ( aElementOf0(X5,slsdtgt0(xb))
      | sdtasdt0(xb,X6) != X5
      | ~ aElement0(X6) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X0] :
        ( ( aElementOf0(X0,xI)
          | ! [X1,X2] :
              ( sdtpldt0(X1,X2) != X0
              | ~ aElementOf0(X2,slsdtgt0(xb))
              | ~ aElementOf0(X1,slsdtgt0(xa)) ) )
        & ( ( sdtpldt0(sK13(X0),sK14(X0)) = X0
            & aElementOf0(sK14(X0),slsdtgt0(xb))
            & aElementOf0(sK13(X0),slsdtgt0(xa)) )
          | ~ aElementOf0(X0,xI) ) )
    & ! [X5] :
        ( ( aElementOf0(X5,slsdtgt0(xb))
          | ! [X6] :
              ( sdtasdt0(xb,X6) != X5
              | ~ aElement0(X6) ) )
        & ( ( sdtasdt0(xb,sK15(X5)) = X5
            & aElement0(sK15(X5)) )
          | ~ aElementOf0(X5,slsdtgt0(xb)) ) )
    & ! [X8] :
        ( ( aElementOf0(X8,slsdtgt0(xa))
          | ! [X9] :
              ( sdtasdt0(xa,X9) != X8
              | ~ aElement0(X9) ) )
        & ( ( sdtasdt0(xa,sK16(X8)) = X8
            & aElement0(sK16(X8)) )
          | ~ aElementOf0(X8,slsdtgt0(xa)) ) )
    & aIdeal0(xI)
    & ! [X11] :
        ( ( ! [X12] :
              ( aElementOf0(sdtasdt0(X12,X11),xI)
              | ~ aElement0(X12) )
          & ! [X13] :
              ( aElementOf0(sdtpldt0(X11,X13),xI)
              | ~ aElementOf0(X13,xI) ) )
        | ~ aElementOf0(X11,xI) )
    & aSet0(xI) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f136,f139,f138,f137]) ).

fof(f137,plain,
    ! [X0] :
      ( ? [X3,X4] :
          ( sdtpldt0(X3,X4) = X0
          & aElementOf0(X4,slsdtgt0(xb))
          & aElementOf0(X3,slsdtgt0(xa)) )
     => ( sdtpldt0(sK13(X0),sK14(X0)) = X0
        & aElementOf0(sK14(X0),slsdtgt0(xb))
        & aElementOf0(sK13(X0),slsdtgt0(xa)) ) ),
    introduced(choice_axiom,[]) ).

fof(f138,plain,
    ! [X5] :
      ( ? [X7] :
          ( sdtasdt0(xb,X7) = X5
          & aElement0(X7) )
     => ( sdtasdt0(xb,sK15(X5)) = X5
        & aElement0(sK15(X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f139,plain,
    ! [X8] :
      ( ? [X10] :
          ( sdtasdt0(xa,X10) = X8
          & aElement0(X10) )
     => ( sdtasdt0(xa,sK16(X8)) = X8
        & aElement0(sK16(X8)) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X0] :
        ( ( aElementOf0(X0,xI)
          | ! [X1,X2] :
              ( sdtpldt0(X1,X2) != X0
              | ~ aElementOf0(X2,slsdtgt0(xb))
              | ~ aElementOf0(X1,slsdtgt0(xa)) ) )
        & ( ? [X3,X4] :
              ( sdtpldt0(X3,X4) = X0
              & aElementOf0(X4,slsdtgt0(xb))
              & aElementOf0(X3,slsdtgt0(xa)) )
          | ~ aElementOf0(X0,xI) ) )
    & ! [X5] :
        ( ( aElementOf0(X5,slsdtgt0(xb))
          | ! [X6] :
              ( sdtasdt0(xb,X6) != X5
              | ~ aElement0(X6) ) )
        & ( ? [X7] :
              ( sdtasdt0(xb,X7) = X5
              & aElement0(X7) )
          | ~ aElementOf0(X5,slsdtgt0(xb)) ) )
    & ! [X8] :
        ( ( aElementOf0(X8,slsdtgt0(xa))
          | ! [X9] :
              ( sdtasdt0(xa,X9) != X8
              | ~ aElement0(X9) ) )
        & ( ? [X10] :
              ( sdtasdt0(xa,X10) = X8
              & aElement0(X10) )
          | ~ aElementOf0(X8,slsdtgt0(xa)) ) )
    & aIdeal0(xI)
    & ! [X11] :
        ( ( ! [X12] :
              ( aElementOf0(sdtasdt0(X12,X11),xI)
              | ~ aElement0(X12) )
          & ! [X13] :
              ( aElementOf0(sdtpldt0(X11,X13),xI)
              | ~ aElementOf0(X13,xI) ) )
        | ~ aElementOf0(X11,xI) )
    & aSet0(xI) ),
    inference(rectify,[],[f135]) ).

fof(f135,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X0] :
        ( ( aElementOf0(X0,xI)
          | ! [X1,X2] :
              ( sdtpldt0(X1,X2) != X0
              | ~ aElementOf0(X2,slsdtgt0(xb))
              | ~ aElementOf0(X1,slsdtgt0(xa)) ) )
        & ( ? [X1,X2] :
              ( sdtpldt0(X1,X2) = X0
              & aElementOf0(X2,slsdtgt0(xb))
              & aElementOf0(X1,slsdtgt0(xa)) )
          | ~ aElementOf0(X0,xI) ) )
    & ! [X3] :
        ( ( aElementOf0(X3,slsdtgt0(xb))
          | ! [X4] :
              ( sdtasdt0(xb,X4) != X3
              | ~ aElement0(X4) ) )
        & ( ? [X4] :
              ( sdtasdt0(xb,X4) = X3
              & aElement0(X4) )
          | ~ aElementOf0(X3,slsdtgt0(xb)) ) )
    & ! [X5] :
        ( ( aElementOf0(X5,slsdtgt0(xa))
          | ! [X6] :
              ( sdtasdt0(xa,X6) != X5
              | ~ aElement0(X6) ) )
        & ( ? [X6] :
              ( sdtasdt0(xa,X6) = X5
              & aElement0(X6) )
          | ~ aElementOf0(X5,slsdtgt0(xa)) ) )
    & aIdeal0(xI)
    & ! [X7] :
        ( ( ! [X8] :
              ( aElementOf0(sdtasdt0(X8,X7),xI)
              | ~ aElement0(X8) )
          & ! [X9] :
              ( aElementOf0(sdtpldt0(X7,X9),xI)
              | ~ aElementOf0(X9,xI) ) )
        | ~ aElementOf0(X7,xI) )
    & aSet0(xI) ),
    inference(nnf_transformation,[],[f58]) ).

fof(f58,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X0] :
        ( aElementOf0(X0,xI)
      <=> ? [X1,X2] :
            ( sdtpldt0(X1,X2) = X0
            & aElementOf0(X2,slsdtgt0(xb))
            & aElementOf0(X1,slsdtgt0(xa)) ) )
    & ! [X3] :
        ( aElementOf0(X3,slsdtgt0(xb))
      <=> ? [X4] :
            ( sdtasdt0(xb,X4) = X3
            & aElement0(X4) ) )
    & ! [X5] :
        ( aElementOf0(X5,slsdtgt0(xa))
      <=> ? [X6] :
            ( sdtasdt0(xa,X6) = X5
            & aElement0(X6) ) )
    & aIdeal0(xI)
    & ! [X7] :
        ( ( ! [X8] :
              ( aElementOf0(sdtasdt0(X8,X7),xI)
              | ~ aElement0(X8) )
          & ! [X9] :
              ( aElementOf0(sdtpldt0(X7,X9),xI)
              | ~ aElementOf0(X9,xI) ) )
        | ~ aElementOf0(X7,xI) )
    & aSet0(xI) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X0] :
        ( aElementOf0(X0,xI)
      <=> ? [X1,X2] :
            ( sdtpldt0(X1,X2) = X0
            & aElementOf0(X2,slsdtgt0(xb))
            & aElementOf0(X1,slsdtgt0(xa)) ) )
    & ! [X3] :
        ( aElementOf0(X3,slsdtgt0(xb))
      <=> ? [X4] :
            ( sdtasdt0(xb,X4) = X3
            & aElement0(X4) ) )
    & ! [X5] :
        ( aElementOf0(X5,slsdtgt0(xa))
      <=> ? [X6] :
            ( sdtasdt0(xa,X6) = X5
            & aElement0(X6) ) )
    & aIdeal0(xI)
    & ! [X7] :
        ( aElementOf0(X7,xI)
       => ( ! [X8] :
              ( aElement0(X8)
             => aElementOf0(sdtasdt0(X8,X7),xI) )
          & ! [X9] :
              ( aElementOf0(X9,xI)
             => aElementOf0(sdtpldt0(X7,X9),xI) ) ) )
    & aSet0(xI) ),
    inference(rectify,[],[f42]) ).

fof(f42,axiom,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X0] :
        ( aElementOf0(X0,xI)
      <=> ? [X1,X2] :
            ( sdtpldt0(X1,X2) = X0
            & aElementOf0(X2,slsdtgt0(xb))
            & aElementOf0(X1,slsdtgt0(xa)) ) )
    & ! [X0] :
        ( aElementOf0(X0,slsdtgt0(xb))
      <=> ? [X1] :
            ( sdtasdt0(xb,X1) = X0
            & aElement0(X1) ) )
    & ! [X0] :
        ( aElementOf0(X0,slsdtgt0(xa))
      <=> ? [X1] :
            ( sdtasdt0(xa,X1) = X0
            & aElement0(X1) ) )
    & aIdeal0(xI)
    & ! [X0] :
        ( aElementOf0(X0,xI)
       => ( ! [X1] :
              ( aElement0(X1)
             => aElementOf0(sdtasdt0(X1,X0),xI) )
          & ! [X1] :
              ( aElementOf0(X1,xI)
             => aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
    & aSet0(xI) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).

fof(f497,plain,
    ( ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElement0(sz10)
    | ~ aElement0(sz00) ),
    inference(resolution,[],[f495,f479]) ).

fof(f479,plain,
    ( aElementOf0(sz00,slsdtgt0(xa))
    | ~ aElement0(sz00) ),
    inference(superposition,[],[f354,f369]) ).

fof(f369,plain,
    sz00 = sdtasdt0(xa,sz00),
    inference(resolution,[],[f259,f250]) ).

fof(f250,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f39]) ).

fof(f354,plain,
    ! [X9] :
      ( aElementOf0(sdtasdt0(xa,X9),slsdtgt0(xa))
      | ~ aElement0(X9) ),
    inference(equality_resolution,[],[f221]) ).

fof(f221,plain,
    ! [X8,X9] :
      ( aElementOf0(X8,slsdtgt0(xa))
      | sdtasdt0(xa,X9) != X8
      | ~ aElement0(X9) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f495,plain,
    ( ~ aElementOf0(sz00,slsdtgt0(xa))
    | ~ aElement0(sz10)
    | ~ aElementOf0(sz00,slsdtgt0(xb)) ),
    inference(resolution,[],[f494,f210]) ).

fof(f210,plain,
    ( ~ sP0
    | ~ aElementOf0(sz00,slsdtgt0(xa)) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ( ( ~ aElementOf0(sz00,slsdtgt0(xa))
      & ! [X0] :
          ( sz00 != sdtasdt0(xa,X0)
          | ~ aElement0(X0) ) )
    | ~ sP0 ),
    inference(rectify,[],[f133]) ).

fof(f133,plain,
    ( ( ~ aElementOf0(sz00,slsdtgt0(xa))
      & ! [X3] :
          ( sz00 != sdtasdt0(xa,X3)
          | ~ aElement0(X3) ) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f110]) ).

fof(f110,plain,
    ( ( ~ aElementOf0(sz00,slsdtgt0(xa))
      & ! [X3] :
          ( sz00 != sdtasdt0(xa,X3)
          | ~ aElement0(X3) ) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f494,plain,
    ( sP0
    | ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElement0(sz10) ),
    inference(duplicate_literal_removal,[],[f492]) ).

fof(f492,plain,
    ( ~ aElement0(sz10)
    | ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElement0(sz10)
    | sP0 ),
    inference(resolution,[],[f490,f429]) ).

fof(f429,plain,
    ( sP1
    | ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElement0(sz10)
    | sP0 ),
    inference(trivial_inequality_removal,[],[f428]) ).

fof(f428,plain,
    ( xb != xb
    | ~ aElement0(sz10)
    | ~ aElementOf0(sz00,slsdtgt0(xb))
    | sP1
    | sP0 ),
    inference(superposition,[],[f212,f410]) ).

fof(f410,plain,
    xb = sdtasdt0(xb,sz10),
    inference(resolution,[],[f263,f251]) ).

fof(f263,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtasdt0(X0,sz10) = X0 ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ( sdtasdt0(sz10,X0) = X0
        & sdtasdt0(X0,sz10) = X0 )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sdtasdt0(sz10,X0) = X0
        & sdtasdt0(X0,sz10) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).

fof(f212,plain,
    ! [X0] :
      ( xb != sdtasdt0(xb,X0)
      | ~ aElement0(X0)
      | ~ aElementOf0(sz00,slsdtgt0(xb))
      | sP1
      | sP0 ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ( ( ~ aElementOf0(xb,slsdtgt0(xb))
      & ! [X0] :
          ( xb != sdtasdt0(xb,X0)
          | ~ aElement0(X0) ) )
    | ( ~ aElementOf0(sz00,slsdtgt0(xb))
      & ! [X1] :
          ( sz00 != sdtasdt0(xb,X1)
          | ~ aElement0(X1) ) )
    | sP1
    | sP0 ),
    inference(definition_folding,[],[f57,f111,f110]) ).

fof(f111,plain,
    ( ( ~ aElementOf0(xa,slsdtgt0(xa))
      & ! [X2] :
          ( xa != sdtasdt0(xa,X2)
          | ~ aElement0(X2) ) )
    | ~ sP1 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f57,plain,
    ( ( ~ aElementOf0(xb,slsdtgt0(xb))
      & ! [X0] :
          ( xb != sdtasdt0(xb,X0)
          | ~ aElement0(X0) ) )
    | ( ~ aElementOf0(sz00,slsdtgt0(xb))
      & ! [X1] :
          ( sz00 != sdtasdt0(xb,X1)
          | ~ aElement0(X1) ) )
    | ( ~ aElementOf0(xa,slsdtgt0(xa))
      & ! [X2] :
          ( xa != sdtasdt0(xa,X2)
          | ~ aElement0(X2) ) )
    | ( ~ aElementOf0(sz00,slsdtgt0(xa))
      & ! [X3] :
          ( sz00 != sdtasdt0(xa,X3)
          | ~ aElement0(X3) ) ) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,plain,
    ~ ( ( aElementOf0(xb,slsdtgt0(xb))
        | ? [X0] :
            ( xb = sdtasdt0(xb,X0)
            & aElement0(X0) ) )
      & ( aElementOf0(sz00,slsdtgt0(xb))
        | ? [X1] :
            ( sz00 = sdtasdt0(xb,X1)
            & aElement0(X1) ) )
      & ( aElementOf0(xa,slsdtgt0(xa))
        | ? [X2] :
            ( xa = sdtasdt0(xa,X2)
            & aElement0(X2) ) )
      & ( aElementOf0(sz00,slsdtgt0(xa))
        | ? [X3] :
            ( sz00 = sdtasdt0(xa,X3)
            & aElement0(X3) ) ) ),
    inference(rectify,[],[f44]) ).

fof(f44,negated_conjecture,
    ~ ( ( aElementOf0(xb,slsdtgt0(xb))
        | ? [X0] :
            ( xb = sdtasdt0(xb,X0)
            & aElement0(X0) ) )
      & ( aElementOf0(sz00,slsdtgt0(xb))
        | ? [X0] :
            ( sz00 = sdtasdt0(xb,X0)
            & aElement0(X0) ) )
      & ( aElementOf0(xa,slsdtgt0(xa))
        | ? [X0] :
            ( xa = sdtasdt0(xa,X0)
            & aElement0(X0) ) )
      & ( aElementOf0(sz00,slsdtgt0(xa))
        | ? [X0] :
            ( sz00 = sdtasdt0(xa,X0)
            & aElement0(X0) ) ) ),
    inference(negated_conjecture,[],[f43]) ).

fof(f43,conjecture,
    ( ( aElementOf0(xb,slsdtgt0(xb))
      | ? [X0] :
          ( xb = sdtasdt0(xb,X0)
          & aElement0(X0) ) )
    & ( aElementOf0(sz00,slsdtgt0(xb))
      | ? [X0] :
          ( sz00 = sdtasdt0(xb,X0)
          & aElement0(X0) ) )
    & ( aElementOf0(xa,slsdtgt0(xa))
      | ? [X0] :
          ( xa = sdtasdt0(xa,X0)
          & aElement0(X0) ) )
    & ( aElementOf0(sz00,slsdtgt0(xa))
      | ? [X0] :
          ( sz00 = sdtasdt0(xa,X0)
          & aElement0(X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f490,plain,
    ( ~ sP1
    | ~ aElement0(sz10) ),
    inference(trivial_inequality_removal,[],[f489]) ).

fof(f489,plain,
    ( xa != xa
    | ~ aElement0(sz10)
    | ~ sP1 ),
    inference(superposition,[],[f207,f409]) ).

fof(f409,plain,
    xa = sdtasdt0(xa,sz10),
    inference(resolution,[],[f263,f250]) ).

fof(f207,plain,
    ! [X0] :
      ( xa != sdtasdt0(xa,X0)
      | ~ aElement0(X0)
      | ~ sP1 ),
    inference(cnf_transformation,[],[f132]) ).

fof(f132,plain,
    ( ( ~ aElementOf0(xa,slsdtgt0(xa))
      & ! [X0] :
          ( xa != sdtasdt0(xa,X0)
          | ~ aElement0(X0) ) )
    | ~ sP1 ),
    inference(rectify,[],[f131]) ).

fof(f131,plain,
    ( ( ~ aElementOf0(xa,slsdtgt0(xa))
      & ! [X2] :
          ( xa != sdtasdt0(xa,X2)
          | ~ aElement0(X2) ) )
    | ~ sP1 ),
    inference(nnf_transformation,[],[f111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : RNG108+4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 02:01:18 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (13158)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (13161)WARNING: value z3 for option sas not known
% 0.14/0.38  % (13159)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (13162)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (13161)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)
% 0.14/0.38  % (13163)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)
% 0.14/0.38  % (13164)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)
% 0.14/0.38  % (13165)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)
% 0.14/0.38  % (13160)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (13164)First to succeed.
% 0.14/0.39  % (13161)Also succeeded, but the first one will report.
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  % (13164)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (13164)------------------------------
% 0.14/0.39  % (13164)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39  % (13164)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (13164)Memory used [KB]: 1197
% 0.14/0.39  % (13164)Time elapsed: 0.016 s
% 0.14/0.39  % (13164)Instructions burned: 25 (million)
% 0.14/0.39  % (13164)------------------------------
% 0.14/0.39  % (13164)------------------------------
% 0.14/0.39  % (13158)Success in time 0.034 s
%------------------------------------------------------------------------------