TSTP Solution File: RNG106+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : RNG106+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n032.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 13:55:19 EDT 2023

% Result   : Theorem 3.98s 1.01s
% Output   : CNFRefutation 3.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   77 (  10 unt;   0 def)
%            Number of atoms       :  447 ( 104 equ)
%            Maximal formula atoms :   29 (   5 avg)
%            Number of connectives :  523 ( 153   ~; 130   |; 209   &)
%                                         (   6 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-4 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-4 aty)
%            Number of variables   :  246 (  18 sgn; 120   !;  67   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    aElement0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).

fof(f13,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sdtasdt0(sz10,X0) = X0
        & sdtasdt0(X0,sz10) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).

fof(f38,axiom,
    aElement0(xc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).

fof(f39,conjecture,
    ( ! [X0,X1,X2] :
        ( ( aElement0(X2)
          & ( aElementOf0(X1,slsdtgt0(xc))
            | ? [X3] :
                ( sdtasdt0(xc,X3) = X1
                & aElement0(X3) ) )
          & ( aElementOf0(X0,slsdtgt0(xc))
            | ? [X3] :
                ( sdtasdt0(xc,X3) = X0
                & aElement0(X3) ) ) )
       => ? [X3] :
            ( ? [X4] :
                ( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
                & ? [X5] :
                    ( sdtasdt0(X2,X0) = sdtasdt0(xc,X5)
                    & aElement0(X5) )
                & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
                & ? [X5] :
                    ( sdtpldt0(X0,X1) = sdtasdt0(xc,X5)
                    & aElement0(X5) )
                & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
                & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
                & sdtasdt0(xc,X4) = X1
                & aElement0(X4) )
            & sdtasdt0(xc,X3) = X0
            & aElement0(X3) ) )
   => ( ( ! [X0] :
            ( aElementOf0(X0,slsdtgt0(xc))
          <=> ? [X1] :
                ( sdtasdt0(xc,X1) = X0
                & aElement0(X1) ) )
        & aSet0(slsdtgt0(xc)) )
     => ( aIdeal0(slsdtgt0(xc))
        | ! [X0] :
            ( aElementOf0(X0,slsdtgt0(xc))
           => ( ! [X1] :
                  ( aElement0(X1)
                 => aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) )
              & ! [X1] :
                  ( aElementOf0(X1,slsdtgt0(xc))
                 => aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f40,negated_conjecture,
    ~ ( ! [X0,X1,X2] :
          ( ( aElement0(X2)
            & ( aElementOf0(X1,slsdtgt0(xc))
              | ? [X3] :
                  ( sdtasdt0(xc,X3) = X1
                  & aElement0(X3) ) )
            & ( aElementOf0(X0,slsdtgt0(xc))
              | ? [X3] :
                  ( sdtasdt0(xc,X3) = X0
                  & aElement0(X3) ) ) )
         => ? [X3] :
              ( ? [X4] :
                  ( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
                  & ? [X5] :
                      ( sdtasdt0(X2,X0) = sdtasdt0(xc,X5)
                      & aElement0(X5) )
                  & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
                  & ? [X5] :
                      ( sdtpldt0(X0,X1) = sdtasdt0(xc,X5)
                      & aElement0(X5) )
                  & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2))
                  & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
                  & sdtasdt0(xc,X4) = X1
                  & aElement0(X4) )
              & sdtasdt0(xc,X3) = X0
              & aElement0(X3) ) )
     => ( ( ! [X0] :
              ( aElementOf0(X0,slsdtgt0(xc))
            <=> ? [X1] :
                  ( sdtasdt0(xc,X1) = X0
                  & aElement0(X1) ) )
          & aSet0(slsdtgt0(xc)) )
       => ( aIdeal0(slsdtgt0(xc))
          | ! [X0] :
              ( aElementOf0(X0,slsdtgt0(xc))
             => ( ! [X1] :
                    ( aElement0(X1)
                   => aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) )
                & ! [X1] :
                    ( aElementOf0(X1,slsdtgt0(xc))
                   => aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc)) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f39]) ).

fof(f48,plain,
    ~ ( ! [X0,X1,X2] :
          ( ( aElement0(X2)
            & ( aElementOf0(X1,slsdtgt0(xc))
              | ? [X3] :
                  ( sdtasdt0(xc,X3) = X1
                  & aElement0(X3) ) )
            & ( aElementOf0(X0,slsdtgt0(xc))
              | ? [X4] :
                  ( sdtasdt0(xc,X4) = X0
                  & aElement0(X4) ) ) )
         => ? [X5] :
              ( ? [X6] :
                  ( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
                  & ? [X7] :
                      ( sdtasdt0(X2,X0) = sdtasdt0(xc,X7)
                      & aElement0(X7) )
                  & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
                  & ? [X8] :
                      ( sdtpldt0(X0,X1) = sdtasdt0(xc,X8)
                      & aElement0(X8) )
                  & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
                  & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
                  & sdtasdt0(xc,X6) = X1
                  & aElement0(X6) )
              & sdtasdt0(xc,X5) = X0
              & aElement0(X5) ) )
     => ( ( ! [X9] :
              ( aElementOf0(X9,slsdtgt0(xc))
            <=> ? [X10] :
                  ( sdtasdt0(xc,X10) = X9
                  & aElement0(X10) ) )
          & aSet0(slsdtgt0(xc)) )
       => ( aIdeal0(slsdtgt0(xc))
          | ! [X11] :
              ( aElementOf0(X11,slsdtgt0(xc))
             => ( ! [X12] :
                    ( aElement0(X12)
                   => aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc)) )
                & ! [X13] :
                    ( aElementOf0(X13,slsdtgt0(xc))
                   => aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc)) ) ) ) ) ) ),
    inference(rectify,[],[f40]) ).

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

fof(f99,plain,
    ( ~ aIdeal0(slsdtgt0(xc))
    & ? [X11] :
        ( ( ? [X12] :
              ( ~ aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc))
              & aElement0(X12) )
          | ? [X13] :
              ( ~ aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc))
              & aElementOf0(X13,slsdtgt0(xc)) ) )
        & aElementOf0(X11,slsdtgt0(xc)) )
    & ! [X9] :
        ( aElementOf0(X9,slsdtgt0(xc))
      <=> ? [X10] :
            ( sdtasdt0(xc,X10) = X9
            & aElement0(X10) ) )
    & aSet0(slsdtgt0(xc))
    & ! [X0,X1,X2] :
        ( ? [X5] :
            ( ? [X6] :
                ( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
                & ? [X7] :
                    ( sdtasdt0(X2,X0) = sdtasdt0(xc,X7)
                    & aElement0(X7) )
                & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
                & ? [X8] :
                    ( sdtpldt0(X0,X1) = sdtasdt0(xc,X8)
                    & aElement0(X8) )
                & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
                & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
                & sdtasdt0(xc,X6) = X1
                & aElement0(X6) )
            & sdtasdt0(xc,X5) = X0
            & aElement0(X5) )
        | ~ aElement0(X2)
        | ( ~ aElementOf0(X1,slsdtgt0(xc))
          & ! [X3] :
              ( sdtasdt0(xc,X3) != X1
              | ~ aElement0(X3) ) )
        | ( ~ aElementOf0(X0,slsdtgt0(xc))
          & ! [X4] :
              ( sdtasdt0(xc,X4) != X0
              | ~ aElement0(X4) ) ) ) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f100,plain,
    ( ~ aIdeal0(slsdtgt0(xc))
    & ? [X11] :
        ( ( ? [X12] :
              ( ~ aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc))
              & aElement0(X12) )
          | ? [X13] :
              ( ~ aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc))
              & aElementOf0(X13,slsdtgt0(xc)) ) )
        & aElementOf0(X11,slsdtgt0(xc)) )
    & ! [X9] :
        ( aElementOf0(X9,slsdtgt0(xc))
      <=> ? [X10] :
            ( sdtasdt0(xc,X10) = X9
            & aElement0(X10) ) )
    & aSet0(slsdtgt0(xc))
    & ! [X0,X1,X2] :
        ( ? [X5] :
            ( ? [X6] :
                ( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
                & ? [X7] :
                    ( sdtasdt0(X2,X0) = sdtasdt0(xc,X7)
                    & aElement0(X7) )
                & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
                & ? [X8] :
                    ( sdtpldt0(X0,X1) = sdtasdt0(xc,X8)
                    & aElement0(X8) )
                & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
                & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
                & sdtasdt0(xc,X6) = X1
                & aElement0(X6) )
            & sdtasdt0(xc,X5) = X0
            & aElement0(X5) )
        | ~ aElement0(X2)
        | ( ~ aElementOf0(X1,slsdtgt0(xc))
          & ! [X3] :
              ( sdtasdt0(xc,X3) != X1
              | ~ aElement0(X3) ) )
        | ( ~ aElementOf0(X0,slsdtgt0(xc))
          & ! [X4] :
              ( sdtasdt0(xc,X4) != X0
              | ~ aElement0(X4) ) ) ) ),
    inference(flattening,[],[f99]) ).

fof(f104,plain,
    ! [X1,X0] :
      ( ? [X8] :
          ( sdtpldt0(X0,X1) = sdtasdt0(xc,X8)
          & aElement0(X8) )
      | ~ sP2(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f105,plain,
    ! [X0,X2] :
      ( ? [X7] :
          ( sdtasdt0(X2,X0) = sdtasdt0(xc,X7)
          & aElement0(X7) )
      | ~ sP3(X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f106,plain,
    ! [X0,X2,X1,X5] :
      ( ? [X6] :
          ( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
          & sP3(X0,X2)
          & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
          & sP2(X1,X0)
          & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
          & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
          & sdtasdt0(xc,X6) = X1
          & aElement0(X6) )
      | ~ sP4(X0,X2,X1,X5) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f107,plain,
    ! [X1,X2,X0] :
      ( ? [X5] :
          ( sP4(X0,X2,X1,X5)
          & sdtasdt0(xc,X5) = X0
          & aElement0(X5) )
      | ~ sP5(X1,X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f108,plain,
    ( ~ aIdeal0(slsdtgt0(xc))
    & ? [X11] :
        ( ( ? [X12] :
              ( ~ aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc))
              & aElement0(X12) )
          | ? [X13] :
              ( ~ aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc))
              & aElementOf0(X13,slsdtgt0(xc)) ) )
        & aElementOf0(X11,slsdtgt0(xc)) )
    & ! [X9] :
        ( aElementOf0(X9,slsdtgt0(xc))
      <=> ? [X10] :
            ( sdtasdt0(xc,X10) = X9
            & aElement0(X10) ) )
    & aSet0(slsdtgt0(xc))
    & ! [X0,X1,X2] :
        ( sP5(X1,X2,X0)
        | ~ aElement0(X2)
        | ( ~ aElementOf0(X1,slsdtgt0(xc))
          & ! [X3] :
              ( sdtasdt0(xc,X3) != X1
              | ~ aElement0(X3) ) )
        | ( ~ aElementOf0(X0,slsdtgt0(xc))
          & ! [X4] :
              ( sdtasdt0(xc,X4) != X0
              | ~ aElement0(X4) ) ) ) ),
    inference(definition_folding,[],[f100,f107,f106,f105,f104]) ).

fof(f158,plain,
    ! [X1,X2,X0] :
      ( ? [X5] :
          ( sP4(X0,X2,X1,X5)
          & sdtasdt0(xc,X5) = X0
          & aElement0(X5) )
      | ~ sP5(X1,X2,X0) ),
    inference(nnf_transformation,[],[f107]) ).

fof(f159,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( sP4(X2,X1,X0,X3)
          & sdtasdt0(xc,X3) = X2
          & aElement0(X3) )
      | ~ sP5(X0,X1,X2) ),
    inference(rectify,[],[f158]) ).

fof(f160,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( sP4(X2,X1,X0,X3)
          & sdtasdt0(xc,X3) = X2
          & aElement0(X3) )
     => ( sP4(X2,X1,X0,sK26(X0,X1,X2))
        & sdtasdt0(xc,sK26(X0,X1,X2)) = X2
        & aElement0(sK26(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f161,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X2,X1,X0,sK26(X0,X1,X2))
        & sdtasdt0(xc,sK26(X0,X1,X2)) = X2
        & aElement0(sK26(X0,X1,X2)) )
      | ~ sP5(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f159,f160]) ).

fof(f162,plain,
    ! [X0,X2,X1,X5] :
      ( ? [X6] :
          ( aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
          & sP3(X0,X2)
          & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
          & sP2(X1,X0)
          & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X5,X2))
          & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X5,X6))
          & sdtasdt0(xc,X6) = X1
          & aElement0(X6) )
      | ~ sP4(X0,X2,X1,X5) ),
    inference(nnf_transformation,[],[f106]) ).

fof(f163,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
          & sP3(X0,X1)
          & aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
          & sP2(X2,X0)
          & sdtasdt0(X1,X0) = sdtasdt0(xc,sdtasdt0(X3,X1))
          & sdtasdt0(xc,sdtpldt0(X3,X4)) = sdtpldt0(X0,X2)
          & sdtasdt0(xc,X4) = X2
          & aElement0(X4) )
      | ~ sP4(X0,X1,X2,X3) ),
    inference(rectify,[],[f162]) ).

fof(f164,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
          & sP3(X0,X1)
          & aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
          & sP2(X2,X0)
          & sdtasdt0(X1,X0) = sdtasdt0(xc,sdtasdt0(X3,X1))
          & sdtasdt0(xc,sdtpldt0(X3,X4)) = sdtpldt0(X0,X2)
          & sdtasdt0(xc,X4) = X2
          & aElement0(X4) )
     => ( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
        & sP3(X0,X1)
        & aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
        & sP2(X2,X0)
        & sdtasdt0(X1,X0) = sdtasdt0(xc,sdtasdt0(X3,X1))
        & sdtpldt0(X0,X2) = sdtasdt0(xc,sdtpldt0(X3,sK27(X0,X1,X2,X3)))
        & sdtasdt0(xc,sK27(X0,X1,X2,X3)) = X2
        & aElement0(sK27(X0,X1,X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f165,plain,
    ! [X0,X1,X2,X3] :
      ( ( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
        & sP3(X0,X1)
        & aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
        & sP2(X2,X0)
        & sdtasdt0(X1,X0) = sdtasdt0(xc,sdtasdt0(X3,X1))
        & sdtpldt0(X0,X2) = sdtasdt0(xc,sdtpldt0(X3,sK27(X0,X1,X2,X3)))
        & sdtasdt0(xc,sK27(X0,X1,X2,X3)) = X2
        & aElement0(sK27(X0,X1,X2,X3)) )
      | ~ sP4(X0,X1,X2,X3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f163,f164]) ).

fof(f174,plain,
    ( ~ aIdeal0(slsdtgt0(xc))
    & ? [X11] :
        ( ( ? [X12] :
              ( ~ aElementOf0(sdtasdt0(X12,X11),slsdtgt0(xc))
              & aElement0(X12) )
          | ? [X13] :
              ( ~ aElementOf0(sdtpldt0(X11,X13),slsdtgt0(xc))
              & aElementOf0(X13,slsdtgt0(xc)) ) )
        & aElementOf0(X11,slsdtgt0(xc)) )
    & ! [X9] :
        ( ( aElementOf0(X9,slsdtgt0(xc))
          | ! [X10] :
              ( sdtasdt0(xc,X10) != X9
              | ~ aElement0(X10) ) )
        & ( ? [X10] :
              ( sdtasdt0(xc,X10) = X9
              & aElement0(X10) )
          | ~ aElementOf0(X9,slsdtgt0(xc)) ) )
    & aSet0(slsdtgt0(xc))
    & ! [X0,X1,X2] :
        ( sP5(X1,X2,X0)
        | ~ aElement0(X2)
        | ( ~ aElementOf0(X1,slsdtgt0(xc))
          & ! [X3] :
              ( sdtasdt0(xc,X3) != X1
              | ~ aElement0(X3) ) )
        | ( ~ aElementOf0(X0,slsdtgt0(xc))
          & ! [X4] :
              ( sdtasdt0(xc,X4) != X0
              | ~ aElement0(X4) ) ) ) ),
    inference(nnf_transformation,[],[f108]) ).

fof(f175,plain,
    ( ~ aIdeal0(slsdtgt0(xc))
    & ? [X0] :
        ( ( ? [X1] :
              ( ~ aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
              & aElement0(X1) )
          | ? [X2] :
              ( ~ aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
              & aElementOf0(X2,slsdtgt0(xc)) ) )
        & aElementOf0(X0,slsdtgt0(xc)) )
    & ! [X3] :
        ( ( aElementOf0(X3,slsdtgt0(xc))
          | ! [X4] :
              ( sdtasdt0(xc,X4) != X3
              | ~ aElement0(X4) ) )
        & ( ? [X5] :
              ( sdtasdt0(xc,X5) = X3
              & aElement0(X5) )
          | ~ aElementOf0(X3,slsdtgt0(xc)) ) )
    & aSet0(slsdtgt0(xc))
    & ! [X6,X7,X8] :
        ( sP5(X7,X8,X6)
        | ~ aElement0(X8)
        | ( ~ aElementOf0(X7,slsdtgt0(xc))
          & ! [X9] :
              ( sdtasdt0(xc,X9) != X7
              | ~ aElement0(X9) ) )
        | ( ~ aElementOf0(X6,slsdtgt0(xc))
          & ! [X10] :
              ( sdtasdt0(xc,X10) != X6
              | ~ aElement0(X10) ) ) ) ),
    inference(rectify,[],[f174]) ).

fof(f176,plain,
    ( ? [X0] :
        ( ( ? [X1] :
              ( ~ aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
              & aElement0(X1) )
          | ? [X2] :
              ( ~ aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
              & aElementOf0(X2,slsdtgt0(xc)) ) )
        & aElementOf0(X0,slsdtgt0(xc)) )
   => ( ( ? [X1] :
            ( ~ aElementOf0(sdtasdt0(X1,sK30),slsdtgt0(xc))
            & aElement0(X1) )
        | ? [X2] :
            ( ~ aElementOf0(sdtpldt0(sK30,X2),slsdtgt0(xc))
            & aElementOf0(X2,slsdtgt0(xc)) ) )
      & aElementOf0(sK30,slsdtgt0(xc)) ) ),
    introduced(choice_axiom,[]) ).

fof(f177,plain,
    ( ? [X1] :
        ( ~ aElementOf0(sdtasdt0(X1,sK30),slsdtgt0(xc))
        & aElement0(X1) )
   => ( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
      & aElement0(sK31) ) ),
    introduced(choice_axiom,[]) ).

fof(f178,plain,
    ( ? [X2] :
        ( ~ aElementOf0(sdtpldt0(sK30,X2),slsdtgt0(xc))
        & aElementOf0(X2,slsdtgt0(xc)) )
   => ( ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc))
      & aElementOf0(sK32,slsdtgt0(xc)) ) ),
    introduced(choice_axiom,[]) ).

fof(f179,plain,
    ! [X3] :
      ( ? [X5] :
          ( sdtasdt0(xc,X5) = X3
          & aElement0(X5) )
     => ( sdtasdt0(xc,sK33(X3)) = X3
        & aElement0(sK33(X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f180,plain,
    ( ~ aIdeal0(slsdtgt0(xc))
    & ( ( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
        & aElement0(sK31) )
      | ( ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc))
        & aElementOf0(sK32,slsdtgt0(xc)) ) )
    & aElementOf0(sK30,slsdtgt0(xc))
    & ! [X3] :
        ( ( aElementOf0(X3,slsdtgt0(xc))
          | ! [X4] :
              ( sdtasdt0(xc,X4) != X3
              | ~ aElement0(X4) ) )
        & ( ( sdtasdt0(xc,sK33(X3)) = X3
            & aElement0(sK33(X3)) )
          | ~ aElementOf0(X3,slsdtgt0(xc)) ) )
    & aSet0(slsdtgt0(xc))
    & ! [X6,X7,X8] :
        ( sP5(X7,X8,X6)
        | ~ aElement0(X8)
        | ( ~ aElementOf0(X7,slsdtgt0(xc))
          & ! [X9] :
              ( sdtasdt0(xc,X9) != X7
              | ~ aElement0(X9) ) )
        | ( ~ aElementOf0(X6,slsdtgt0(xc))
          & ! [X10] :
              ( sdtasdt0(xc,X10) != X6
              | ~ aElement0(X10) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33])],[f175,f179,f178,f177,f176]) ).

fof(f182,plain,
    aElement0(sz10),
    inference(cnf_transformation,[],[f3]) ).

fof(f194,plain,
    ! [X0] :
      ( sdtasdt0(X0,sz10) = X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f270,plain,
    aElement0(xc),
    inference(cnf_transformation,[],[f38]) ).

fof(f273,plain,
    ! [X2,X0,X1] :
      ( sP4(X2,X1,X0,sK26(X0,X1,X2))
      | ~ sP5(X0,X1,X2) ),
    inference(cnf_transformation,[],[f161]) ).

fof(f279,plain,
    ! [X2,X3,X0,X1] :
      ( aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc))
      | ~ sP4(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f281,plain,
    ! [X2,X3,X0,X1] :
      ( aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc))
      | ~ sP4(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f289,plain,
    ! [X8,X6,X7] :
      ( sP5(X7,X8,X6)
      | ~ aElement0(X8)
      | ~ aElementOf0(X7,slsdtgt0(xc))
      | ~ aElementOf0(X6,slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f293,plain,
    ! [X3,X4] :
      ( aElementOf0(X3,slsdtgt0(xc))
      | sdtasdt0(xc,X4) != X3
      | ~ aElement0(X4) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f294,plain,
    aElementOf0(sK30,slsdtgt0(xc)),
    inference(cnf_transformation,[],[f180]) ).

fof(f295,plain,
    ( aElement0(sK31)
    | aElementOf0(sK32,slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f296,plain,
    ( aElement0(sK31)
    | ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f297,plain,
    ( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
    | aElementOf0(sK32,slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f298,plain,
    ( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
    | ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f312,plain,
    ! [X4] :
      ( aElementOf0(sdtasdt0(xc,X4),slsdtgt0(xc))
      | ~ aElement0(X4) ),
    inference(equality_resolution,[],[f293]) ).

cnf(c_50,plain,
    aElement0(sz10),
    inference(cnf_transformation,[],[f182]) ).

cnf(c_63,plain,
    ( ~ aElement0(X0)
    | sdtasdt0(X0,sz10) = X0 ),
    inference(cnf_transformation,[],[f194]) ).

cnf(c_138,plain,
    aElement0(xc),
    inference(cnf_transformation,[],[f270]) ).

cnf(c_139,plain,
    ( ~ sP5(X0,X1,X2)
    | sP4(X2,X1,X0,sK26(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f273]) ).

cnf(c_142,plain,
    ( ~ sP4(X0,X1,X2,X3)
    | aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f281]) ).

cnf(c_144,plain,
    ( ~ sP4(X0,X1,X2,X3)
    | aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f279]) ).

cnf(c_155,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc))
    | ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f298]) ).

cnf(c_156,negated_conjecture,
    ( ~ aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc))
    | aElementOf0(sK32,slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f297]) ).

cnf(c_157,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc))
    | aElement0(sK31) ),
    inference(cnf_transformation,[],[f296]) ).

cnf(c_158,negated_conjecture,
    ( aElementOf0(sK32,slsdtgt0(xc))
    | aElement0(sK31) ),
    inference(cnf_transformation,[],[f295]) ).

cnf(c_159,negated_conjecture,
    aElementOf0(sK30,slsdtgt0(xc)),
    inference(cnf_transformation,[],[f294]) ).

cnf(c_160,negated_conjecture,
    ( ~ aElement0(X0)
    | aElementOf0(sdtasdt0(xc,X0),slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f312]) ).

cnf(c_164,negated_conjecture,
    ( ~ aElementOf0(X0,slsdtgt0(xc))
    | ~ aElementOf0(X1,slsdtgt0(xc))
    | ~ aElement0(X2)
    | sP5(X1,X2,X0) ),
    inference(cnf_transformation,[],[f289]) ).

cnf(c_304,plain,
    ( ~ sP5(X0,X1,X2)
    | sP4(X2,X1,X0,sK26(X0,X1,X2)) ),
    inference(prop_impl_just,[status(thm)],[c_139]) ).

cnf(c_310,plain,
    ( ~ sP4(X0,X1,X2,X3)
    | aElementOf0(sdtasdt0(X1,X0),slsdtgt0(xc)) ),
    inference(prop_impl_just,[status(thm)],[c_142]) ).

cnf(c_314,plain,
    ( ~ sP4(X0,X1,X2,X3)
    | aElementOf0(sdtpldt0(X0,X2),slsdtgt0(xc)) ),
    inference(prop_impl_just,[status(thm)],[c_144]) ).

cnf(c_551,plain,
    ( sK26(X0,X1,X2) != X3
    | X0 != X4
    | X1 != X5
    | X2 != X6
    | ~ sP5(X0,X1,X2)
    | aElementOf0(sdtpldt0(X6,X4),slsdtgt0(xc)) ),
    inference(resolution_lifted,[status(thm)],[c_304,c_314]) ).

cnf(c_552,plain,
    ( ~ sP5(X0,X1,X2)
    | aElementOf0(sdtpldt0(X2,X0),slsdtgt0(xc)) ),
    inference(unflattening,[status(thm)],[c_551]) ).

cnf(c_560,plain,
    ( sK26(X0,X1,X2) != X3
    | X0 != X4
    | X1 != X5
    | X2 != X6
    | ~ sP5(X0,X1,X2)
    | aElementOf0(sdtasdt0(X5,X6),slsdtgt0(xc)) ),
    inference(resolution_lifted,[status(thm)],[c_304,c_310]) ).

cnf(c_561,plain,
    ( ~ sP5(X0,X1,X2)
    | aElementOf0(sdtasdt0(X1,X2),slsdtgt0(xc)) ),
    inference(unflattening,[status(thm)],[c_560]) ).

cnf(c_2732,plain,
    ( ~ sP5(X0,X1,X2)
    | aElementOf0(sdtpldt0(X2,X0),slsdtgt0(xc)) ),
    inference(prop_impl_just,[status(thm)],[c_552]) ).

cnf(c_2734,plain,
    ( ~ sP5(X0,X1,X2)
    | aElementOf0(sdtasdt0(X1,X2),slsdtgt0(xc)) ),
    inference(prop_impl_just,[status(thm)],[c_561]) ).

cnf(c_5125,plain,
    sdtasdt0(xc,sz10) = xc,
    inference(superposition,[status(thm)],[c_138,c_63]) ).

cnf(c_6082,plain,
    ( ~ sP5(X0,sK31,sK30)
    | aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc)) ),
    inference(instantiation,[status(thm)],[c_2734]) ).

cnf(c_6083,plain,
    ( ~ sP5(xc,sK31,sK30)
    | aElementOf0(sdtasdt0(sK31,sK30),slsdtgt0(xc)) ),
    inference(instantiation,[status(thm)],[c_6082]) ).

cnf(c_6194,plain,
    ( ~ sP5(sK32,X0,sK30)
    | aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc)) ),
    inference(instantiation,[status(thm)],[c_2732]) ).

cnf(c_6195,plain,
    ( ~ sP5(sK32,xc,sK30)
    | aElementOf0(sdtpldt0(sK30,sK32),slsdtgt0(xc)) ),
    inference(instantiation,[status(thm)],[c_6194]) ).

cnf(c_6655,plain,
    ( ~ aElementOf0(X0,slsdtgt0(xc))
    | ~ aElementOf0(sK32,slsdtgt0(xc))
    | ~ aElement0(X1)
    | sP5(sK32,X1,X0) ),
    inference(instantiation,[status(thm)],[c_164]) ).

cnf(c_10432,plain,
    ( ~ aElementOf0(X0,slsdtgt0(xc))
    | ~ aElementOf0(sK30,slsdtgt0(xc))
    | ~ aElement0(sK31)
    | sP5(X0,sK31,sK30) ),
    inference(instantiation,[status(thm)],[c_164]) ).

cnf(c_10433,plain,
    ( ~ aElementOf0(xc,slsdtgt0(xc))
    | ~ aElementOf0(sK30,slsdtgt0(xc))
    | ~ aElement0(sK31)
    | sP5(xc,sK31,sK30) ),
    inference(instantiation,[status(thm)],[c_10432]) ).

cnf(c_12710,plain,
    ( ~ aElement0(sz10)
    | aElementOf0(xc,slsdtgt0(xc)) ),
    inference(superposition,[status(thm)],[c_5125,c_160]) ).

cnf(c_13025,plain,
    ( ~ aElementOf0(sK30,slsdtgt0(xc))
    | ~ aElementOf0(sK32,slsdtgt0(xc))
    | ~ aElement0(X0)
    | sP5(sK32,X0,sK30) ),
    inference(instantiation,[status(thm)],[c_6655]) ).

cnf(c_13026,plain,
    ( ~ aElementOf0(sK30,slsdtgt0(xc))
    | ~ aElementOf0(sK32,slsdtgt0(xc))
    | ~ aElement0(xc)
    | sP5(sK32,xc,sK30) ),
    inference(instantiation,[status(thm)],[c_13025]) ).

cnf(c_13239,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_13026,c_12710,c_10433,c_6195,c_6083,c_155,c_156,c_157,c_158,c_159,c_50,c_138]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : RNG106+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09  % Command  : run_iprover %s %d THM
% 0.10/0.28  % Computer : n032.cluster.edu
% 0.10/0.28  % Model    : x86_64 x86_64
% 0.10/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28  % Memory   : 8042.1875MB
% 0.10/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28  % CPULimit : 300
% 0.10/0.28  % WCLimit  : 300
% 0.10/0.28  % DateTime : Sun Aug 27 01:45:44 EDT 2023
% 0.10/0.28  % CPUTime  : 
% 0.13/0.37  Running first-order theorem proving
% 0.13/0.37  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.98/1.01  % SZS status Started for theBenchmark.p
% 3.98/1.01  % SZS status Theorem for theBenchmark.p
% 3.98/1.01  
% 3.98/1.01  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.98/1.01  
% 3.98/1.01  ------  iProver source info
% 3.98/1.01  
% 3.98/1.01  git: date: 2023-05-31 18:12:56 +0000
% 3.98/1.01  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.98/1.01  git: non_committed_changes: false
% 3.98/1.01  git: last_make_outside_of_git: false
% 3.98/1.01  
% 3.98/1.01  ------ Parsing...
% 3.98/1.01  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.98/1.01  
% 3.98/1.01  ------ Preprocessing... sup_sim: 0  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  pe_s  pe_e 
% 3.98/1.01  
% 3.98/1.01  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  scvd_s sp: 1 0s scvd_e  snvd_s sp: 0 0s snvd_e 
% 3.98/1.01  
% 3.98/1.01  ------ Preprocessing...
% 3.98/1.01  ------ Proving...
% 3.98/1.01  ------ Problem Properties 
% 3.98/1.01  
% 3.98/1.01  
% 3.98/1.01  clauses                                 112
% 3.98/1.01  conjectures                             14
% 3.98/1.01  EPR                                     14
% 3.98/1.01  Horn                                    87
% 3.98/1.01  unary                                   7
% 3.98/1.01  binary                                  33
% 3.98/1.01  lits                                    379
% 3.98/1.01  lits eq                                 49
% 3.98/1.01  fd_pure                                 0
% 3.98/1.01  fd_pseudo                               0
% 3.98/1.01  fd_cond                                 3
% 3.98/1.01  fd_pseudo_cond                          11
% 3.98/1.01  AC symbols                              0
% 3.98/1.01  
% 3.98/1.01  ------ Input Options Time Limit: Unbounded
% 3.98/1.01  
% 3.98/1.01  
% 3.98/1.01  ------ 
% 3.98/1.01  Current options:
% 3.98/1.01  ------ 
% 3.98/1.01  
% 3.98/1.01  
% 3.98/1.01  
% 3.98/1.01  
% 3.98/1.01  ------ Proving...
% 3.98/1.01  
% 3.98/1.01  
% 3.98/1.01  % SZS status Theorem for theBenchmark.p
% 3.98/1.01  
% 3.98/1.01  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.98/1.01  
% 3.98/1.01  
%------------------------------------------------------------------------------