TSTP Solution File: RNG095+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Thu Aug 31 13:55:14 EDT 2023

% Result   : Theorem 10.11s 2.15s
% Output   : CNFRefutation 10.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   76 (   8 unt;   0 def)
%            Number of atoms       :  366 (  49 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  456 ( 166   ~; 159   |; 105   &)
%                                         (  12 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   3 con; 0-3 aty)
%            Number of variables   :  225 (   0 sgn; 127   !;  52   ?)

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

fof(f22,axiom,
    ! [X0,X1] :
      ( ( aSet0(X1)
        & aSet0(X0) )
     => ! [X2] :
          ( sdtpldt1(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ? [X4,X5] :
                    ( sdtpldt0(X4,X5) = X3
                    & aElementOf0(X5,X1)
                    & aElementOf0(X4,X0) ) )
            & aSet0(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSSum) ).

fof(f24,axiom,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) )
              & ! [X2] :
                  ( aElementOf0(X2,X0)
                 => aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
        & aSet0(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).

fof(f28,axiom,
    ( aIdeal0(xJ)
    & aIdeal0(xI) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).

fof(f29,axiom,
    ! [X0] :
      ( aElement0(X0)
     => aElementOf0(X0,sdtpldt1(xI,xJ)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205_03) ).

fof(f31,conjecture,
    ? [X0,X1] :
      ( sz10 = sdtpldt0(X0,X1)
      & aElementOf0(X1,xJ)
      & aElementOf0(X0,xI) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f32,negated_conjecture,
    ~ ? [X0,X1] :
        ( sz10 = sdtpldt0(X0,X1)
        & aElementOf0(X1,xJ)
        & aElementOf0(X0,xI) ),
    inference(negated_conjecture,[],[f31]) ).

fof(f36,plain,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) )
              & ! [X3] :
                  ( aElementOf0(X3,X0)
                 => aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
        & aSet0(X0) ) ),
    inference(rectify,[],[f24]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtpldt1(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ? [X4,X5] :
                    ( sdtpldt0(X4,X5) = X3
                    & aElementOf0(X5,X1)
                    & aElementOf0(X4,X0) ) )
            & aSet0(X2) ) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtpldt1(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ? [X4,X5] :
                    ( sdtpldt0(X4,X5) = X3
                    & aElementOf0(X5,X1)
                    & aElementOf0(X4,X0) ) )
            & aSet0(X2) ) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f62]) ).

fof(f66,plain,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( ( ! [X2] :
                  ( aElementOf0(sdtasdt0(X2,X1),X0)
                  | ~ aElement0(X2) )
              & ! [X3] :
                  ( aElementOf0(sdtpldt0(X1,X3),X0)
                  | ~ aElementOf0(X3,X0) ) )
            | ~ aElementOf0(X1,X0) )
        & aSet0(X0) ) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f73,plain,
    ! [X0] :
      ( aElementOf0(X0,sdtpldt1(xI,xJ))
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( sz10 != sdtpldt0(X0,X1)
      | ~ aElementOf0(X1,xJ)
      | ~ aElementOf0(X0,xI) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f75,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ( ! [X3] :
            ( aElementOf0(X3,X2)
          <=> ? [X4,X5] :
                ( sdtpldt0(X4,X5) = X3
                & aElementOf0(X5,X1)
                & aElementOf0(X4,X0) ) )
        & aSet0(X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtpldt1(X0,X1) = X2
        <=> sP0(X1,X0,X2) )
      | ~ sP1(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(definition_folding,[],[f63,f76,f75]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtpldt1(X0,X1) = X2
            | ~ sP0(X1,X0,X2) )
          & ( sP0(X1,X0,X2)
            | sdtpldt1(X0,X1) != X2 ) )
      | ~ sP1(X0,X1) ),
    inference(nnf_transformation,[],[f76]) ).

fof(f82,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( sdtpldt0(X4,X5) != X3
                  | ~ aElementOf0(X5,X1)
                  | ~ aElementOf0(X4,X0) )
              | ~ aElementOf0(X3,X2) )
            & ( ? [X4,X5] :
                  ( sdtpldt0(X4,X5) = X3
                  & aElementOf0(X5,X1)
                  & aElementOf0(X4,X0) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X3] :
              ( ( aElementOf0(X3,X2)
                | ! [X4,X5] :
                    ( sdtpldt0(X4,X5) != X3
                    | ~ aElementOf0(X5,X1)
                    | ~ aElementOf0(X4,X0) ) )
              & ( ? [X4,X5] :
                    ( sdtpldt0(X4,X5) = X3
                    & aElementOf0(X5,X1)
                    & aElementOf0(X4,X0) )
                | ~ aElementOf0(X3,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f83,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( sdtpldt0(X4,X5) != X3
                  | ~ aElementOf0(X5,X1)
                  | ~ aElementOf0(X4,X0) )
              | ~ aElementOf0(X3,X2) )
            & ( ? [X4,X5] :
                  ( sdtpldt0(X4,X5) = X3
                  & aElementOf0(X5,X1)
                  & aElementOf0(X4,X0) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X3] :
              ( ( aElementOf0(X3,X2)
                | ! [X4,X5] :
                    ( sdtpldt0(X4,X5) != X3
                    | ~ aElementOf0(X5,X1)
                    | ~ aElementOf0(X4,X0) ) )
              & ( ? [X4,X5] :
                    ( sdtpldt0(X4,X5) = X3
                    & aElementOf0(X5,X1)
                    & aElementOf0(X4,X0) )
                | ~ aElementOf0(X3,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(flattening,[],[f82]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( sdtpldt0(X4,X5) != X3
                  | ~ aElementOf0(X5,X0)
                  | ~ aElementOf0(X4,X1) )
              | ~ aElementOf0(X3,X2) )
            & ( ? [X6,X7] :
                  ( sdtpldt0(X6,X7) = X3
                  & aElementOf0(X7,X0)
                  & aElementOf0(X6,X1) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X8] :
              ( ( aElementOf0(X8,X2)
                | ! [X9,X10] :
                    ( sdtpldt0(X9,X10) != X8
                    | ~ aElementOf0(X10,X0)
                    | ~ aElementOf0(X9,X1) ) )
              & ( ? [X11,X12] :
                    ( sdtpldt0(X11,X12) = X8
                    & aElementOf0(X12,X0)
                    & aElementOf0(X11,X1) )
                | ~ aElementOf0(X8,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f83]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4,X5] :
                ( sdtpldt0(X4,X5) != X3
                | ~ aElementOf0(X5,X0)
                | ~ aElementOf0(X4,X1) )
            | ~ aElementOf0(X3,X2) )
          & ( ? [X6,X7] :
                ( sdtpldt0(X6,X7) = X3
                & aElementOf0(X7,X0)
                & aElementOf0(X6,X1) )
            | aElementOf0(X3,X2) ) )
     => ( ( ! [X5,X4] :
              ( sdtpldt0(X4,X5) != sK4(X0,X1,X2)
              | ~ aElementOf0(X5,X0)
              | ~ aElementOf0(X4,X1) )
          | ~ aElementOf0(sK4(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( sdtpldt0(X6,X7) = sK4(X0,X1,X2)
              & aElementOf0(X7,X0)
              & aElementOf0(X6,X1) )
          | aElementOf0(sK4(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( sdtpldt0(X6,X7) = sK4(X0,X1,X2)
          & aElementOf0(X7,X0)
          & aElementOf0(X6,X1) )
     => ( sK4(X0,X1,X2) = sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2))
        & aElementOf0(sK6(X0,X1,X2),X0)
        & aElementOf0(sK5(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( sdtpldt0(X11,X12) = X8
          & aElementOf0(X12,X0)
          & aElementOf0(X11,X1) )
     => ( sdtpldt0(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
        & aElementOf0(sK8(X0,X1,X8),X0)
        & aElementOf0(sK7(X0,X1,X8),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ! [X4,X5] :
                ( sdtpldt0(X4,X5) != sK4(X0,X1,X2)
                | ~ aElementOf0(X5,X0)
                | ~ aElementOf0(X4,X1) )
            | ~ aElementOf0(sK4(X0,X1,X2),X2) )
          & ( ( sK4(X0,X1,X2) = sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2))
              & aElementOf0(sK6(X0,X1,X2),X0)
              & aElementOf0(sK5(X0,X1,X2),X1) )
            | aElementOf0(sK4(X0,X1,X2),X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X8] :
              ( ( aElementOf0(X8,X2)
                | ! [X9,X10] :
                    ( sdtpldt0(X9,X10) != X8
                    | ~ aElementOf0(X10,X0)
                    | ~ aElementOf0(X9,X1) ) )
              & ( ( sdtpldt0(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
                  & aElementOf0(sK8(X0,X1,X8),X0)
                  & aElementOf0(sK7(X0,X1,X8),X1) )
                | ~ aElementOf0(X8,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f84,f87,f86,f85]) ).

fof(f94,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X1] :
              ( ( ! [X2] :
                    ( aElementOf0(sdtasdt0(X2,X1),X0)
                    | ~ aElement0(X2) )
                & ! [X3] :
                    ( aElementOf0(sdtpldt0(X1,X3),X0)
                    | ~ aElementOf0(X3,X0) ) )
              | ~ aElementOf0(X1,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(nnf_transformation,[],[f66]) ).

fof(f95,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X1] :
              ( ( ! [X2] :
                    ( aElementOf0(sdtasdt0(X2,X1),X0)
                    | ~ aElement0(X2) )
                & ! [X3] :
                    ( aElementOf0(sdtpldt0(X1,X3),X0)
                    | ~ aElementOf0(X3,X0) ) )
              | ~ aElementOf0(X1,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(flattening,[],[f94]) ).

fof(f96,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtasdt0(X5,X4),X0)
                    | ~ aElement0(X5) )
                & ! [X6] :
                    ( aElementOf0(sdtpldt0(X4,X6),X0)
                    | ~ aElementOf0(X6,X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(rectify,[],[f95]) ).

fof(f97,plain,
    ! [X0] :
      ( ? [X1] :
          ( ( ? [X2] :
                ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                & aElement0(X2) )
            | ? [X3] :
                ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                & aElementOf0(X3,X0) ) )
          & aElementOf0(X1,X0) )
     => ( ( ? [X2] :
              ( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
              & aElement0(X2) )
          | ? [X3] :
              ( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
              & aElementOf0(X3,X0) ) )
        & aElementOf0(sK10(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0] :
      ( ? [X2] :
          ( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
          & aElement0(X2) )
     => ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
        & aElement0(sK11(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ! [X0] :
      ( ? [X3] :
          ( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
          & aElementOf0(X3,X0) )
     => ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
        & aElementOf0(sK12(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ( ( ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
              & aElement0(sK11(X0)) )
            | ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
              & aElementOf0(sK12(X0),X0) ) )
          & aElementOf0(sK10(X0),X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtasdt0(X5,X4),X0)
                    | ~ aElement0(X5) )
                & ! [X6] :
                    ( aElementOf0(sdtpldt0(X4,X6),X0)
                    | ~ aElementOf0(X6,X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f96,f99,f98,f97]) ).

fof(f103,plain,
    aElement0(sz10),
    inference(cnf_transformation,[],[f3]) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X0,X2)
      | sdtpldt1(X0,X1) != X2
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f133,plain,
    ! [X2,X0,X1,X8] :
      ( aElementOf0(sK7(X0,X1,X8),X1)
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f134,plain,
    ! [X2,X0,X1,X8] :
      ( aElementOf0(sK8(X0,X1,X8),X0)
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f135,plain,
    ! [X2,X0,X1,X8] :
      ( sdtpldt0(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f149,plain,
    ! [X0] :
      ( aSet0(X0)
      | ~ aIdeal0(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f161,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[],[f28]) ).

fof(f162,plain,
    aIdeal0(xJ),
    inference(cnf_transformation,[],[f28]) ).

fof(f163,plain,
    ! [X0] :
      ( aElementOf0(X0,sdtpldt1(xI,xJ))
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( sz10 != sdtpldt0(X0,X1)
      | ~ aElementOf0(X1,xJ)
      | ~ aElementOf0(X0,xI) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( sP0(X1,X0,sdtpldt1(X0,X1))
      | ~ sP1(X0,X1) ),
    inference(equality_resolution,[],[f130]) ).

cnf(c_50,plain,
    aElement0(sz10),
    inference(cnf_transformation,[],[f103]) ).

cnf(c_78,plain,
    ( ~ sP1(X0,X1)
    | sP0(X1,X0,sdtpldt1(X0,X1)) ),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_84,plain,
    ( ~ sP0(X0,X1,X2)
    | ~ aElementOf0(X3,X2)
    | sdtpldt0(sK7(X0,X1,X3),sK8(X0,X1,X3)) = X3 ),
    inference(cnf_transformation,[],[f135]) ).

cnf(c_85,plain,
    ( ~ sP0(X0,X1,X2)
    | ~ aElementOf0(X3,X2)
    | aElementOf0(sK8(X0,X1,X3),X0) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_86,plain,
    ( ~ sP0(X0,X1,X2)
    | ~ aElementOf0(X3,X2)
    | aElementOf0(sK7(X0,X1,X3),X1) ),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_88,plain,
    ( ~ aSet0(X0)
    | ~ aSet0(X1)
    | sP1(X0,X1) ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_103,plain,
    ( ~ aIdeal0(X0)
    | aSet0(X0) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_108,plain,
    aIdeal0(xJ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_109,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_110,plain,
    ( ~ aElement0(X0)
    | aElementOf0(X0,sdtpldt1(xI,xJ)) ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_113,negated_conjecture,
    ( sdtpldt0(X0,X1) != sz10
    | ~ aElementOf0(X0,xI)
    | ~ aElementOf0(X1,xJ) ),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_601,plain,
    ( X0 != X1
    | X2 != X3
    | ~ aSet0(X0)
    | ~ aSet0(X2)
    | sP0(X3,X1,sdtpldt1(X1,X3)) ),
    inference(resolution_lifted,[status(thm)],[c_88,c_78]) ).

cnf(c_602,plain,
    ( ~ aSet0(X0)
    | ~ aSet0(X1)
    | sP0(X1,X0,sdtpldt1(X0,X1)) ),
    inference(unflattening,[status(thm)],[c_601]) ).

cnf(c_3316,plain,
    ( ~ aElement0(sz10)
    | aElementOf0(sz10,sdtpldt1(xI,xJ)) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_3370,plain,
    ( ~ aIdeal0(xJ)
    | aSet0(xJ) ),
    inference(instantiation,[status(thm)],[c_103]) ).

cnf(c_3388,plain,
    ( ~ aIdeal0(xI)
    | aSet0(xI) ),
    inference(instantiation,[status(thm)],[c_103]) ).

cnf(c_4110,plain,
    ( ~ sP0(X0,X1,sdtpldt1(xI,xJ))
    | ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
    | sdtpldt0(sK7(X0,X1,sz10),sK8(X0,X1,sz10)) = sz10 ),
    inference(instantiation,[status(thm)],[c_84]) ).

cnf(c_4111,plain,
    ( ~ sP0(X0,X1,sdtpldt1(xI,xJ))
    | ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
    | aElementOf0(sK8(X0,X1,sz10),X0) ),
    inference(instantiation,[status(thm)],[c_85]) ).

cnf(c_4112,plain,
    ( ~ sP0(X0,X1,sdtpldt1(xI,xJ))
    | ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
    | aElementOf0(sK7(X0,X1,sz10),X1) ),
    inference(instantiation,[status(thm)],[c_86]) ).

cnf(c_5374,plain,
    ( ~ aSet0(X0)
    | ~ aSet0(xI)
    | sP0(X0,xI,sdtpldt1(xI,X0)) ),
    inference(instantiation,[status(thm)],[c_602]) ).

cnf(c_5382,plain,
    ( ~ aSet0(X0)
    | sP0(X0,xI,sdtpldt1(xI,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_5374,c_109,c_3388,c_5374]) ).

cnf(c_6118,plain,
    ( ~ aSet0(xJ)
    | sP0(xJ,xI,sdtpldt1(xI,xJ)) ),
    inference(instantiation,[status(thm)],[c_5382]) ).

cnf(c_6684,plain,
    ( ~ sP0(X0,X1,sdtpldt1(xI,xJ))
    | ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
    | sdtpldt0(sK7(X0,X1,sz10),sK8(X0,X1,sz10)) = sz10 ),
    inference(instantiation,[status(thm)],[c_84]) ).

cnf(c_6685,plain,
    ( ~ sP0(X0,X1,sdtpldt1(xI,xJ))
    | ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
    | aElementOf0(sK8(X0,X1,sz10),X0) ),
    inference(instantiation,[status(thm)],[c_85]) ).

cnf(c_6686,plain,
    ( ~ sP0(X0,X1,sdtpldt1(xI,xJ))
    | ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
    | aElementOf0(sK7(X0,X1,sz10),X1) ),
    inference(instantiation,[status(thm)],[c_86]) ).

cnf(c_6687,plain,
    ( ~ sP0(X0,X1,sdtpldt1(xI,xJ))
    | aElementOf0(sK7(X0,X1,sz10),X1) ),
    inference(global_subsumption_just,[status(thm)],[c_6686,c_50,c_3316,c_4112]) ).

cnf(c_6689,plain,
    ( ~ sP0(X0,X1,sdtpldt1(xI,xJ))
    | aElementOf0(sK8(X0,X1,sz10),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_6685,c_50,c_3316,c_4111]) ).

cnf(c_6691,plain,
    ( ~ sP0(X0,X1,sdtpldt1(xI,xJ))
    | sdtpldt0(sK7(X0,X1,sz10),sK8(X0,X1,sz10)) = sz10 ),
    inference(global_subsumption_just,[status(thm)],[c_6684,c_50,c_3316,c_4110]) ).

cnf(c_10148,plain,
    ( ~ sP0(xJ,xI,sdtpldt1(xI,xJ))
    | sdtpldt0(sK7(xJ,xI,sz10),sK8(xJ,xI,sz10)) = sz10 ),
    inference(instantiation,[status(thm)],[c_6691]) ).

cnf(c_10149,plain,
    ( ~ sP0(xJ,xI,sdtpldt1(xI,xJ))
    | aElementOf0(sK8(xJ,xI,sz10),xJ) ),
    inference(instantiation,[status(thm)],[c_6689]) ).

cnf(c_10150,plain,
    ( ~ sP0(xJ,xI,sdtpldt1(xI,xJ))
    | aElementOf0(sK7(xJ,xI,sz10),xI) ),
    inference(instantiation,[status(thm)],[c_6687]) ).

cnf(c_20583,plain,
    ( sdtpldt0(sK7(xJ,xI,sz10),sK8(xJ,xI,sz10)) != sz10
    | ~ aElementOf0(sK7(xJ,xI,sz10),xI)
    | ~ aElementOf0(sK8(xJ,xI,sz10),xJ) ),
    inference(instantiation,[status(thm)],[c_113]) ).

cnf(c_20584,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_20583,c_10148,c_10149,c_10150,c_6118,c_3370,c_108]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun Aug 27 02:16:05 EDT 2023
% 0.14/0.34  % 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
% 10.11/2.15  % SZS status Started for theBenchmark.p
% 10.11/2.15  % SZS status Theorem for theBenchmark.p
% 10.11/2.15  
% 10.11/2.15  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 10.11/2.15  
% 10.11/2.15  ------  iProver source info
% 10.11/2.15  
% 10.11/2.15  git: date: 2023-05-31 18:12:56 +0000
% 10.11/2.15  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 10.11/2.15  git: non_committed_changes: false
% 10.11/2.15  git: last_make_outside_of_git: false
% 10.11/2.15  
% 10.11/2.15  ------ Parsing...
% 10.11/2.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 10.11/2.15  
% 10.11/2.15  ------ 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 
% 10.11/2.15  
% 10.11/2.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 10.11/2.15  
% 10.11/2.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 10.11/2.15  ------ Proving...
% 10.11/2.15  ------ Problem Properties 
% 10.11/2.15  
% 10.11/2.15  
% 10.11/2.15  clauses                                 62
% 10.11/2.15  conjectures                             1
% 10.11/2.15  EPR                                     10
% 10.11/2.15  Horn                                    49
% 10.11/2.15  unary                                   7
% 10.11/2.15  binary                                  14
% 10.11/2.15  lits                                    200
% 10.11/2.15  lits eq                                 32
% 10.11/2.15  fd_pure                                 0
% 10.11/2.15  fd_pseudo                               0
% 10.11/2.15  fd_cond                                 1
% 10.11/2.15  fd_pseudo_cond                          8
% 10.11/2.15  AC symbols                              0
% 10.11/2.15  
% 10.11/2.15  ------ Input Options Time Limit: Unbounded
% 10.11/2.15  
% 10.11/2.15  
% 10.11/2.15  ------ 
% 10.11/2.15  Current options:
% 10.11/2.15  ------ 
% 10.11/2.15  
% 10.11/2.15  
% 10.11/2.15  
% 10.11/2.15  
% 10.11/2.15  ------ Proving...
% 10.11/2.15  
% 10.11/2.15  
% 10.11/2.15  % SZS status Theorem for theBenchmark.p
% 10.11/2.15  
% 10.11/2.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.11/2.15  
% 10.11/2.15  
%------------------------------------------------------------------------------