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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : RNG120+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:39:13 PM UTC 2026

% Result   : Theorem 15.48s 3.27s
% Output   : CNFRefutation 15.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   60 (  22 unt;   2 def)
%            Number of atoms       :  308 (  68 equ)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives :  341 ( 107   ~;  92   |; 120   &)
%                                         (   9 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   3 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  10 con; 0-2 aty)
%            Number of variables   :  127 (   0 sgn  91   !;  36   ?;   8   :)

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

fof(f4,axiom,
    ! [X0] :
      ( aElement0(X0)
     => aElement0(smndt0(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aElement0(X0) )
     => aElement0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).

fof(f15,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
        & sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).

fof(f20,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aElementOf0(X1,X0)
         => aElement0(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).

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(f45,axiom,
    ( ! [X0] :
        ( ( X0 != sz00
          & ( aElementOf0(X0,xI)
            | ? [X1,X2] :
                ( sdtpldt0(X1,X2) = X0
                & aElementOf0(X2,slsdtgt0(xb))
                & aElementOf0(X1,slsdtgt0(xa)) ) ) )
       => ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
    & xu != sz00
    & aElementOf0(xu,xI)
    & ? [X0,X1] :
        ( sdtpldt0(X0,X1) = xu
        & aElementOf0(X1,slsdtgt0(xb))
        & aElementOf0(X0,slsdtgt0(xa)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).

fof(f50,axiom,
    ( ( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
      | xr = sz00 )
    & xb = sdtpldt0(sdtasdt0(xq,xu),xr)
    & aElement0(xr)
    & aElement0(xq) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).

fof(f52,conjecture,
    ( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
    | ? [X0,X1] :
        ( sdtpldt0(X0,X1) = smndt0(sdtasdt0(xq,xu))
        & aElementOf0(X1,slsdtgt0(xb))
        & aElementOf0(X0,slsdtgt0(xa)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f53,negated_conjecture,
    ~ ( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
      | ? [X0,X1] :
          ( sdtpldt0(X0,X1) = smndt0(sdtasdt0(xq,xu))
          & aElementOf0(X1,slsdtgt0(xb))
          & aElementOf0(X0,slsdtgt0(xa)) ) ),
    inference(negated_conjecture,[status(cth)],[f52]) ).

fof(f62,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X7] :
        ( aElementOf0(X7,xI)
      <=> ? [X8,X9] :
            ( sdtpldt0(X8,X9) = X7
            & aElementOf0(X9,slsdtgt0(xb))
            & aElementOf0(X8,slsdtgt0(xa)) ) )
    & ! [X5] :
        ( aElementOf0(X5,slsdtgt0(xb))
      <=> ? [X6] :
            ( sdtasdt0(xb,X6) = X5
            & aElement0(X6) ) )
    & ! [X3] :
        ( aElementOf0(X3,slsdtgt0(xa))
      <=> ? [X4] :
            ( sdtasdt0(xa,X4) = X3
            & aElement0(X4) ) )
    & aIdeal0(xI)
    & ! [X0] :
        ( aElementOf0(X0,xI)
       => ( ! [X2] :
              ( aElement0(X2)
             => aElementOf0(sdtasdt0(X2,X0),xI) )
          & ! [X1] :
              ( aElementOf0(X1,xI)
             => aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
    & aSet0(xI) ),
    inference(rectify,[],[f42]) ).

fof(f65,plain,
    ( ! [X2] :
        ( ( sz00 != X2
          & ( aElementOf0(X2,xI)
            | ? [X3,X4] :
                ( sdtpldt0(X3,X4) = X2
                & aElementOf0(X4,slsdtgt0(xb))
                & aElementOf0(X3,slsdtgt0(xa)) ) ) )
       => ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
    & xu != sz00
    & aElementOf0(xu,xI)
    & ? [X0,X1] :
        ( sdtpldt0(X0,X1) = xu
        & aElementOf0(X1,slsdtgt0(xb))
        & aElementOf0(X0,slsdtgt0(xa)) ) ),
    inference(rectify,[],[f45]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | aElement0(smndt0(X0)) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ~ aElement0(X1)
      | ~ aElement0(X0)
      | aElement0(sdtasdt0(X0,X1)) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ aElement0(X1)
      | ~ aElement0(X0)
      | aElement0(sdtasdt0(X0,X1)) ),
    inference(flattening,[],[f72]) ).

fof(f87,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
        & sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f91,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | ! [X1] :
          ( ~ aElementOf0(X1,X0)
          | aElement0(X1) ) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f120,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X7] :
        ( aElementOf0(X7,xI)
      <=> ? [X8,X9] :
            ( sdtpldt0(X8,X9) = X7
            & aElementOf0(X9,slsdtgt0(xb))
            & aElementOf0(X8,slsdtgt0(xa)) ) )
    & ! [X5] :
        ( aElementOf0(X5,slsdtgt0(xb))
      <=> ? [X6] :
            ( sdtasdt0(xb,X6) = X5
            & aElement0(X6) ) )
    & ! [X3] :
        ( aElementOf0(X3,slsdtgt0(xa))
      <=> ? [X4] :
            ( sdtasdt0(xa,X4) = X3
            & aElement0(X4) ) )
    & aIdeal0(xI)
    & ! [X0] :
        ( ~ aElementOf0(X0,xI)
        | ( ! [X2] :
              ( ~ aElement0(X2)
              | aElementOf0(sdtasdt0(X2,X0),xI) )
          & ! [X1] :
              ( ~ aElementOf0(X1,xI)
              | aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
    & aSet0(xI) ),
    inference(ennf_transformation,[],[f62]) ).

fof(f121,plain,
    ( ! [X2] :
        ( sz00 = X2
        | ( ~ aElementOf0(X2,xI)
          & ! [X3,X4] :
              ( sdtpldt0(X3,X4) != X2
              | ~ aElementOf0(X4,slsdtgt0(xb))
              | ~ aElementOf0(X3,slsdtgt0(xa)) ) )
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
    & xu != sz00
    & aElementOf0(xu,xI)
    & ? [X0,X1] :
        ( sdtpldt0(X0,X1) = xu
        & aElementOf0(X1,slsdtgt0(xb))
        & aElementOf0(X0,slsdtgt0(xa)) ) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f122,plain,
    ( ! [X2] :
        ( sz00 = X2
        | ( ~ aElementOf0(X2,xI)
          & ! [X3,X4] :
              ( sdtpldt0(X3,X4) != X2
              | ~ aElementOf0(X4,slsdtgt0(xb))
              | ~ aElementOf0(X3,slsdtgt0(xa)) ) )
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
    & xu != sz00
    & aElementOf0(xu,xI)
    & ? [X0,X1] :
        ( sdtpldt0(X0,X1) = xu
        & aElementOf0(X1,slsdtgt0(xb))
        & aElementOf0(X0,slsdtgt0(xa)) ) ),
    inference(flattening,[],[f121]) ).

fof(f125,plain,
    ( ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
    & ! [X0,X1] :
        ( sdtpldt0(X0,X1) != smndt0(sdtasdt0(xq,xu))
        | ~ aElementOf0(X1,slsdtgt0(xb))
        | ~ aElementOf0(X0,slsdtgt0(xa)) ) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f173,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X7] :
        ( ( ~ aElementOf0(X7,xI)
          | ? [X8,X9] :
              ( sdtpldt0(X8,X9) = X7
              & aElementOf0(X9,slsdtgt0(xb))
              & aElementOf0(X8,slsdtgt0(xa)) ) )
        & ( ! [X8,X9] :
              ( sdtpldt0(X8,X9) != X7
              | ~ aElementOf0(X9,slsdtgt0(xb))
              | ~ aElementOf0(X8,slsdtgt0(xa)) )
          | aElementOf0(X7,xI) ) )
    & ! [X5] :
        ( ( ~ aElementOf0(X5,slsdtgt0(xb))
          | ? [X6] :
              ( sdtasdt0(xb,X6) = X5
              & aElement0(X6) ) )
        & ( ! [X6] :
              ( sdtasdt0(xb,X6) != X5
              | ~ aElement0(X6) )
          | aElementOf0(X5,slsdtgt0(xb)) ) )
    & ! [X3] :
        ( ( ~ aElementOf0(X3,slsdtgt0(xa))
          | ? [X4] :
              ( sdtasdt0(xa,X4) = X3
              & aElement0(X4) ) )
        & ( ! [X4] :
              ( sdtasdt0(xa,X4) != X3
              | ~ aElement0(X4) )
          | aElementOf0(X3,slsdtgt0(xa)) ) )
    & aIdeal0(xI)
    & ! [X0] :
        ( ~ aElementOf0(X0,xI)
        | ( ! [X2] :
              ( ~ aElement0(X2)
              | aElementOf0(sdtasdt0(X2,X0),xI) )
          & ! [X1] :
              ( ~ aElementOf0(X1,xI)
              | aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
    & aSet0(xI) ),
    inference(nnf_transformation,[],[f120]) ).

fof(f174,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X9] :
        ( ( ~ aElementOf0(X9,xI)
          | ? [X12,X13] :
              ( sdtpldt0(X12,X13) = X9
              & aElementOf0(X13,slsdtgt0(xb))
              & aElementOf0(X12,slsdtgt0(xa)) ) )
        & ( ! [X10,X11] :
              ( sdtpldt0(X10,X11) != X9
              | ~ aElementOf0(X11,slsdtgt0(xb))
              | ~ aElementOf0(X10,slsdtgt0(xa)) )
          | aElementOf0(X9,xI) ) )
    & ! [X6] :
        ( ( ~ aElementOf0(X6,slsdtgt0(xb))
          | ? [X8] :
              ( sdtasdt0(xb,X8) = X6
              & aElement0(X8) ) )
        & ( ! [X7] :
              ( sdtasdt0(xb,X7) != X6
              | ~ aElement0(X7) )
          | aElementOf0(X6,slsdtgt0(xb)) ) )
    & ! [X3] :
        ( ( ~ aElementOf0(X3,slsdtgt0(xa))
          | ? [X5] :
              ( sdtasdt0(xa,X5) = X3
              & aElement0(X5) ) )
        & ( ! [X4] :
              ( sdtasdt0(xa,X4) != X3
              | ~ aElement0(X4) )
          | aElementOf0(X3,slsdtgt0(xa)) ) )
    & aIdeal0(xI)
    & ! [X0] :
        ( ~ aElementOf0(X0,xI)
        | ( ! [X2] :
              ( ~ aElement0(X2)
              | aElementOf0(sdtasdt0(X2,X0),xI) )
          & ! [X1] :
              ( ~ aElementOf0(X1,xI)
              | aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
    & aSet0(xI) ),
    inference(rectify,[],[f173]) ).

fof(f175,plain,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & ! [X9] :
        ( ( ~ aElementOf0(X9,xI)
          | ( sdtpldt0(sK30(X9),sK31(X9)) = X9
            & aElementOf0(sK31(X9),slsdtgt0(xb))
            & aElementOf0(sK30(X9),slsdtgt0(xa)) ) )
        & ( ! [X10,X11] :
              ( sdtpldt0(X10,X11) != X9
              | ~ aElementOf0(X11,slsdtgt0(xb))
              | ~ aElementOf0(X10,slsdtgt0(xa)) )
          | aElementOf0(X9,xI) ) )
    & ! [X6] :
        ( ( ~ aElementOf0(X6,slsdtgt0(xb))
          | ( sdtasdt0(xb,sK29(X6)) = X6
            & aElement0(sK29(X6)) ) )
        & ( ! [X7] :
              ( sdtasdt0(xb,X7) != X6
              | ~ aElement0(X7) )
          | aElementOf0(X6,slsdtgt0(xb)) ) )
    & ! [X3] :
        ( ( ~ aElementOf0(X3,slsdtgt0(xa))
          | ( sdtasdt0(xa,sK28(X3)) = X3
            & aElement0(sK28(X3)) ) )
        & ( ! [X4] :
              ( sdtasdt0(xa,X4) != X3
              | ~ aElement0(X4) )
          | aElementOf0(X3,slsdtgt0(xa)) ) )
    & aIdeal0(xI)
    & ! [X0] :
        ( ~ aElementOf0(X0,xI)
        | ( ! [X2] :
              ( ~ aElement0(X2)
              | aElementOf0(sdtasdt0(X2,X0),xI) )
          & ! [X1] :
              ( ~ aElementOf0(X1,xI)
              | aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
    & aSet0(xI) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31]),skolemize(X5,sK28(X3)),skolemize(X8,sK29(X6)),skolemize(X12,sK30(X9)),skolemize(X13,sK31(X9))],[f174]) ).

fof(f180,plain,
    ( ! [X2] :
        ( sz00 = X2
        | ( ~ aElementOf0(X2,xI)
          & ! [X3,X4] :
              ( sdtpldt0(X3,X4) != X2
              | ~ aElementOf0(X4,slsdtgt0(xb))
              | ~ aElementOf0(X3,slsdtgt0(xa)) ) )
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
    & xu != sz00
    & aElementOf0(xu,xI)
    & xu = sdtpldt0(sK41,sK42)
    & aElementOf0(sK42,slsdtgt0(xb))
    & aElementOf0(sK41,slsdtgt0(xa)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41,sK42]),skolemize(X0,sK41),skolemize(X1,sK42)],[f122]) ).

fof(f186,plain,
    aElement0(sz10),
    inference(cnf_transformation,[],[f3]) ).

fof(f187,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | aElement0(smndt0(X0)) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( ~ aElement0(X1)
      | ~ aElement0(X0)
      | aElement0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f203,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f208,plain,
    ! [X0,X1] :
      ( ~ aSet0(X0)
      | ~ aElementOf0(X1,X0)
      | aElement0(X1) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f311,plain,
    ! [X2,X0] :
      ( ~ aElementOf0(X0,xI)
      | ~ aElement0(X2)
      | aElementOf0(sdtasdt0(X2,X0),xI) ),
    inference(cnf_transformation,[],[f175]) ).

fof(f313,plain,
    aSet0(xI),
    inference(cnf_transformation,[],[f175]) ).

fof(f340,plain,
    aElementOf0(xu,xI),
    inference(cnf_transformation,[],[f180]) ).

fof(f361,plain,
    aElement0(xq),
    inference(cnf_transformation,[],[f50]) ).

fof(f363,plain,
    ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(cnf_transformation,[],[f125]) ).

tcf(c_50,plain,
    aElement0(sz10),
    inference(cnf_transformation,[],[f186]) ).

tcf(c_51,plain,
    ! [X0: $i] :
      ( aElement0(smndt0(X0))
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f187]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i] :
      ( aElement0(sdtasdt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f189]) ).

tcf(c_66,plain,
    ! [X0: $i] :
      ( ( sdtasdt0(smndt0(sz10),X0) = smndt0(X0) )
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f203]) ).

tcf(c_72,plain,
    ! [X0: $i,X1: $i] :
      ( aElement0(X0)
      | ~ aSet0(X1)
      | ~ aElementOf0(X0,X1) ),
    inference(cnf_transformation,[],[f208]) ).

tcf(c_163,plain,
    aSet0(xI),
    inference(cnf_transformation,[],[f313]) ).

tcf(c_165,plain,
    ! [X0: $i,X1: $i] :
      ( aElementOf0(sdtasdt0(X1,X0),xI)
      | ~ aElement0(X1)
      | ~ aElementOf0(X0,xI) ),
    inference(cnf_transformation,[],[f311]) ).

tcf(c_204,plain,
    aElementOf0(xu,xI),
    inference(cnf_transformation,[],[f340]) ).

tcf(c_222,plain,
    aElement0(xq),
    inference(cnf_transformation,[],[f361]) ).

tcf(c_228,negated_conjecture,
    ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(cnf_transformation,[],[f363]) ).

tcf(c_7784,definition,
    iPr_def_10 = sdtasdt0(xq,xu),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_7785,definition,
    iPr_def_11 = smndt0(iPr_def_10),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_7788,negated_conjecture,
    ~ aElementOf0(iPr_def_11,xI),
    inference(demodulation,[status(thm)],[c_228,c_7784,c_7785]) ).

tcf(c_10367,plain,
    ( aElement0(xu)
    | ~ aSet0(xI) ),
    inference(superposition,[status(thm)],[c_204,c_72]) ).

tcf(c_10382,plain,
    aElement0(xu),
    inference(forward_subsumption_resolution,[status(thm)],[c_10367,c_163]) ).

tcf(c_10760,plain,
    ( aElement0(iPr_def_10)
    | ~ aElement0(xq)
    | ~ aElement0(xu) ),
    inference(superposition,[status(thm)],[c_7784,c_53]) ).

tcf(c_10767,plain,
    aElement0(iPr_def_10),
    inference(forward_subsumption_resolution,[status(thm)],[c_10760,c_222,c_10382]) ).

tcf(c_11324,plain,
    sdtasdt0(smndt0(sz10),iPr_def_10) = smndt0(iPr_def_10),
    inference(superposition,[status(thm)],[c_10767,c_66]) ).

tcf(c_11344,plain,
    sdtasdt0(smndt0(sz10),iPr_def_10) = iPr_def_11,
    inference(light_normalisation,[status(thm)],[c_11324,c_7785]) ).

tcf(c_11743,plain,
    ( aElementOf0(iPr_def_10,xI)
    | ~ aElement0(xq)
    | ~ aElementOf0(xu,xI) ),
    inference(superposition,[status(thm)],[c_7784,c_165]) ).

tcf(c_11749,plain,
    aElementOf0(iPr_def_10,xI),
    inference(forward_subsumption_resolution,[status(thm)],[c_11743,c_222,c_204]) ).

tcf(c_38524,plain,
    ( aElementOf0(iPr_def_11,xI)
    | ~ aElementOf0(iPr_def_10,xI)
    | ~ aElement0(smndt0(sz10)) ),
    inference(superposition,[status(thm)],[c_11344,c_165]) ).

tcf(c_38526,plain,
    ~ aElement0(smndt0(sz10)),
    inference(forward_subsumption_resolution,[status(thm)],[c_38524,c_7788,c_11749]) ).

tcf(c_38527,plain,
    ~ aElement0(sz10),
    inference(superposition,[status(thm)],[c_51,c_38526]) ).

tcf(c_38528,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_38527,c_50]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : RNG120+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37  % Computer : n010.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Thu Sep 24 08:20:58 UTC 2026
% 0.10/0.38  % CPUTime  : 
% 0.10/0.38  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41  Running first-order theorem proving
% 0.10/0.41  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43  
% 0.10/0.43  % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43  
% 0.10/0.43  % Detected problem language: tptp
% 0.10/0.44  % Proving...
% 15.48/3.27  % SZS status Started for theBenchmark.p
% 15.48/3.27  % SZS status Theorem for theBenchmark.p
% 15.48/3.27  
% 15.48/3.27  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.48/3.27  
% 15.48/3.27  % ------  iProver source info
% 15.48/3.27  
% 15.48/3.27  % git: date: 2026-07-19 20:42:38 +0200
% 15.48/3.27  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.48/3.27  % git: non_committed_changes: false
% 15.48/3.27  
% 15.48/3.27  % ------ Parsing...
% 15.48/3.27  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 15.48/3.27  
% 15.48/3.27  % ------ Preprocessing... sup_sim: 1  sf_s  rm: 2 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e % 
% 15.48/3.27  
% 15.48/3.27  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 15.48/3.27  
% 15.48/3.27  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 15.48/3.27  % ------ Proving...
% 15.48/3.27  % ------ Problem Properties 
% 15.48/3.27  
% 15.48/3.27  % 
% 15.48/3.27  % clauses                               171
% 15.48/3.27  % conjectures                           2
% 15.48/3.27  % EPR                                   48
% 15.48/3.27  % Horn                                  144
% 15.48/3.27  % unary                                 58
% 15.48/3.27  % binary                                33
% 15.48/3.27  % lits                                  455
% 15.48/3.27  % lits eq                               77
% 15.48/3.27  % fd_pure                               0
% 15.48/3.27  % fd_pseudo                             0
% 15.48/3.27  % fd_cond                               5
% 15.48/3.27  % fd_pseudo_cond                        11
% 15.48/3.27  % AC symbols                            0
% 15.48/3.27  
% 15.48/3.27  % ------ Schedule dynamic 5 is on 
% 15.48/3.27  
% 15.48/3.27  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.48/3.27  
% 15.48/3.27  
% 15.48/3.27  % ------ 
% 15.48/3.27  % Current options:
% 15.48/3.27  % ------ 
% 15.48/3.27  
% 15.48/3.27  
% 15.48/3.27  % 
% 15.48/3.27  
% 15.48/3.27  % ------ Proving...
% 15.48/3.27  % 
% 15.48/3.27  
% 15.48/3.27  % SZS status Theorem for theBenchmark.p
% 15.48/3.27  
% 15.48/3.27  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.48/3.28  
% 15.48/3.28  
%------------------------------------------------------------------------------