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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : NUM607+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n014.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 02:26:12 PM UTC 2026

% Result   : Theorem 7.51s 1.68s
% Output   : CNFRefutation 7.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   74 (  29 unt;   0 def)
%            Number of atoms       :  290 (  43 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  366 ( 150   ~; 149   |;  54   &)
%                                         (   8 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   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  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   8 con; 0-3 aty)
%            Number of variables   :  104 (   0 sgn  98   !;   6   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f10,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,X0) )
            & aSet0(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( ( aSet0(X2)
        & aSet0(X1)
        & aSet0(X0) )
     => ( ( aSubsetOf0(X1,X2)
          & aSubsetOf0(X0,X1) )
       => aSubsetOf0(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).

fof(f23,axiom,
    ( isCountable0(szNzAzT0)
    & aSet0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

fof(f57,axiom,
    ! [X0,X1] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aSet0(X0) )
     => ! [X2] :
          ( X2 = slbdtsldtrb0(X0,X1)
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( sbrdtbr0(X3) = X1
                  & aSubsetOf0(X3,X0) ) )
            & aSet0(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).

fof(f74,axiom,
    aElementOf0(xK,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).

fof(f75,axiom,
    ( isCountable0(xS)
    & aSubsetOf0(xS,szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).

fof(f76,axiom,
    ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & aFunction0(xc) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).

fof(f96,axiom,
    ( isCountable0(xO)
    & aSet0(xO) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).

fof(f98,axiom,
    aSubsetOf0(xO,xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4998) ).

fof(f99,axiom,
    aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).

fof(f100,axiom,
    ( xQ != slcrc0
    & aSubsetOf0(xQ,xO) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).

fof(f101,axiom,
    aSubsetOf0(xQ,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).

fof(f102,conjecture,
    aElementOf0(xQ,szDzozmdt0(xc)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f103,negated_conjecture,
    ~ aElementOf0(xQ,szDzozmdt0(xc)),
    inference(negated_conjecture,[status(cth)],[f102]) ).

fof(f111,plain,
    ~ aElementOf0(xQ,szDzozmdt0(xc)),
    inference(flattening,[],[f103]) ).

fof(f118,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( ~ aElementOf0(X2,X1)
                | aElementOf0(X2,X0) )
            & aSet0(X1) ) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f124,plain,
    ! [X0,X1,X2] :
      ( ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSet0(X0)
      | ~ aSubsetOf0(X1,X2)
      | ~ aSubsetOf0(X0,X1)
      | aSubsetOf0(X0,X2) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f125,plain,
    ! [X0,X1,X2] :
      ( ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSet0(X0)
      | ~ aSubsetOf0(X1,X2)
      | ~ aSubsetOf0(X0,X1)
      | aSubsetOf0(X0,X2) ),
    inference(flattening,[],[f124]) ).

fof(f186,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0)
      | ! [X2] :
          ( X2 = slbdtsldtrb0(X0,X1)
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( sbrdtbr0(X3) = X1
                  & aSubsetOf0(X3,X0) ) )
            & aSet0(X2) ) ) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f187,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0)
      | ! [X2] :
          ( X2 = slbdtsldtrb0(X0,X1)
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( sbrdtbr0(X3) = X1
                  & aSubsetOf0(X3,X0) ) )
            & aSet0(X2) ) ) ),
    inference(flattening,[],[f186]) ).

fof(f245,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | ! [X1] :
          ( ( ~ aSubsetOf0(X1,X0)
            | ( ! [X2] :
                  ( ~ aElementOf0(X2,X1)
                  | aElementOf0(X2,X0) )
              & aSet0(X1) ) )
          & ( ? [X2] :
                ( aElementOf0(X2,X1)
                & ~ aElementOf0(X2,X0) )
            | ~ aSet0(X1)
            | aSubsetOf0(X1,X0) ) ) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f246,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | ! [X1] :
          ( ( ~ aSubsetOf0(X1,X0)
            | ( ! [X2] :
                  ( ~ aElementOf0(X2,X1)
                  | aElementOf0(X2,X0) )
              & aSet0(X1) ) )
          & ( ? [X2] :
                ( aElementOf0(X2,X1)
                & ~ aElementOf0(X2,X0) )
            | ~ aSet0(X1)
            | aSubsetOf0(X1,X0) ) ) ),
    inference(flattening,[],[f245]) ).

fof(f247,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | ! [X1] :
          ( ( ~ aSubsetOf0(X1,X0)
            | ( ! [X3] :
                  ( ~ aElementOf0(X3,X1)
                  | aElementOf0(X3,X0) )
              & aSet0(X1) ) )
          & ( ? [X2] :
                ( aElementOf0(X2,X1)
                & ~ aElementOf0(X2,X0) )
            | ~ aSet0(X1)
            | aSubsetOf0(X1,X0) ) ) ),
    inference(rectify,[],[f246]) ).

fof(f248,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | ! [X1] :
          ( ( ~ aSubsetOf0(X1,X0)
            | ( ! [X3] :
                  ( ~ aElementOf0(X3,X1)
                  | aElementOf0(X3,X0) )
              & aSet0(X1) ) )
          & ( ( aElementOf0(sK5(X0,X1),X1)
              & ~ aElementOf0(sK5(X0,X1),X0) )
            | ~ aSet0(X1)
            | aSubsetOf0(X1,X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f247]) ).

fof(f282,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0)
      | ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) != X2
            | ( ! [X3] :
                  ( ( ~ aElementOf0(X3,X2)
                    | ( sbrdtbr0(X3) = X1
                      & aSubsetOf0(X3,X0) ) )
                  & ( sbrdtbr0(X3) != X1
                    | ~ aSubsetOf0(X3,X0)
                    | aElementOf0(X3,X2) ) )
              & aSet0(X2) ) )
          & ( ? [X3] :
                ( ( aElementOf0(X3,X2)
                  | ( sbrdtbr0(X3) = X1
                    & aSubsetOf0(X3,X0) ) )
                & ( ~ aElementOf0(X3,X2)
                  | sbrdtbr0(X3) != X1
                  | ~ aSubsetOf0(X3,X0) ) )
            | ~ aSet0(X2)
            | X2 = slbdtsldtrb0(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f187]) ).

fof(f283,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0)
      | ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) != X2
            | ( ! [X3] :
                  ( ( ~ aElementOf0(X3,X2)
                    | ( sbrdtbr0(X3) = X1
                      & aSubsetOf0(X3,X0) ) )
                  & ( sbrdtbr0(X3) != X1
                    | ~ aSubsetOf0(X3,X0)
                    | aElementOf0(X3,X2) ) )
              & aSet0(X2) ) )
          & ( ? [X3] :
                ( ( aElementOf0(X3,X2)
                  | ( sbrdtbr0(X3) = X1
                    & aSubsetOf0(X3,X0) ) )
                & ( ~ aElementOf0(X3,X2)
                  | sbrdtbr0(X3) != X1
                  | ~ aSubsetOf0(X3,X0) ) )
            | ~ aSet0(X2)
            | X2 = slbdtsldtrb0(X0,X1) ) ) ),
    inference(flattening,[],[f282]) ).

fof(f284,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0)
      | ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) != X2
            | ( ! [X4] :
                  ( ( ~ aElementOf0(X4,X2)
                    | ( sbrdtbr0(X4) = X1
                      & aSubsetOf0(X4,X0) ) )
                  & ( sbrdtbr0(X4) != X1
                    | ~ aSubsetOf0(X4,X0)
                    | aElementOf0(X4,X2) ) )
              & aSet0(X2) ) )
          & ( ? [X3] :
                ( ( aElementOf0(X3,X2)
                  | ( sbrdtbr0(X3) = X1
                    & aSubsetOf0(X3,X0) ) )
                & ( ~ aElementOf0(X3,X2)
                  | sbrdtbr0(X3) != X1
                  | ~ aSubsetOf0(X3,X0) ) )
            | ~ aSet0(X2)
            | X2 = slbdtsldtrb0(X0,X1) ) ) ),
    inference(rectify,[],[f283]) ).

fof(f285,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0)
      | ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) != X2
            | ( ! [X4] :
                  ( ( ~ aElementOf0(X4,X2)
                    | ( sbrdtbr0(X4) = X1
                      & aSubsetOf0(X4,X0) ) )
                  & ( sbrdtbr0(X4) != X1
                    | ~ aSubsetOf0(X4,X0)
                    | aElementOf0(X4,X2) ) )
              & aSet0(X2) ) )
          & ( ( ( aElementOf0(sK14(X0,X1,X2),X2)
                | ( sbrdtbr0(sK14(X0,X1,X2)) = X1
                  & aSubsetOf0(sK14(X0,X1,X2),X0) ) )
              & ( ~ aElementOf0(sK14(X0,X1,X2),X2)
                | sbrdtbr0(sK14(X0,X1,X2)) != X1
                | ~ aSubsetOf0(sK14(X0,X1,X2),X0) ) )
            | ~ aSet0(X2)
            | X2 = slbdtsldtrb0(X0,X1) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f284]) ).

fof(f312,plain,
    ! [X0,X1] :
      ( ~ aSet0(X0)
      | ~ aSubsetOf0(X1,X0)
      | aSet0(X1) ),
    inference(cnf_transformation,[],[f248]) ).

fof(f318,plain,
    ! [X2,X0,X1] :
      ( ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSet0(X0)
      | ~ aSubsetOf0(X1,X2)
      | ~ aSubsetOf0(X0,X1)
      | aSubsetOf0(X0,X2) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f350,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f23]) ).

fof(f404,plain,
    ! [X2,X0,X1,X4] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0)
      | slbdtsldtrb0(X0,X1) != X2
      | ~ aElementOf0(X4,X2)
      | sbrdtbr0(X4) = X1 ),
    inference(cnf_transformation,[],[f285]) ).

fof(f406,plain,
    ! [X2,X0,X1,X4] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0)
      | slbdtsldtrb0(X0,X1) != X2
      | sbrdtbr0(X4) != X1
      | ~ aSubsetOf0(X4,X0)
      | aElementOf0(X4,X2) ),
    inference(cnf_transformation,[],[f285]) ).

fof(f449,plain,
    aElementOf0(xK,szNzAzT0),
    inference(cnf_transformation,[],[f74]) ).

fof(f451,plain,
    aSubsetOf0(xS,szNzAzT0),
    inference(cnf_transformation,[],[f75]) ).

fof(f453,plain,
    szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
    inference(cnf_transformation,[],[f76]) ).

fof(f498,plain,
    aSet0(xO),
    inference(cnf_transformation,[],[f96]) ).

fof(f502,plain,
    aSubsetOf0(xO,xS),
    inference(cnf_transformation,[],[f98]) ).

fof(f503,plain,
    aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
    inference(cnf_transformation,[],[f99]) ).

fof(f505,plain,
    aSubsetOf0(xQ,xO),
    inference(cnf_transformation,[],[f100]) ).

fof(f506,plain,
    aSubsetOf0(xQ,szNzAzT0),
    inference(cnf_transformation,[],[f101]) ).

fof(f507,plain,
    ~ aElementOf0(xQ,szDzozmdt0(xc)),
    inference(cnf_transformation,[],[f111]) ).

fof(f526,plain,
    ! [X2,X0,X4] :
      ( ~ aElementOf0(sbrdtbr0(X4),szNzAzT0)
      | ~ aSet0(X0)
      | slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
      | ~ aSubsetOf0(X4,X0)
      | aElementOf0(X4,X2) ),
    inference(equality_resolution,[],[f406]) ).

fof(f527,plain,
    ! [X0,X4] :
      ( ~ aElementOf0(sbrdtbr0(X4),szNzAzT0)
      | ~ aSet0(X0)
      | ~ aSubsetOf0(X4,X0)
      | aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4))) ),
    inference(equality_resolution,[],[f526]) ).

fof(f529,plain,
    ! [X0,X1,X4] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0)
      | ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
      | sbrdtbr0(X4) = X1 ),
    inference(equality_resolution,[],[f404]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i] :
      ( aSet0(X0)
      | ~ aSet0(X1)
      | ~ aSubsetOf0(X0,X1) ),
    inference(cnf_transformation,[],[f312]) ).

tcf(c_63,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( aSubsetOf0(X2,X1)
      | ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSet0(X0)
      | ~ aSubsetOf0(X2,X0)
      | ~ aSubsetOf0(X0,X1) ),
    inference(cnf_transformation,[],[f318]) ).

tcf(c_94,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f350]) ).

tcf(c_153,plain,
    ! [X0: $i,X1: $i] :
      ( aElementOf0(X0,slbdtsldtrb0(X1,sbrdtbr0(X0)))
      | ~ aSet0(X1)
      | ~ aSubsetOf0(X0,X1)
      | ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ),
    inference(cnf_transformation,[],[f527]) ).

tcf(c_155,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( sbrdtbr0(X0) = X2 )
      | ~ aSet0(X1)
      | ~ aElementOf0(X2,szNzAzT0)
      | ~ aElementOf0(X0,slbdtsldtrb0(X1,X2)) ),
    inference(cnf_transformation,[],[f529]) ).

tcf(c_194,plain,
    aElementOf0(xK,szNzAzT0),
    inference(cnf_transformation,[],[f449]) ).

tcf(c_195,plain,
    aSubsetOf0(xS,szNzAzT0),
    inference(cnf_transformation,[],[f451]) ).

tcf(c_198,plain,
    slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
    inference(cnf_transformation,[],[f453]) ).

tcf(c_242,plain,
    aSet0(xO),
    inference(cnf_transformation,[],[f498]) ).

tcf(c_247,plain,
    aSubsetOf0(xO,xS),
    inference(cnf_transformation,[],[f502]) ).

tcf(c_248,plain,
    aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
    inference(cnf_transformation,[],[f503]) ).

tcf(c_249,plain,
    aSubsetOf0(xQ,xO),
    inference(cnf_transformation,[],[f505]) ).

tcf(c_251,plain,
    aSubsetOf0(xQ,szNzAzT0),
    inference(cnf_transformation,[],[f506]) ).

tcf(c_252,negated_conjecture,
    ~ aElementOf0(xQ,szDzozmdt0(xc)),
    inference(cnf_transformation,[],[f507]) ).

tcf(c_2099,plain,
    ( aSet0(xS)
    | ~ aSet0(szNzAzT0) ),
    inference(superposition,[status(thm)],[c_195,c_58]) ).

tcf(c_2104,plain,
    ( aSet0(xQ)
    | ~ aSet0(szNzAzT0) ),
    inference(superposition,[status(thm)],[c_251,c_58]) ).

tcf(c_2372,plain,
    ( ( sbrdtbr0(xQ) = xK )
    | ~ aSet0(xO)
    | ~ aElementOf0(xK,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_248,c_155]) ).

tcf(c_2586,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( aSubsetOf0(X2,X1)
      | ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSubsetOf0(X0,X1)
      | ~ aSubsetOf0(X2,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_63,c_58,c_63]) ).

tcf(c_2587,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( aSubsetOf0(X2,X1)
      | ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSubsetOf0(X2,X0)
      | ~ aSubsetOf0(X0,X1) ),
    inference(renaming,[status(thm)],[c_2586]) ).

tcf(c_2604,plain,
    ! [X0: $i] :
      ( aSubsetOf0(X0,xS)
      | ~ aSet0(xS)
      | ~ aSet0(X0)
      | ~ aSubsetOf0(X0,xO) ),
    inference(superposition,[status(thm)],[c_247,c_2587]) ).

tcf(c_3913,plain,
    sbrdtbr0(xQ) = xK,
    inference(global_subsumption_just,[status(thm)],[c_2372,c_242,c_194,c_2372]) ).

tcf(c_3917,plain,
    ! [X0: $i] :
      ( aElementOf0(xQ,slbdtsldtrb0(X0,xK))
      | ~ aSet0(X0)
      | ~ aSubsetOf0(xQ,X0)
      | ~ aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),
    inference(superposition,[status(thm)],[c_3913,c_153]) ).

tcf(c_4753,plain,
    ! [X0: $i] :
      ( aSubsetOf0(X0,xS)
      | ~ aSubsetOf0(X0,xO)
      | ~ aSet0(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_2604,c_94,c_2099,c_2604]) ).

tcf(c_4754,plain,
    ! [X0: $i] :
      ( aSubsetOf0(X0,xS)
      | ~ aSet0(X0)
      | ~ aSubsetOf0(X0,xO) ),
    inference(renaming,[status(thm)],[c_4753]) ).

tcf(c_4763,plain,
    ( aSubsetOf0(xQ,xS)
    | ~ aSet0(xQ) ),
    inference(superposition,[status(thm)],[c_249,c_4754]) ).

tcf(c_12415,plain,
    ! [X0: $i] :
      ( aElementOf0(xQ,slbdtsldtrb0(X0,xK))
      | ~ aSet0(X0)
      | ~ aElementOf0(xK,szNzAzT0)
      | ~ aSubsetOf0(xQ,X0) ),
    inference(light_normalisation,[status(thm)],[c_3917,c_3913]) ).

tcf(c_12420,plain,
    ! [X0: $i] :
      ( aElementOf0(xQ,slbdtsldtrb0(X0,xK))
      | ~ aSet0(X0)
      | ~ aSubsetOf0(xQ,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12415,c_194]) ).

tcf(c_12427,plain,
    ( aElementOf0(xQ,szDzozmdt0(xc))
    | ~ aSet0(xS)
    | ~ aSubsetOf0(xQ,xS) ),
    inference(superposition,[status(thm)],[c_198,c_12420]) ).

tcf(c_12434,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_12427,c_4763,c_2099,c_2104,c_94,c_252]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM607+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36  % Computer : n014.cluster.edu
% 0.08/0.36  % Model    : x86_64 x86_64
% 0.08/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36  % Memory   : 8046.5625MB
% 0.08/0.36  % OS       : Linux 6.8.0-71-generic
% 0.08/0.37  % CPULimit : 300
% 0.08/0.37  % WCLimit  : 300
% 0.08/0.37  % DateTime : Thu Sep 24 04:52:49 UTC 2026
% 0.08/0.37  % CPUTime  : 
% 0.08/0.37  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.41  Running first-order theorem proving
% 0.08/0.41  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.42  
% 0.08/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42  
% 0.08/0.42  % Detected problem language: tptp
% 0.08/0.43  % Proving...
% 7.51/1.68  % SZS status Started for theBenchmark.p
% 7.51/1.68  % SZS status Theorem for theBenchmark.p
% 7.51/1.68  
% 7.51/1.68  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.51/1.68  
% 7.51/1.68  % ------  iProver source info
% 7.51/1.68  
% 7.51/1.68  % git: date: 2026-07-19 20:42:38 +0200
% 7.51/1.68  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.51/1.68  % git: non_committed_changes: false
% 7.51/1.68  
% 7.51/1.68  % ------ Parsing...
% 7.51/1.68  % ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.51/1.68  % ------ Proving...
% 7.51/1.68  % ------ Problem Properties 
% 7.51/1.68  
% 7.51/1.68  % 
% 7.51/1.68  % clauses                               204
% 7.51/1.68  % conjectures                           1
% 7.51/1.68  % EPR                                   51
% 7.51/1.68  % Horn                                  165
% 7.51/1.68  % unary                                 41
% 7.51/1.68  % binary                                35
% 7.51/1.68  % lits                                  675
% 7.51/1.68  % lits eq                               101
% 7.51/1.68  % fd_pure                               0
% 7.51/1.68  % fd_pseudo                             0
% 7.51/1.68  % fd_cond                               10
% 7.51/1.68  % fd_pseudo_cond                        25
% 7.51/1.68  % AC symbols                            0
% 7.51/1.68  
% 7.51/1.68  % ------ Input Options Time Limit: Unbounded
% 7.51/1.68  
% 7.51/1.68  
% 7.51/1.68  % ------ 
% 7.51/1.68  % Current options:
% 7.51/1.68  % ------ 
% 7.51/1.68  
% 7.51/1.68  
% 7.51/1.68  % 
% 7.51/1.68  
% 7.51/1.68  % ------ Proving...
% 7.51/1.68  % 
% 7.51/1.68  
% 7.51/1.68  % ------ Proving...
% 7.51/1.68  % 
% 7.51/1.68  
% 7.51/1.68  % ------ Proving...
% 7.51/1.68  % 
% 7.51/1.68  
% 7.51/1.68  % SZS status Theorem for theBenchmark.p
% 7.51/1.68  
% 7.51/1.68  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.51/1.68  
% 7.51/1.68  
%------------------------------------------------------------------------------