TSTP Solution File: NUM566+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM566+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 : Mon Jun 24 12:53:44 EDT 2024

% Result   : Theorem 6.96s 1.68s
% Output   : CNFRefutation 6.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  130 (  29 unt;   0 def)
%            Number of atoms       :  499 (  60 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  659 ( 290   ~; 278   |;  69   &)
%                                         (   8 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :  195 (   0 sgn 100   !;  14   ?)

% 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(f12,axiom,
    ! [X0] :
      ( aSet0(X0)
     => aSubsetOf0(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).

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

fof(f69,axiom,
    ! [X0] :
      ( aFunction0(X0)
     => ! [X1] :
          ( aElementOf0(X1,szDzozmdt0(X0))
         => aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).

fof(f73,axiom,
    ( isFinite0(xT)
    & aSet0(xT) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).

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(f78,axiom,
    sz00 = xK,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).

fof(f79,axiom,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3476) ).

fof(f80,axiom,
    ! [X0] :
      ( aElementOf0(X0,slbdtsldtrb0(xS,sz00))
     => sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3507) ).

fof(f81,conjecture,
    ? [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( aElementOf0(X2,slbdtsldtrb0(X1,xK))
             => sdtlpdtrp0(xc,X2) = X0 )
          & isCountable0(X1)
          & aSubsetOf0(X1,xS) )
      & aElementOf0(X0,xT) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f82,negated_conjecture,
    ~ ? [X0] :
        ( ? [X1] :
            ( ! [X2] :
                ( aElementOf0(X2,slbdtsldtrb0(X1,xK))
               => sdtlpdtrp0(xc,X2) = X0 )
            & isCountable0(X1)
            & aSubsetOf0(X1,xS) )
        & aElementOf0(X0,xT) ),
    inference(negated_conjecture,[],[f81]) ).

fof(f96,plain,
    ! [X0] :
      ( ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X0)
                | ~ aElementOf0(X2,X1) )
            & aSet0(X1) ) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f99,plain,
    ! [X0] :
      ( aSubsetOf0(X0,X0)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( aSubsetOf0(X0,X2)
      | ~ aSubsetOf0(X1,X2)
      | ~ aSubsetOf0(X0,X1)
      | ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( aSubsetOf0(X0,X2)
      | ~ aSubsetOf0(X1,X2)
      | ~ aSubsetOf0(X0,X1)
      | ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f102]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( slbdtsldtrb0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( sbrdtbr0(X3) = X1
                  & aSubsetOf0(X3,X0) ) )
            & aSet0(X2) ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( slbdtsldtrb0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( sbrdtbr0(X3) = X1
                  & aSubsetOf0(X3,X0) ) )
            & aSet0(X2) ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f164]) ).

fof(f183,plain,
    ! [X0] :
      ( ! [X1] :
          ( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
          | ~ aElementOf0(X1,szDzozmdt0(X0)) )
      | ~ aFunction0(X0) ),
    inference(ennf_transformation,[],[f69]) ).

fof(f191,plain,
    ! [X0] :
      ( sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0)
      | ~ aElementOf0(X0,slbdtsldtrb0(xS,sz00)) ),
    inference(ennf_transformation,[],[f80]) ).

fof(f192,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( sdtlpdtrp0(xc,X2) != X0
              & aElementOf0(X2,slbdtsldtrb0(X1,xK)) )
          | ~ isCountable0(X1)
          | ~ aSubsetOf0(X1,xS) )
      | ~ aElementOf0(X0,xT) ),
    inference(ennf_transformation,[],[f82]) ).

fof(f204,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f96]) ).

fof(f205,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(flattening,[],[f204]) ).

fof(f206,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(rectify,[],[f205]) ).

fof(f207,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK5(X0,X1),X0)
        & aElementOf0(sK5(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f208,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ( ~ aElementOf0(sK5(X0,X1),X0)
              & aElementOf0(sK5(X0,X1),X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f206,f207]) ).

fof(f248,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) = X2
            | ? [X3] :
                ( ( sbrdtbr0(X3) != X1
                  | ~ aSubsetOf0(X3,X0)
                  | ~ aElementOf0(X3,X2) )
                & ( ( sbrdtbr0(X3) = X1
                    & aSubsetOf0(X3,X0) )
                  | aElementOf0(X3,X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X3] :
                  ( ( aElementOf0(X3,X2)
                    | sbrdtbr0(X3) != X1
                    | ~ aSubsetOf0(X3,X0) )
                  & ( ( sbrdtbr0(X3) = X1
                      & aSubsetOf0(X3,X0) )
                    | ~ aElementOf0(X3,X2) ) )
              & aSet0(X2) )
            | slbdtsldtrb0(X0,X1) != X2 ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f165]) ).

fof(f249,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) = X2
            | ? [X3] :
                ( ( sbrdtbr0(X3) != X1
                  | ~ aSubsetOf0(X3,X0)
                  | ~ aElementOf0(X3,X2) )
                & ( ( sbrdtbr0(X3) = X1
                    & aSubsetOf0(X3,X0) )
                  | aElementOf0(X3,X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X3] :
                  ( ( aElementOf0(X3,X2)
                    | sbrdtbr0(X3) != X1
                    | ~ aSubsetOf0(X3,X0) )
                  & ( ( sbrdtbr0(X3) = X1
                      & aSubsetOf0(X3,X0) )
                    | ~ aElementOf0(X3,X2) ) )
              & aSet0(X2) )
            | slbdtsldtrb0(X0,X1) != X2 ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f248]) ).

fof(f250,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) = X2
            | ? [X3] :
                ( ( sbrdtbr0(X3) != X1
                  | ~ aSubsetOf0(X3,X0)
                  | ~ aElementOf0(X3,X2) )
                & ( ( sbrdtbr0(X3) = X1
                    & aSubsetOf0(X3,X0) )
                  | aElementOf0(X3,X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X4] :
                  ( ( aElementOf0(X4,X2)
                    | sbrdtbr0(X4) != X1
                    | ~ aSubsetOf0(X4,X0) )
                  & ( ( sbrdtbr0(X4) = X1
                      & aSubsetOf0(X4,X0) )
                    | ~ aElementOf0(X4,X2) ) )
              & aSet0(X2) )
            | slbdtsldtrb0(X0,X1) != X2 ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(rectify,[],[f249]) ).

fof(f251,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( sbrdtbr0(X3) != X1
            | ~ aSubsetOf0(X3,X0)
            | ~ aElementOf0(X3,X2) )
          & ( ( sbrdtbr0(X3) = X1
              & aSubsetOf0(X3,X0) )
            | aElementOf0(X3,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) )
          | aElementOf0(sK14(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) = 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) )
                | aElementOf0(sK14(X0,X1,X2),X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X4] :
                  ( ( aElementOf0(X4,X2)
                    | sbrdtbr0(X4) != X1
                    | ~ aSubsetOf0(X4,X0) )
                  & ( ( sbrdtbr0(X4) = X1
                      & aSubsetOf0(X4,X0) )
                    | ~ aElementOf0(X4,X2) ) )
              & aSet0(X2) )
            | slbdtsldtrb0(X0,X1) != X2 ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f250,f251]) ).

fof(f277,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtlpdtrp0(xc,X2) != X0
          & aElementOf0(X2,slbdtsldtrb0(X1,xK)) )
     => ( sdtlpdtrp0(xc,sK25(X0,X1)) != X0
        & aElementOf0(sK25(X0,X1),slbdtsldtrb0(X1,xK)) ) ),
    introduced(choice_axiom,[]) ).

fof(f278,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sdtlpdtrp0(xc,sK25(X0,X1)) != X0
            & aElementOf0(sK25(X0,X1),slbdtsldtrb0(X1,xK)) )
          | ~ isCountable0(X1)
          | ~ aSubsetOf0(X1,xS) )
      | ~ aElementOf0(X0,xT) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f192,f277]) ).

fof(f286,plain,
    ! [X0,X1] :
      ( aSet0(X1)
      | ~ aSubsetOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f208]) ).

fof(f287,plain,
    ! [X3,X0,X1] :
      ( aElementOf0(X3,X0)
      | ~ aElementOf0(X3,X1)
      | ~ aSubsetOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f208]) ).

fof(f291,plain,
    ! [X0] :
      ( aSubsetOf0(X0,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f293,plain,
    ! [X2,X0,X1] :
      ( aSubsetOf0(X0,X2)
      | ~ aSubsetOf0(X1,X2)
      | ~ aSubsetOf0(X0,X1)
      | ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f324,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f23]) ).

fof(f380,plain,
    ! [X2,X0,X1,X4] :
      ( aSubsetOf0(X4,X0)
      | ~ aElementOf0(X4,X2)
      | slbdtsldtrb0(X0,X1) != X2
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f252]) ).

fof(f410,plain,
    ! [X0,X1] :
      ( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
      | ~ aElementOf0(X1,szDzozmdt0(X0))
      | ~ aFunction0(X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f422,plain,
    aSet0(xT),
    inference(cnf_transformation,[],[f73]) ).

fof(f424,plain,
    aElementOf0(xK,szNzAzT0),
    inference(cnf_transformation,[],[f74]) ).

fof(f425,plain,
    aSubsetOf0(xS,szNzAzT0),
    inference(cnf_transformation,[],[f75]) ).

fof(f426,plain,
    isCountable0(xS),
    inference(cnf_transformation,[],[f75]) ).

fof(f427,plain,
    aFunction0(xc),
    inference(cnf_transformation,[],[f76]) ).

fof(f428,plain,
    szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
    inference(cnf_transformation,[],[f76]) ).

fof(f429,plain,
    aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
    inference(cnf_transformation,[],[f76]) ).

fof(f434,plain,
    sz00 = xK,
    inference(cnf_transformation,[],[f78]) ).

fof(f435,plain,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    inference(cnf_transformation,[],[f79]) ).

fof(f436,plain,
    ! [X0] :
      ( sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0)
      | ~ aElementOf0(X0,slbdtsldtrb0(xS,sz00)) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f437,plain,
    ! [X0,X1] :
      ( aElementOf0(sK25(X0,X1),slbdtsldtrb0(X1,xK))
      | ~ isCountable0(X1)
      | ~ aSubsetOf0(X1,xS)
      | ~ aElementOf0(X0,xT) ),
    inference(cnf_transformation,[],[f278]) ).

fof(f438,plain,
    ! [X0,X1] :
      ( sdtlpdtrp0(xc,sK25(X0,X1)) != X0
      | ~ isCountable0(X1)
      | ~ aSubsetOf0(X1,xS)
      | ~ aElementOf0(X0,xT) ),
    inference(cnf_transformation,[],[f278]) ).

fof(f450,plain,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
    inference(definition_unfolding,[],[f435,f434]) ).

fof(f451,plain,
    ! [X0] :
      ( sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0)
      | ~ aElementOf0(X0,slbdtsldtrb0(xS,xK)) ),
    inference(definition_unfolding,[],[f436,f434]) ).

fof(f472,plain,
    ! [X0,X1,X4] :
      ( aSubsetOf0(X4,X0)
      | ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(equality_resolution,[],[f380]) ).

cnf(c_58,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ aSubsetOf0(X1,X2)
    | ~ aSet0(X2)
    | aElementOf0(X0,X2) ),
    inference(cnf_transformation,[],[f287]) ).

cnf(c_59,plain,
    ( ~ aSubsetOf0(X0,X1)
    | ~ aSet0(X1)
    | aSet0(X0) ),
    inference(cnf_transformation,[],[f286]) ).

cnf(c_61,plain,
    ( ~ aSet0(X0)
    | aSubsetOf0(X0,X0) ),
    inference(cnf_transformation,[],[f291]) ).

cnf(c_63,plain,
    ( ~ aSubsetOf0(X0,X1)
    | ~ aSubsetOf0(X2,X0)
    | ~ aSet0(X0)
    | ~ aSet0(X1)
    | ~ aSet0(X2)
    | aSubsetOf0(X2,X1) ),
    inference(cnf_transformation,[],[f293]) ).

cnf(c_95,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f324]) ).

cnf(c_154,plain,
    ( ~ aElementOf0(X0,slbdtsldtrb0(X1,X2))
    | ~ aElementOf0(X2,szNzAzT0)
    | ~ aSet0(X1)
    | aSubsetOf0(X0,X1) ),
    inference(cnf_transformation,[],[f472]) ).

cnf(c_180,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(X1))
    | ~ aFunction0(X1)
    | aElementOf0(sdtlpdtrp0(X1,X0),sdtlcdtrc0(X1,szDzozmdt0(X1))) ),
    inference(cnf_transformation,[],[f410]) ).

cnf(c_193,plain,
    aSet0(xT),
    inference(cnf_transformation,[],[f422]) ).

cnf(c_194,plain,
    aElementOf0(xK,szNzAzT0),
    inference(cnf_transformation,[],[f424]) ).

cnf(c_195,plain,
    isCountable0(xS),
    inference(cnf_transformation,[],[f426]) ).

cnf(c_196,plain,
    aSubsetOf0(xS,szNzAzT0),
    inference(cnf_transformation,[],[f425]) ).

cnf(c_197,plain,
    aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
    inference(cnf_transformation,[],[f429]) ).

cnf(c_198,plain,
    slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
    inference(cnf_transformation,[],[f428]) ).

cnf(c_199,plain,
    aFunction0(xc),
    inference(cnf_transformation,[],[f427]) ).

cnf(c_204,plain,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
    inference(cnf_transformation,[],[f450]) ).

cnf(c_205,plain,
    ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xK))
    | sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ),
    inference(cnf_transformation,[],[f451]) ).

cnf(c_206,negated_conjecture,
    ( sdtlpdtrp0(xc,sK25(X0,X1)) != X0
    | ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(X1,xS)
    | ~ isCountable0(X1) ),
    inference(cnf_transformation,[],[f438]) ).

cnf(c_207,negated_conjecture,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(X1,xS)
    | ~ isCountable0(X1)
    | aElementOf0(sK25(X0,X1),slbdtsldtrb0(X1,xK)) ),
    inference(cnf_transformation,[],[f437]) ).

cnf(c_334,plain,
    ( ~ aSubsetOf0(X2,X0)
    | ~ aSubsetOf0(X0,X1)
    | ~ aSet0(X1)
    | ~ aSet0(X2)
    | aSubsetOf0(X2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_63,c_59,c_63]) ).

cnf(c_335,plain,
    ( ~ aSubsetOf0(X0,X1)
    | ~ aSubsetOf0(X2,X0)
    | ~ aSet0(X1)
    | ~ aSet0(X2)
    | aSubsetOf0(X2,X1) ),
    inference(renaming,[status(thm)],[c_334]) ).

cnf(c_1518,plain,
    aElementOf0(slcrc0,szDzozmdt0(xc)),
    inference(demodulation,[status(thm)],[c_204,c_198]) ).

cnf(c_1795,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ),
    inference(light_normalisation,[status(thm)],[c_205,c_198]) ).

cnf(c_14341,negated_conjecture,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(X1,xS)
    | ~ isCountable0(X1)
    | aElementOf0(sK25(X0,X1),slbdtsldtrb0(X1,xK)) ),
    inference(demodulation,[status(thm)],[c_207]) ).

cnf(c_14342,negated_conjecture,
    ( sdtlpdtrp0(xc,sK25(X0,X1)) != X0
    | ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(X1,xS)
    | ~ isCountable0(X1) ),
    inference(demodulation,[status(thm)],[c_206]) ).

cnf(c_16842,plain,
    ( ~ aSet0(szNzAzT0)
    | aSet0(xS) ),
    inference(superposition,[status(thm)],[c_196,c_59]) ).

cnf(c_16920,plain,
    ( ~ aSubsetOf0(sdtlcdtrc0(X0,szDzozmdt0(X0)),X1)
    | ~ aElementOf0(X2,szDzozmdt0(X0))
    | ~ aSet0(X1)
    | ~ aFunction0(X0)
    | aElementOf0(sdtlpdtrp0(X0,X2),X1) ),
    inference(superposition,[status(thm)],[c_180,c_58]) ).

cnf(c_16939,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | ~ aElementOf0(xK,szNzAzT0)
    | ~ aSet0(xS)
    | aSubsetOf0(X0,xS) ),
    inference(superposition,[status(thm)],[c_198,c_154]) ).

cnf(c_16952,plain,
    ( ~ aSubsetOf0(X0,xS)
    | ~ aSet0(X0)
    | ~ aSet0(szNzAzT0)
    | aSubsetOf0(X0,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_196,c_335]) ).

cnf(c_16963,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | ~ isCountable0(xS)
    | aElementOf0(sK25(X0,xS),szDzozmdt0(xc)) ),
    inference(superposition,[status(thm)],[c_198,c_14341]) ).

cnf(c_16965,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(X1,xS)
    | ~ aElementOf0(xK,szNzAzT0)
    | ~ aSet0(X1)
    | ~ isCountable0(X1)
    | aSubsetOf0(sK25(X0,X1),X1) ),
    inference(superposition,[status(thm)],[c_14341,c_154]) ).

cnf(c_17111,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | ~ aSet0(xT)
    | ~ aFunction0(xc)
    | aElementOf0(sdtlpdtrp0(xc,X0),xT) ),
    inference(superposition,[status(thm)],[c_197,c_16920]) ).

cnf(c_17124,plain,
    ( ~ aSet0(szNzAzT0)
    | aSet0(xS) ),
    inference(superposition,[status(thm)],[c_196,c_59]) ).

cnf(c_17128,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | aSubsetOf0(X0,xS) ),
    inference(global_subsumption_just,[status(thm)],[c_16939,c_95,c_194,c_16842,c_16939]) ).

cnf(c_17136,plain,
    ( ~ aSet0(X0)
    | ~ aSubsetOf0(X0,xS)
    | aSubsetOf0(X0,szNzAzT0) ),
    inference(global_subsumption_just,[status(thm)],[c_16952,c_95,c_16952]) ).

cnf(c_17137,plain,
    ( ~ aSubsetOf0(X0,xS)
    | ~ aSet0(X0)
    | aSubsetOf0(X0,szNzAzT0) ),
    inference(renaming,[status(thm)],[c_17136]) ).

cnf(c_17162,plain,
    ( ~ aSubsetOf0(xS,xS)
    | ~ aElementOf0(X0,xT)
    | aElementOf0(sK25(X0,xS),szDzozmdt0(xc)) ),
    inference(global_subsumption_just,[status(thm)],[c_16963,c_195,c_16963]) ).

cnf(c_17163,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | aElementOf0(sK25(X0,xS),szDzozmdt0(xc)) ),
    inference(renaming,[status(thm)],[c_17162]) ).

cnf(c_17173,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | aSubsetOf0(sK25(X0,xS),xS) ),
    inference(superposition,[status(thm)],[c_17163,c_17128]) ).

cnf(c_17174,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | sdtlpdtrp0(xc,sK25(X0,xS)) = sdtlpdtrp0(xc,slcrc0) ),
    inference(superposition,[status(thm)],[c_17163,c_1795]) ).

cnf(c_17198,plain,
    ( ~ aSubsetOf0(X1,xS)
    | ~ aElementOf0(X0,xT)
    | ~ aSet0(X1)
    | ~ isCountable0(X1)
    | aSubsetOf0(sK25(X0,X1),X1) ),
    inference(global_subsumption_just,[status(thm)],[c_16965,c_194,c_16965]) ).

cnf(c_17199,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(X1,xS)
    | ~ aSet0(X1)
    | ~ isCountable0(X1)
    | aSubsetOf0(sK25(X0,X1),X1) ),
    inference(renaming,[status(thm)],[c_17198]) ).

cnf(c_17214,plain,
    ( ~ aSet0(sK25(X0,xS))
    | ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | ~ aSet0(xS)
    | ~ isCountable0(xS)
    | aSubsetOf0(sK25(X0,xS),szNzAzT0) ),
    inference(superposition,[status(thm)],[c_17199,c_17137]) ).

cnf(c_17327,plain,
    ( ~ aSubsetOf0(sdtlcdtrc0(X0,szDzozmdt0(X0)),X1)
    | ~ aElementOf0(X2,szDzozmdt0(X0))
    | ~ aSet0(X1)
    | ~ aFunction0(X0)
    | aElementOf0(sdtlpdtrp0(X0,X2),X1) ),
    inference(superposition,[status(thm)],[c_180,c_58]) ).

cnf(c_17404,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | aElementOf0(sdtlpdtrp0(xc,X0),xT) ),
    inference(global_subsumption_just,[status(thm)],[c_17111,c_199,c_193,c_17111]) ).

cnf(c_17426,plain,
    ( ~ aSubsetOf0(X0,xS)
    | ~ aSet0(X0)
    | ~ aSet0(szNzAzT0)
    | aSubsetOf0(X0,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_196,c_335]) ).

cnf(c_17454,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(X1,xS)
    | ~ aElementOf0(xK,szNzAzT0)
    | ~ aSet0(X1)
    | ~ isCountable0(X1)
    | aSubsetOf0(sK25(X0,X1),X1) ),
    inference(superposition,[status(thm)],[c_14341,c_154]) ).

cnf(c_17463,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | ~ aSet0(xS)
    | aSet0(sK25(X0,xS)) ),
    inference(superposition,[status(thm)],[c_17173,c_59]) ).

cnf(c_17484,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | ~ aSubsetOf0(xS,xS)
    | sdtlpdtrp0(xc,sK25(sdtlpdtrp0(xc,X0),xS)) = sdtlpdtrp0(xc,slcrc0) ),
    inference(superposition,[status(thm)],[c_17404,c_17174]) ).

cnf(c_17595,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | aSubsetOf0(sK25(X0,xS),szNzAzT0) ),
    inference(global_subsumption_just,[status(thm)],[c_17214,c_195,c_95,c_16842,c_17214,c_17463]) ).

cnf(c_17609,plain,
    aSet0(xS),
    inference(global_subsumption_just,[status(thm)],[c_17124,c_95,c_16842]) ).

cnf(c_17853,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | ~ aSet0(xT)
    | ~ aFunction0(xc)
    | aElementOf0(sdtlpdtrp0(xc,X0),xT) ),
    inference(superposition,[status(thm)],[c_197,c_17327]) ).

cnf(c_17920,plain,
    ( ~ aSet0(X0)
    | ~ aSubsetOf0(X0,xS)
    | aSubsetOf0(X0,szNzAzT0) ),
    inference(global_subsumption_just,[status(thm)],[c_17426,c_95,c_16952]) ).

cnf(c_17921,plain,
    ( ~ aSubsetOf0(X0,xS)
    | ~ aSet0(X0)
    | aSubsetOf0(X0,szNzAzT0) ),
    inference(renaming,[status(thm)],[c_17920]) ).

cnf(c_17935,plain,
    ( ~ aSubsetOf0(xS,xS)
    | sdtlpdtrp0(xc,sK25(sdtlpdtrp0(xc,slcrc0),xS)) = sdtlpdtrp0(xc,slcrc0) ),
    inference(superposition,[status(thm)],[c_1518,c_17484]) ).

cnf(c_18133,plain,
    ( ~ aSubsetOf0(X1,xS)
    | ~ aElementOf0(X0,xT)
    | ~ aSet0(X1)
    | ~ isCountable0(X1)
    | aSubsetOf0(sK25(X0,X1),X1) ),
    inference(global_subsumption_just,[status(thm)],[c_17454,c_17199]) ).

cnf(c_18134,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(X1,xS)
    | ~ aSet0(X1)
    | ~ isCountable0(X1)
    | aSubsetOf0(sK25(X0,X1),X1) ),
    inference(renaming,[status(thm)],[c_18133]) ).

cnf(c_18148,plain,
    ( ~ aSet0(sK25(X0,xS))
    | ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | ~ aSet0(xS)
    | ~ isCountable0(xS)
    | aSubsetOf0(sK25(X0,xS),szNzAzT0) ),
    inference(superposition,[status(thm)],[c_18134,c_17921]) ).

cnf(c_18452,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | aElementOf0(sdtlpdtrp0(xc,X0),xT) ),
    inference(global_subsumption_just,[status(thm)],[c_17853,c_199,c_193,c_17111]) ).

cnf(c_18458,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | ~ aSubsetOf0(xT,X1)
    | ~ aSet0(X1)
    | aElementOf0(sdtlpdtrp0(xc,X0),X1) ),
    inference(superposition,[status(thm)],[c_18452,c_58]) ).

cnf(c_18743,plain,
    ( ~ aSet0(xS)
    | sdtlpdtrp0(xc,sK25(sdtlpdtrp0(xc,slcrc0),xS)) = sdtlpdtrp0(xc,slcrc0) ),
    inference(superposition,[status(thm)],[c_61,c_17935]) ).

cnf(c_18841,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | aSubsetOf0(sK25(X0,xS),szNzAzT0) ),
    inference(global_subsumption_just,[status(thm)],[c_18148,c_17595]) ).

cnf(c_19144,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | ~ aSubsetOf0(X1,X2)
    | ~ aSubsetOf0(xT,X1)
    | ~ aSet0(X1)
    | ~ aSet0(X2)
    | aElementOf0(sdtlpdtrp0(xc,X0),X2) ),
    inference(superposition,[status(thm)],[c_18458,c_58]) ).

cnf(c_20021,plain,
    sdtlpdtrp0(xc,sK25(sdtlpdtrp0(xc,slcrc0),xS)) = sdtlpdtrp0(xc,slcrc0),
    inference(global_subsumption_just,[status(thm)],[c_18743,c_95,c_16842,c_18743]) ).

cnf(c_20037,plain,
    ( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
    | ~ aSubsetOf0(xS,xS)
    | ~ isCountable0(xS) ),
    inference(superposition,[status(thm)],[c_20021,c_14342]) ).

cnf(c_20575,plain,
    ( ~ aElementOf0(X0,szDzozmdt0(xc))
    | ~ aSubsetOf0(X1,X2)
    | ~ aSubsetOf0(xT,X1)
    | ~ aSet0(X2)
    | aElementOf0(sdtlpdtrp0(xc,X0),X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19144,c_59]) ).

cnf(c_20598,plain,
    ( ~ aSubsetOf0(xT,sK25(X0,xS))
    | ~ aElementOf0(X1,szDzozmdt0(xc))
    | ~ aElementOf0(X0,xT)
    | ~ aSubsetOf0(xS,xS)
    | ~ aSet0(szNzAzT0)
    | aElementOf0(sdtlpdtrp0(xc,X1),szNzAzT0) ),
    inference(superposition,[status(thm)],[c_18841,c_20575]) ).

cnf(c_22804,plain,
    ( ~ aSubsetOf0(xS,xS)
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(global_subsumption_just,[status(thm)],[c_20037,c_195,c_20037]) ).

cnf(c_22805,plain,
    ( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
    | ~ aSubsetOf0(xS,xS) ),
    inference(renaming,[status(thm)],[c_22804]) ).

cnf(c_22810,plain,
    ( ~ aElementOf0(slcrc0,szDzozmdt0(xc))
    | ~ aSubsetOf0(xS,xS) ),
    inference(superposition,[status(thm)],[c_17404,c_22805]) ).

cnf(c_22817,plain,
    ~ aSubsetOf0(xS,xS),
    inference(global_subsumption_just,[status(thm)],[c_20598,c_1518,c_22810]) ).

cnf(c_22819,plain,
    ~ aSet0(xS),
    inference(superposition,[status(thm)],[c_61,c_22817]) ).

cnf(c_22820,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_17609,c_22819]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUM566+1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Jun 22 23:20:54 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.22/0.50  Running first-order theorem proving
% 0.22/0.50  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.96/1.68  % SZS status Started for theBenchmark.p
% 6.96/1.68  % SZS status Theorem for theBenchmark.p
% 6.96/1.68  
% 6.96/1.68  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 6.96/1.68  
% 6.96/1.68  ------  iProver source info
% 6.96/1.68  
% 6.96/1.68  git: date: 2024-06-12 09:56:46 +0000
% 6.96/1.68  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 6.96/1.68  git: non_committed_changes: false
% 6.96/1.68  
% 6.96/1.68  ------ Parsing...
% 6.96/1.68  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 6.96/1.68  
% 6.96/1.68  ------ Preprocessing... sup_sim: 2  sf_s  rm: 1 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 
% 6.96/1.68  
% 6.96/1.68  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 6.96/1.68  
% 6.96/1.68  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 6.96/1.68  ------ Proving...
% 6.96/1.68  ------ Problem Properties 
% 6.96/1.68  
% 6.96/1.68  
% 6.96/1.68  clauses                                 151
% 6.96/1.68  conjectures                             2
% 6.96/1.68  EPR                                     34
% 6.96/1.68  Horn                                    112
% 6.96/1.68  unary                                   17
% 6.96/1.68  binary                                  18
% 6.96/1.68  lits                                    543
% 6.96/1.68  lits eq                                 79
% 6.96/1.68  fd_pure                                 0
% 6.96/1.68  fd_pseudo                               0
% 6.96/1.68  fd_cond                                 10
% 6.96/1.68  fd_pseudo_cond                          24
% 6.96/1.68  AC symbols                              0
% 6.96/1.68  
% 6.96/1.68  ------ Input Options Time Limit: Unbounded
% 6.96/1.68  
% 6.96/1.68  
% 6.96/1.68  ------ 
% 6.96/1.68  Current options:
% 6.96/1.68  ------ 
% 6.96/1.68  
% 6.96/1.68  
% 6.96/1.68  
% 6.96/1.68  
% 6.96/1.68  ------ Proving...
% 6.96/1.68  
% 6.96/1.68  
% 6.96/1.68  % SZS status Theorem for theBenchmark.p
% 6.96/1.68  
% 6.96/1.68  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.96/1.68  
% 7.42/1.69  
%------------------------------------------------------------------------------