TSTP Solution File: NUM620+3 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM620+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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  : 600s
% DateTime : Mon Jul 18 12:28:18 EDT 2022

% Result   : Theorem 9.66s 9.83s
% Output   : CNFRefutation 9.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   35 (  12 unt;   0 def)
%            Number of atoms       :   89 (  21 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   83 (  29   ~;  25   |;  21   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn  17   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__4660,hypothesis,
    ( aFunction0(xe)
    & szDzozmdt0(xe) = szNzAzT0
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
          & sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ).

fof(m__5389,hypothesis,
    ( aElementOf0(xm,szNzAzT0)
    & xx = sdtlpdtrp0(xe,xm) ) ).

fof(m__,conjecture,
    ( ( ! [W0] :
          ( aElementOf0(W0,sdtlpdtrp0(xN,xm))
         => aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
      & aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
   => aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ).

fof(subgoal_0,plain,
    ( ( ! [W0] :
          ( aElementOf0(W0,sdtlpdtrp0(xN,xm))
         => aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
      & aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
   => aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ( ( ! [W0] :
            ( aElementOf0(W0,sdtlpdtrp0(xN,xm))
           => aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
        & aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
     => aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( xx = sdtlpdtrp0(xe,xm)
    & aElementOf0(xm,szNzAzT0) ),
    inference(canonicalize,[],[m__5389]) ).

fof(normalize_0_1,plain,
    aElementOf0(xm,szNzAzT0),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ( szDzozmdt0(xe) = szNzAzT0
    & aFunction0(xe)
    & ! [W0] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
          & aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
    inference(canonicalize,[],[m__4660]) ).

fof(normalize_0_3,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
        & aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
        & ! [W1] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0))
        & aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
        & ! [W1] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [W0,W1] :
      ( ( ~ aElementOf0(W0,szNzAzT0)
        | sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
      & ( ~ aElementOf0(W0,szNzAzT0)
        | aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) )
      & ( ~ aElementOf0(W0,szNzAzT0)
        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
        | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    xx = sdtlpdtrp0(xe,xm),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_8,plain,
    ( ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    & aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
        | aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_9,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
      | aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
      | aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(specialize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(conjunct,[],[normalize_0_8]) ).

cnf(refute_0_0,plain,
    aElementOf0(xm,szNzAzT0),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( ~ aElementOf0(W0,szNzAzT0)
    | aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0)) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    ( ~ aElementOf0(xm,szNzAzT0)
    | aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm)) ),
    inference(subst,[],[refute_0_1:[bind(W0,$fot(xm))]]) ).

cnf(refute_0_3,plain,
    aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm)),
    inference(resolve,[$cnf( aElementOf0(xm,szNzAzT0) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    xx = sdtlpdtrp0(xe,xm),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_5,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_6,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_7,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( xx != sdtlpdtrp0(xe,xm)
    | sdtlpdtrp0(xe,xm) = xx ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(xx)),bind(Y,$fot(sdtlpdtrp0(xe,xm)))]]) ).

cnf(refute_0_9,plain,
    sdtlpdtrp0(xe,xm) = xx,
    inference(resolve,[$cnf( $equal(xx,sdtlpdtrp0(xe,xm)) )],[refute_0_4,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( sdtlpdtrp0(xe,xm) != xx
    | ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm))
    | aElementOf0(xx,sdtlpdtrp0(xN,xm)) ),
    introduced(tautology,[equality,[$cnf( aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm)) ),[0],$fot(xx)]]) ).

cnf(refute_0_11,plain,
    ( ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm))
    | aElementOf0(xx,sdtlpdtrp0(xN,xm)) ),
    inference(resolve,[$cnf( $equal(sdtlpdtrp0(xe,xm),xx) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    aElementOf0(xx,sdtlpdtrp0(xN,xm)),
    inference(resolve,[$cnf( aElementOf0(sdtlpdtrp0(xe,xm),sdtlpdtrp0(xN,xm)) )],[refute_0_3,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xm))
    | aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_14,plain,
    ( ~ aElementOf0(xx,sdtlpdtrp0(xN,xm))
    | aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(subst,[],[refute_0_13:[bind(W0,$fot(xx))]]) ).

cnf(refute_0_15,plain,
    aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(resolve,[$cnf( aElementOf0(xx,sdtlpdtrp0(xN,xm)) )],[refute_0_12,refute_0_14]) ).

cnf(refute_0_16,plain,
    ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )],[refute_0_15,refute_0_16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : NUM620+3 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n007.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  : 600
% 0.13/0.35  % DateTime : Thu Jul  7 12:47:14 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.13/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.66/9.83  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.66/9.83  
% 9.66/9.83  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.66/9.83  
%------------------------------------------------------------------------------