TSTP Solution File: NUN069+2 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUN069+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 16:34:55 EDT 2022

% Result   : Theorem 0.14s 0.37s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   34 (   9 unt;   0 def)
%            Number of atoms       :   90 (  28 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   88 (  32   ~;  19   |;  37   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   70 (   5 sgn  30   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
    ? [Y24] :
    ! [X19] :
      ( ( ~ r1(X19)
        & X19 != Y24 )
      | ( r1(X19)
        & X19 = Y24 ) ) ).

fof(axiom_2a,axiom,
    ! [X2,X9] :
    ? [Y2] :
      ( ? [Y3] :
          ( ? [Y14] :
              ( r2(X9,Y14)
              & r4(X2,Y14,Y3) )
          & Y3 = Y2 )
      & ? [Y6] :
          ( r3(Y6,X2,Y2)
          & r4(X2,X9,Y6) ) ) ).

fof(oneeqone,conjecture,
    ? [Y1] :
      ( Y1 = Y1
      & ? [Y2] :
          ( r1(Y2)
          & r2(Y2,Y1) ) ) ).

fof(subgoal_0,plain,
    ? [Y1] :
      ( Y1 = Y1
      & ? [Y2] :
          ( r1(Y2)
          & r2(Y2,Y1) ) ),
    inference(strip,[],[oneeqone]) ).

fof(negate_0_0,plain,
    ~ ? [Y1] :
        ( Y1 = Y1
        & ? [Y2] :
            ( r1(Y2)
            & r2(Y2,Y1) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [Y24] :
    ! [X19] :
      ( ( X19 != Y24
        & ~ r1(X19) )
      | ( X19 = Y24
        & r1(X19) ) ),
    inference(canonicalize,[],[axiom_1]) ).

fof(normalize_0_1,plain,
    ! [X19] :
      ( ( X19 != skolemFOFtoCNF_Y24
        & ~ r1(X19) )
      | ( X19 = skolemFOFtoCNF_Y24
        & r1(X19) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X19] :
      ( ( X19 != skolemFOFtoCNF_Y24
        & ~ r1(X19) )
      | ( X19 = skolemFOFtoCNF_Y24
        & r1(X19) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X19] :
      ( ( X19 != skolemFOFtoCNF_Y24
        | r1(X19) )
      & ( ~ r1(X19)
        | X19 = skolemFOFtoCNF_Y24 ) ),
    inference(clausify,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X19] :
      ( X19 != skolemFOFtoCNF_Y24
      | r1(X19) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X2,X9] :
    ? [Y2] :
      ( ? [Y3] :
          ( Y3 = Y2
          & ? [Y14] :
              ( r2(X9,Y14)
              & r4(X2,Y14,Y3) ) )
      & ? [Y6] :
          ( r3(Y6,X2,Y2)
          & r4(X2,X9,Y6) ) ),
    inference(canonicalize,[],[axiom_2a]) ).

fof(normalize_0_6,plain,
    ! [X2,X9] :
    ? [Y2] :
      ( ? [Y3] :
          ( Y3 = Y2
          & ? [Y14] :
              ( r2(X9,Y14)
              & r4(X2,Y14,Y3) ) )
      & ? [Y6] :
          ( r3(Y6,X2,Y2)
          & r4(X2,X9,Y6) ) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X2,X9] :
      ( ? [Y3] :
          ( Y3 = skolemFOFtoCNF_Y2(X2,X9)
          & ? [Y14] :
              ( r2(X9,Y14)
              & r4(X2,Y14,Y3) ) )
      & ? [Y6] :
          ( r3(Y6,X2,skolemFOFtoCNF_Y2(X2,X9))
          & r4(X2,X9,Y6) ) ),
    inference(skolemize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X2,X9] :
    ? [Y3] :
      ( Y3 = skolemFOFtoCNF_Y2(X2,X9)
      & ? [Y14] :
          ( r2(X9,Y14)
          & r4(X2,Y14,Y3) ) ),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X2,X9] :
      ( skolemFOFtoCNF_Y3(X2,X9) = skolemFOFtoCNF_Y2(X2,X9)
      & ? [Y14] :
          ( r2(X9,Y14)
          & r4(X2,Y14,skolemFOFtoCNF_Y3(X2,X9)) ) ),
    inference(skolemize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X2,X9] :
    ? [Y14] :
      ( r2(X9,Y14)
      & r4(X2,Y14,skolemFOFtoCNF_Y3(X2,X9)) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X2,X9] :
      ( r2(X9,skolemFOFtoCNF_Y14(X2,X9))
      & r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9)) ),
    inference(skolemize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X2,X9] : r2(X9,skolemFOFtoCNF_Y14(X2,X9)),
    inference(conjunct,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [Y1] :
      ( Y1 != Y1
      | ! [Y2] :
          ( ~ r1(Y2)
          | ~ r2(Y2,Y1) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_14,plain,
    ! [Y1] :
      ( Y1 != Y1
      | ! [Y2] :
          ( ~ r1(Y2)
          | ~ r2(Y2,Y1) ) ),
    inference(specialize,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [Y1,Y2] :
      ( Y1 != Y1
      | ~ r1(Y2)
      | ~ r2(Y2,Y1) ),
    inference(clausify,[],[normalize_0_14]) ).

cnf(refute_0_0,plain,
    ( X19 != skolemFOFtoCNF_Y24
    | r1(X19) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_1,plain,
    ( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y24
    | r1(skolemFOFtoCNF_Y24) ),
    inference(subst,[],[refute_0_0:[bind(X19,$fot(skolemFOFtoCNF_Y24))]]) ).

cnf(refute_0_2,plain,
    skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y24,
    introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y24)]]) ).

cnf(refute_0_3,plain,
    r1(skolemFOFtoCNF_Y24),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_2,refute_0_1]) ).

cnf(refute_0_4,plain,
    r2(X9,skolemFOFtoCNF_Y14(X2,X9)),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_5,plain,
    r2(X_34,skolemFOFtoCNF_Y14(X2,X_34)),
    inference(subst,[],[refute_0_4:[bind(X9,$fot(X_34))]]) ).

cnf(refute_0_6,plain,
    ( Y1 != Y1
    | ~ r1(Y2)
    | ~ r2(Y2,Y1) ),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_7,plain,
    Y1 = Y1,
    introduced(tautology,[refl,[$fot(Y1)]]) ).

cnf(refute_0_8,plain,
    ( ~ r1(Y2)
    | ~ r2(Y2,Y1) ),
    inference(resolve,[$cnf( $equal(Y1,Y1) )],[refute_0_7,refute_0_6]) ).

cnf(refute_0_9,plain,
    ( ~ r1(X_34)
    | ~ r2(X_34,skolemFOFtoCNF_Y14(X2,X_34)) ),
    inference(subst,[],[refute_0_8:[bind(Y1,$fot(skolemFOFtoCNF_Y14(X2,X_34))),bind(Y2,$fot(X_34))]]) ).

cnf(refute_0_10,plain,
    ~ r1(X_34),
    inference(resolve,[$cnf( r2(X_34,skolemFOFtoCNF_Y14(X2,X_34)) )],[refute_0_5,refute_0_9]) ).

cnf(refute_0_11,plain,
    ~ r1(skolemFOFtoCNF_Y24),
    inference(subst,[],[refute_0_10:[bind(X_34,$fot(skolemFOFtoCNF_Y24))]]) ).

cnf(refute_0_12,plain,
    $false,
    inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y24) )],[refute_0_3,refute_0_11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUN069+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Thu Jun  2 05:02:31 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37  
% 0.14/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37  
%------------------------------------------------------------------------------