TSTP Solution File: NUN089+2 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUN089+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 16:34:58 EDT 2022

% Result   : Theorem 0.12s 0.37s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   29 (  10 unt;   0 def)
%            Number of atoms       :   72 (  17 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   89 (  46   ~;  25   |;  14   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   43 (   3 sgn  24   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_7a,axiom,
    ! [X7,Y10] :
      ( ! [Y20] :
          ( ~ r1(Y20)
          | Y20 != Y10 )
      | ~ r2(X7,Y10) ) ).

fof(zerouneqtwo,conjecture,
    ! [Y1] :
      ( ! [Y2] :
          ( ! [Y3] :
              ( ~ r1(Y3)
              | ~ r2(Y3,Y2) )
          | ~ r2(Y2,Y1) )
      | ! [Y4] :
          ( Y4 != Y1
          | ~ r1(Y4) ) ) ).

fof(subgoal_0,plain,
    ! [Y1] :
      ( ~ ! [Y2] :
            ( ! [Y3] :
                ( ~ r1(Y3)
                | ~ r2(Y3,Y2) )
            | ~ r2(Y2,Y1) )
     => ! [Y4] :
          ( ~ ( Y4 != Y1 )
         => ~ r1(Y4) ) ),
    inference(strip,[],[zerouneqtwo]) ).

fof(negate_0_0,plain,
    ~ ! [Y1] :
        ( ~ ! [Y2] :
              ( ! [Y3] :
                  ( ~ r1(Y3)
                  | ~ r2(Y3,Y2) )
              | ~ r2(Y2,Y1) )
       => ! [Y4] :
            ( ~ ( Y4 != Y1 )
           => ~ r1(Y4) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [Y1] :
      ( ? [Y2] :
          ( r2(Y2,Y1)
          & ? [Y3] :
              ( r1(Y3)
              & r2(Y3,Y2) ) )
      & ? [Y4] :
          ( Y4 = Y1
          & r1(Y4) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ? [Y2] :
        ( r2(Y2,skolemFOFtoCNF_Y1_1)
        & ? [Y3] :
            ( r1(Y3)
            & r2(Y3,Y2) ) )
    & ? [Y4] :
        ( Y4 = skolemFOFtoCNF_Y1_1
        & r1(Y4) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ? [Y2] :
      ( r2(Y2,skolemFOFtoCNF_Y1_1)
      & ? [Y3] :
          ( r1(Y3)
          & r2(Y3,Y2) ) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1)
    & ? [Y3] :
        ( r1(Y3)
        & r2(Y3,skolemFOFtoCNF_Y2_1) ) ),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X7,Y10] :
      ( ~ r2(X7,Y10)
      | ! [Y20] :
          ( Y20 != Y10
          | ~ r1(Y20) ) ),
    inference(canonicalize,[],[axiom_7a]) ).

fof(normalize_0_6,plain,
    ! [X7,Y10] :
      ( ~ r2(X7,Y10)
      | ! [Y20] :
          ( Y20 != Y10
          | ~ r1(Y20) ) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X7,Y10,Y20] :
      ( Y20 != Y10
      | ~ r1(Y20)
      | ~ r2(X7,Y10) ),
    inference(clausify,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ? [Y4] :
      ( Y4 = skolemFOFtoCNF_Y1_1
      & r1(Y4) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_9,plain,
    ( skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y1_1
    & r1(skolemFOFtoCNF_Y4_1) ),
    inference(skolemize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    r1(skolemFOFtoCNF_Y4_1),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y1_1,
    inference(conjunct,[],[normalize_0_9]) ).

cnf(refute_0_0,plain,
    r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_1,plain,
    ( Y20 != Y10
    | ~ r1(Y20)
    | ~ r2(X7,Y10) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_2,plain,
    ( Y10 != Y10
    | ~ r1(Y10)
    | ~ r2(X7,Y10) ),
    inference(subst,[],[refute_0_1:[bind(Y20,$fot(Y10))]]) ).

cnf(refute_0_3,plain,
    Y10 = Y10,
    introduced(tautology,[refl,[$fot(Y10)]]) ).

cnf(refute_0_4,plain,
    ( ~ r1(Y10)
    | ~ r2(X7,Y10) ),
    inference(resolve,[$cnf( $equal(Y10,Y10) )],[refute_0_3,refute_0_2]) ).

cnf(refute_0_5,plain,
    ( ~ r1(skolemFOFtoCNF_Y1_1)
    | ~ r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) ),
    inference(subst,[],[refute_0_4:[bind(X7,$fot(skolemFOFtoCNF_Y2_1)),bind(Y10,$fot(skolemFOFtoCNF_Y1_1))]]) ).

cnf(refute_0_6,plain,
    ~ r1(skolemFOFtoCNF_Y1_1),
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) )],[refute_0_0,refute_0_5]) ).

cnf(refute_0_7,plain,
    r1(skolemFOFtoCNF_Y4_1),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_8,plain,
    skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y1_1,
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_9,plain,
    ( skolemFOFtoCNF_Y4_1 != skolemFOFtoCNF_Y1_1
    | ~ r1(skolemFOFtoCNF_Y4_1)
    | r1(skolemFOFtoCNF_Y1_1) ),
    introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y4_1) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).

cnf(refute_0_10,plain,
    ( ~ r1(skolemFOFtoCNF_Y4_1)
    | r1(skolemFOFtoCNF_Y1_1) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    r1(skolemFOFtoCNF_Y1_1),
    inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1) )],[refute_0_7,refute_0_10]) ).

cnf(refute_0_12,plain,
    $false,
    inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y1_1) )],[refute_0_11,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUN089+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun  2 04:09:15 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37  
% 0.12/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37  
%------------------------------------------------------------------------------