TSTP Solution File: NUN073+2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 1.24s 1.45s
% Output   : CNFRefutation 1.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   99 (  31 unt;   0 def)
%            Number of atoms       :  240 (  92 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  266 ( 125   ~;  95   |;  42   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-1 aty)
%            Number of variables   :  116 (   3 sgn  64   !;  22   ?)

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

fof(axiom_2,axiom,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( ~ r2(X11,X12)
        & X12 != Y21 )
      | ( r2(X11,X12)
        & X12 = Y21 ) ) ).

fof(axiom_3a,axiom,
    ! [X3,X10] :
      ( ! [Y12] :
          ( ! [Y13] :
              ( ~ r2(X3,Y13)
              | Y13 != Y12 )
          | ~ r2(X10,Y12) )
      | X3 = X10 ) ).

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

fof(oneuneqtwo,conjecture,
    ! [Y1] :
      ( ! [Y2] :
          ( ! [Y4] :
              ( ~ r1(Y4)
              | ~ r2(Y4,Y2) )
          | Y2 != Y1 )
      | ! [Y3] :
          ( ! [Y5] :
              ( ~ r1(Y5)
              | ~ r2(Y5,Y3) )
          | ~ r2(Y3,Y1) ) ) ).

fof(subgoal_0,plain,
    ! [Y1] :
      ( ~ ! [Y2] :
            ( ! [Y4] :
                ( ~ r1(Y4)
                | ~ r2(Y4,Y2) )
            | Y2 != Y1 )
     => ! [Y3] :
          ( ~ ! [Y5] :
                ( ~ r1(Y5)
                | ~ r2(Y5,Y3) )
         => ~ r2(Y3,Y1) ) ),
    inference(strip,[],[oneuneqtwo]) ).

fof(negate_0_0,plain,
    ~ ! [Y1] :
        ( ~ ! [Y2] :
              ( ! [Y4] :
                  ( ~ r1(Y4)
                  | ~ r2(Y4,Y2) )
              | Y2 != Y1 )
       => ! [Y3] :
            ( ~ ! [Y5] :
                  ( ~ r1(Y5)
                  | ~ r2(Y5,Y3) )
           => ~ r2(Y3,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,
    ? [Y1] :
      ( ? [Y2] :
          ( Y2 = Y1
          & ? [Y4] :
              ( r1(Y4)
              & r2(Y4,Y2) ) )
      & ? [Y3] :
          ( r2(Y3,Y1)
          & ? [Y5] :
              ( r1(Y5)
              & r2(Y5,Y3) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_6,plain,
    ( ? [Y2] :
        ( Y2 = skolemFOFtoCNF_Y1_1
        & ? [Y4] :
            ( r1(Y4)
            & r2(Y4,Y2) ) )
    & ? [Y3] :
        ( r2(Y3,skolemFOFtoCNF_Y1_1)
        & ? [Y5] :
            ( r1(Y5)
            & r2(Y5,Y3) ) ) ),
    inference(skolemize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ? [Y2] :
      ( Y2 = skolemFOFtoCNF_Y1_1
      & ? [Y4] :
          ( r1(Y4)
          & r2(Y4,Y2) ) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ( skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y1_1
    & ? [Y4] :
        ( r1(Y4)
        & r2(Y4,skolemFOFtoCNF_Y2_1) ) ),
    inference(skolemize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ? [Y4] :
      ( r1(Y4)
      & r2(Y4,skolemFOFtoCNF_Y2_1) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ( r1(skolemFOFtoCNF_Y4_1)
    & r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1) ),
    inference(skolemize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y1_1,
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_13,plain,
    r1(skolemFOFtoCNF_Y4_1),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_14,plain,
    ! [X19] :
      ( ~ r1(X19)
      | X19 = skolemFOFtoCNF_Y24 ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_15,plain,
    ? [Y3] :
      ( r2(Y3,skolemFOFtoCNF_Y1_1)
      & ? [Y5] :
          ( r1(Y5)
          & r2(Y5,Y3) ) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_16,plain,
    ( r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1)
    & ? [Y5] :
        ( r1(Y5)
        & r2(Y5,skolemFOFtoCNF_Y3_1) ) ),
    inference(skolemize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1),
    inference(conjunct,[],[normalize_0_16]) ).

fof(normalize_0_18,plain,
    ? [Y5] :
      ( r1(Y5)
      & r2(Y5,skolemFOFtoCNF_Y3_1) ),
    inference(conjunct,[],[normalize_0_16]) ).

fof(normalize_0_19,plain,
    ( r1(skolemFOFtoCNF_Y5_1)
    & r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1) ),
    inference(skolemize,[],[normalize_0_18]) ).

fof(normalize_0_20,plain,
    r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1),
    inference(conjunct,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
    r1(skolemFOFtoCNF_Y5_1),
    inference(conjunct,[],[normalize_0_19]) ).

fof(normalize_0_22,plain,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( X12 != Y21
        & ~ r2(X11,X12) )
      | ( X12 = Y21
        & r2(X11,X12) ) ),
    inference(canonicalize,[],[axiom_2]) ).

fof(normalize_0_23,plain,
    ! [X11] :
    ? [Y21] :
    ! [X12] :
      ( ( X12 != Y21
        & ~ r2(X11,X12) )
      | ( X12 = Y21
        & r2(X11,X12) ) ),
    inference(specialize,[],[normalize_0_22]) ).

fof(normalize_0_24,plain,
    ! [X11,X12] :
      ( ( X12 != skolemFOFtoCNF_Y21(X11)
        & ~ r2(X11,X12) )
      | ( X12 = skolemFOFtoCNF_Y21(X11)
        & r2(X11,X12) ) ),
    inference(skolemize,[],[normalize_0_23]) ).

fof(normalize_0_25,plain,
    ! [X11,X12] :
      ( ( X12 != skolemFOFtoCNF_Y21(X11)
        & ~ r2(X11,X12) )
      | ( X12 = skolemFOFtoCNF_Y21(X11)
        & r2(X11,X12) ) ),
    inference(specialize,[],[normalize_0_24]) ).

fof(normalize_0_26,plain,
    ! [X11,X12] :
      ( ( X12 != skolemFOFtoCNF_Y21(X11)
        | r2(X11,X12) )
      & ( ~ r2(X11,X12)
        | X12 = skolemFOFtoCNF_Y21(X11) ) ),
    inference(clausify,[],[normalize_0_25]) ).

fof(normalize_0_27,plain,
    ! [X11,X12] :
      ( ~ r2(X11,X12)
      | X12 = skolemFOFtoCNF_Y21(X11) ),
    inference(conjunct,[],[normalize_0_26]) ).

fof(normalize_0_28,plain,
    ! [X10,X3] :
      ( X3 = X10
      | ! [Y12] :
          ( ~ r2(X10,Y12)
          | ! [Y13] :
              ( Y13 != Y12
              | ~ r2(X3,Y13) ) ) ),
    inference(canonicalize,[],[axiom_3a]) ).

fof(normalize_0_29,plain,
    ! [X10,X3] :
      ( X3 = X10
      | ! [Y12] :
          ( ~ r2(X10,Y12)
          | ! [Y13] :
              ( Y13 != Y12
              | ~ r2(X3,Y13) ) ) ),
    inference(specialize,[],[normalize_0_28]) ).

fof(normalize_0_30,plain,
    ! [X10,X3,Y12,Y13] :
      ( Y13 != Y12
      | ~ r2(X10,Y12)
      | ~ r2(X3,Y13)
      | X3 = X10 ),
    inference(clausify,[],[normalize_0_29]) ).

fof(normalize_0_31,plain,
    ! [X7,Y10] :
      ( ~ r2(X7,Y10)
      | ! [Y20] :
          ( Y20 != Y10
          | ~ r1(Y20) ) ),
    inference(canonicalize,[],[axiom_7a]) ).

fof(normalize_0_32,plain,
    ! [X7,Y10] :
      ( ~ r2(X7,Y10)
      | ! [Y20] :
          ( Y20 != Y10
          | ~ r1(Y20) ) ),
    inference(specialize,[],[normalize_0_31]) ).

fof(normalize_0_33,plain,
    ! [X7,Y10,Y20] :
      ( Y20 != Y10
      | ~ r1(Y20)
      | ~ r2(X7,Y10) ),
    inference(clausify,[],[normalize_0_32]) ).

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(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_5,plain,
    skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y1_1,
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_6,plain,
    ( skolemFOFtoCNF_Y2_1 != skolemFOFtoCNF_Y1_1
    | ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1)
    | r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) ),
    introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1) ),[1],$fot(skolemFOFtoCNF_Y1_1)]]) ).

cnf(refute_0_7,plain,
    ( ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1)
    | r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1),
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1) )],[refute_0_4,refute_0_7]) ).

cnf(refute_0_9,plain,
    r1(skolemFOFtoCNF_Y4_1),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_10,plain,
    ( ~ r1(X19)
    | X19 = skolemFOFtoCNF_Y24 ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_11,plain,
    ( ~ r1(skolemFOFtoCNF_Y4_1)
    | skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y24 ),
    inference(subst,[],[refute_0_10:[bind(X19,$fot(skolemFOFtoCNF_Y4_1))]]) ).

cnf(refute_0_12,plain,
    skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y24,
    inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1) )],[refute_0_9,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( skolemFOFtoCNF_Y4_1 != skolemFOFtoCNF_Y24
    | ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1)
    | r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) ),
    introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).

cnf(refute_0_14,plain,
    ( ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1)
    | r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y24) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1),
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) )],[refute_0_8,refute_0_14]) ).

cnf(refute_0_16,plain,
    r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_17,plain,
    r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1),
    inference(canonicalize,[],[normalize_0_20]) ).

cnf(refute_0_18,plain,
    r1(skolemFOFtoCNF_Y5_1),
    inference(canonicalize,[],[normalize_0_21]) ).

cnf(refute_0_19,plain,
    ( ~ r1(skolemFOFtoCNF_Y5_1)
    | skolemFOFtoCNF_Y5_1 = skolemFOFtoCNF_Y24 ),
    inference(subst,[],[refute_0_10:[bind(X19,$fot(skolemFOFtoCNF_Y5_1))]]) ).

cnf(refute_0_20,plain,
    skolemFOFtoCNF_Y5_1 = skolemFOFtoCNF_Y24,
    inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y5_1) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( skolemFOFtoCNF_Y5_1 != skolemFOFtoCNF_Y24
    | ~ r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1)
    | r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1) ),
    introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).

cnf(refute_0_22,plain,
    ( ~ r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1)
    | r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y24) )],[refute_0_20,refute_0_21]) ).

cnf(refute_0_23,plain,
    r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1),
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1) )],[refute_0_17,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( ~ r2(X11,X12)
    | X12 = skolemFOFtoCNF_Y21(X11) ),
    inference(canonicalize,[],[normalize_0_27]) ).

cnf(refute_0_25,plain,
    ( ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1)
    | skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
    inference(subst,[],[refute_0_24:[bind(X11,$fot(skolemFOFtoCNF_Y24)),bind(X12,$fot(skolemFOFtoCNF_Y3_1))]]) ).

cnf(refute_0_26,plain,
    skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1) )],[refute_0_23,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1)
    | skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
    inference(subst,[],[refute_0_24:[bind(X11,$fot(skolemFOFtoCNF_Y24)),bind(X12,$fot(skolemFOFtoCNF_Y1_1))]]) ).

cnf(refute_0_28,plain,
    skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_15,refute_0_27]) ).

cnf(refute_0_29,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_30,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_31,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
    | skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y1_1 ),
    inference(subst,[],[refute_0_31:[bind(X,$fot(skolemFOFtoCNF_Y1_1)),bind(Y,$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)))]]) ).

cnf(refute_0_33,plain,
    skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y1_1,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_28,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y1_1
    | skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
    | skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1 ),
    introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),[1],$fot(skolemFOFtoCNF_Y1_1)]]) ).

cnf(refute_0_35,plain,
    ( skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
    | skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1 ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y1_1) )],[refute_0_33,refute_0_34]) ).

cnf(refute_0_36,plain,
    skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_26,refute_0_35]) ).

cnf(refute_0_37,plain,
    ( skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y1_1
    | ~ r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1)
    | r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) ),
    introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).

cnf(refute_0_38,plain,
    ( ~ r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1)
    | r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) )],[refute_0_36,refute_0_37]) ).

cnf(refute_0_39,plain,
    r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1),
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) )],[refute_0_16,refute_0_38]) ).

cnf(refute_0_40,plain,
    ( Y13 != Y12
    | ~ r2(X10,Y12)
    | ~ r2(X3,Y13)
    | X3 = X10 ),
    inference(canonicalize,[],[normalize_0_30]) ).

cnf(refute_0_41,plain,
    ( Y12 != Y12
    | ~ r2(X10,Y12)
    | ~ r2(X3,Y12)
    | X3 = X10 ),
    inference(subst,[],[refute_0_40:[bind(Y13,$fot(Y12))]]) ).

cnf(refute_0_42,plain,
    Y12 = Y12,
    introduced(tautology,[refl,[$fot(Y12)]]) ).

cnf(refute_0_43,plain,
    ( ~ r2(X10,Y12)
    | ~ r2(X3,Y12)
    | X3 = X10 ),
    inference(resolve,[$cnf( $equal(Y12,Y12) )],[refute_0_42,refute_0_41]) ).

cnf(refute_0_44,plain,
    ( ~ r2(X_663,skolemFOFtoCNF_Y1_1)
    | ~ r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1)
    | X_663 = skolemFOFtoCNF_Y1_1 ),
    inference(subst,[],[refute_0_43:[bind(X10,$fot(skolemFOFtoCNF_Y1_1)),bind(X3,$fot(X_663)),bind(Y12,$fot(skolemFOFtoCNF_Y1_1))]]) ).

cnf(refute_0_45,plain,
    ( ~ r2(X_663,skolemFOFtoCNF_Y1_1)
    | X_663 = skolemFOFtoCNF_Y1_1 ),
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) )],[refute_0_39,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1)
    | skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y1_1 ),
    inference(subst,[],[refute_0_45:[bind(X_663,$fot(skolemFOFtoCNF_Y24))]]) ).

cnf(refute_0_47,plain,
    skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y1_1,
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_15,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y1_1
    | ~ r1(skolemFOFtoCNF_Y24)
    | r1(skolemFOFtoCNF_Y1_1) ),
    introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y24) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).

cnf(refute_0_49,plain,
    ( ~ r1(skolemFOFtoCNF_Y24)
    | r1(skolemFOFtoCNF_Y1_1) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_47,refute_0_48]) ).

cnf(refute_0_50,plain,
    r1(skolemFOFtoCNF_Y1_1),
    inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y24) )],[refute_0_3,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( Y20 != Y10
    | ~ r1(Y20)
    | ~ r2(X7,Y10) ),
    inference(canonicalize,[],[normalize_0_33]) ).

cnf(refute_0_52,plain,
    ( Y10 != Y10
    | ~ r1(Y10)
    | ~ r2(X7,Y10) ),
    inference(subst,[],[refute_0_51:[bind(Y20,$fot(Y10))]]) ).

cnf(refute_0_53,plain,
    Y10 = Y10,
    introduced(tautology,[refl,[$fot(Y10)]]) ).

cnf(refute_0_54,plain,
    ( ~ r1(Y10)
    | ~ r2(X7,Y10) ),
    inference(resolve,[$cnf( $equal(Y10,Y10) )],[refute_0_53,refute_0_52]) ).

cnf(refute_0_55,plain,
    ( ~ r1(skolemFOFtoCNF_Y1_1)
    | ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) ),
    inference(subst,[],[refute_0_54:[bind(X7,$fot(skolemFOFtoCNF_Y24)),bind(Y10,$fot(skolemFOFtoCNF_Y1_1))]]) ).

cnf(refute_0_56,plain,
    ~ r1(skolemFOFtoCNF_Y1_1),
    inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_15,refute_0_55]) ).

cnf(refute_0_57,plain,
    $false,
    inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y1_1) )],[refute_0_50,refute_0_56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Thu Jun  2 06:46:49 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.24/1.45  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.24/1.45  
% 1.24/1.45  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.31/1.46  
%------------------------------------------------------------------------------