TSTP Solution File: SYN077+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN077+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n022.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 : Thu Jul 21 08:59:22 EDT 2022

% Result   : Theorem 1.99s 2.14s
% Output   : CNFRefutation 1.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   73 (   9 unt;   0 def)
%            Number of atoms       :  203 (  17 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  234 ( 104   ~;  99   |;  17   &)
%                                         (  11 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :  100 (   0 sgn  44   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(pel54_1,axiom,
    ! [Y] :
    ? [Z] :
    ! [X] :
      ( big_f(X,Z)
    <=> X = Y ) ).

fof(pel54,conjecture,
    ~ ? [W] :
      ! [X] :
        ( big_f(X,W)
      <=> ! [U] :
            ( big_f(X,U)
           => ? [Y] :
                ( big_f(Y,U)
                & ~ ? [Z] :
                      ( big_f(Z,U)
                      & big_f(Z,Y) ) ) ) ) ).

fof(subgoal_0,plain,
    ! [W] :
      ~ ! [X] :
          ( big_f(X,W)
        <=> ! [U] :
              ( big_f(X,U)
             => ? [Y] :
                  ( big_f(Y,U)
                  & ~ ? [Z] :
                        ( big_f(Z,U)
                        & big_f(Z,Y) ) ) ) ),
    inference(strip,[],[pel54]) ).

fof(negate_0_0,plain,
    ~ ! [W] :
        ~ ! [X] :
            ( big_f(X,W)
          <=> ! [U] :
                ( big_f(X,U)
               => ? [Y] :
                    ( big_f(Y,U)
                    & ~ ? [Z] :
                          ( big_f(Z,U)
                          & big_f(Z,Y) ) ) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [Y] :
    ? [Z] :
    ! [X] :
      ( X != Y
    <=> ~ big_f(X,Z) ),
    inference(canonicalize,[],[pel54_1]) ).

fof(normalize_0_1,plain,
    ! [Y] :
    ? [Z] :
    ! [X] :
      ( X != Y
    <=> ~ big_f(X,Z) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [Y,X] :
      ( X != Y
    <=> ~ big_f(X,skolemFOFtoCNF_Z(Y)) ),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X,Y] :
      ( X != Y
    <=> ~ big_f(X,skolemFOFtoCNF_Z(Y)) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ( X != Y
        | big_f(X,skolemFOFtoCNF_Z(Y)) )
      & ( ~ big_f(X,skolemFOFtoCNF_Z(Y))
        | X = Y ) ),
    inference(clausify,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X,Y] :
      ( X != Y
      | big_f(X,skolemFOFtoCNF_Z(Y)) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ? [W] :
    ! [X] :
      ( ~ big_f(X,W)
    <=> ? [U] :
          ( big_f(X,U)
          & ! [Y] :
              ( ~ big_f(Y,U)
              | ? [Z] :
                  ( big_f(Z,U)
                  & big_f(Z,Y) ) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_7,plain,
    ! [X] :
      ( ~ big_f(X,skolemFOFtoCNF_W)
    <=> ? [U] :
          ( big_f(X,U)
          & ! [Y] :
              ( ~ big_f(Y,U)
              | ? [Z] :
                  ( big_f(Z,U)
                  & big_f(Z,Y) ) ) ) ),
    inference(skolemize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X] :
      ( ~ big_f(X,skolemFOFtoCNF_W)
    <=> ? [U] :
          ( big_f(X,U)
          & ! [Y] :
              ( ~ big_f(Y,U)
              | ? [Z] :
                  ( big_f(Z,U)
                  & big_f(Z,Y) ) ) ) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [U,X,Y,Z] :
      ( ( big_f(X,skolemFOFtoCNF_U(X))
        | big_f(X,skolemFOFtoCNF_W) )
      & ( ~ big_f(X,U)
        | ~ big_f(X,skolemFOFtoCNF_W)
        | big_f(skolemFOFtoCNF_Y(U),U) )
      & ( ~ big_f(Y,skolemFOFtoCNF_U(X))
        | big_f(X,skolemFOFtoCNF_W)
        | big_f(skolemFOFtoCNF_Z_1(X,Y),Y) )
      & ( ~ big_f(Y,skolemFOFtoCNF_U(X))
        | big_f(X,skolemFOFtoCNF_W)
        | big_f(skolemFOFtoCNF_Z_1(X,Y),skolemFOFtoCNF_U(X)) )
      & ( ~ big_f(X,U)
        | ~ big_f(X,skolemFOFtoCNF_W)
        | ~ big_f(Z,U)
        | ~ big_f(Z,skolemFOFtoCNF_Y(U)) ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [U,X,Z] :
      ( ~ big_f(X,U)
      | ~ big_f(X,skolemFOFtoCNF_W)
      | ~ big_f(Z,U)
      | ~ big_f(Z,skolemFOFtoCNF_Y(U)) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [U,X] :
      ( ~ big_f(X,U)
      | ~ big_f(X,skolemFOFtoCNF_W)
      | big_f(skolemFOFtoCNF_Y(U),U) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_12,plain,
    ! [X] :
      ( big_f(X,skolemFOFtoCNF_U(X))
      | big_f(X,skolemFOFtoCNF_W) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_13,plain,
    ! [X,Y] :
      ( ~ big_f(Y,skolemFOFtoCNF_U(X))
      | big_f(X,skolemFOFtoCNF_W)
      | big_f(skolemFOFtoCNF_Z_1(X,Y),Y) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_14,plain,
    ! [X,Y] :
      ( ~ big_f(Y,skolemFOFtoCNF_U(X))
      | big_f(X,skolemFOFtoCNF_W)
      | big_f(skolemFOFtoCNF_Z_1(X,Y),skolemFOFtoCNF_U(X)) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_15,plain,
    ! [X,Y] :
      ( ~ big_f(X,skolemFOFtoCNF_Z(Y))
      | X = Y ),
    inference(conjunct,[],[normalize_0_4]) ).

cnf(refute_0_0,plain,
    ( X != Y
    | big_f(X,skolemFOFtoCNF_Z(Y)) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_1,plain,
    ( Y != Y
    | big_f(Y,skolemFOFtoCNF_Z(Y)) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(Y))]]) ).

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

cnf(refute_0_3,plain,
    big_f(Y,skolemFOFtoCNF_Z(Y)),
    inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_2,refute_0_1]) ).

cnf(refute_0_4,plain,
    big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),
    inference(subst,[],[refute_0_3:[bind(Y,$fot(skolemFOFtoCNF_W))]]) ).

cnf(refute_0_5,plain,
    ( ~ big_f(X,U)
    | ~ big_f(X,skolemFOFtoCNF_W)
    | ~ big_f(Z,U)
    | ~ big_f(Z,skolemFOFtoCNF_Y(U)) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_6,plain,
    ( ~ big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)))
    | ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
    | ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W)
    | ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) ),
    inference(subst,[],[refute_0_5:[bind(U,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))),bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))))]]) ).

cnf(refute_0_7,plain,
    big_f(X_6,skolemFOFtoCNF_Z(X_6)),
    inference(subst,[],[refute_0_3:[bind(Y,$fot(X_6))]]) ).

cnf(refute_0_8,plain,
    ( ~ big_f(X,U)
    | ~ big_f(X,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Y(U),U) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_9,plain,
    ( ~ big_f(X_6,skolemFOFtoCNF_W)
    | ~ big_f(X_6,skolemFOFtoCNF_Z(X_6))
    | big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(X_6)),skolemFOFtoCNF_Z(X_6)) ),
    inference(subst,[],[refute_0_8:[bind(U,$fot(skolemFOFtoCNF_Z(X_6))),bind(X,$fot(X_6))]]) ).

cnf(refute_0_10,plain,
    ( ~ big_f(X_6,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(X_6)),skolemFOFtoCNF_Z(X_6)) ),
    inference(resolve,[$cnf( big_f(X_6,skolemFOFtoCNF_Z(X_6)) )],[refute_0_7,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) ),
    inference(subst,[],[refute_0_10:[bind(X_6,$fot(skolemFOFtoCNF_W))]]) ).

cnf(refute_0_12,plain,
    ( big_f(X,skolemFOFtoCNF_U(X))
    | big_f(X,skolemFOFtoCNF_W) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_13,plain,
    ( big_f(X_10,skolemFOFtoCNF_U(X_10))
    | big_f(X_10,skolemFOFtoCNF_W) ),
    inference(subst,[],[refute_0_12:[bind(X,$fot(X_10))]]) ).

cnf(refute_0_14,plain,
    ( ~ big_f(Y,skolemFOFtoCNF_U(X))
    | big_f(X,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(X,Y),Y) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_15,plain,
    ( ~ big_f(X_10,skolemFOFtoCNF_U(X_10))
    | big_f(X_10,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(X_10,X_10),X_10) ),
    inference(subst,[],[refute_0_14:[bind(X,$fot(X_10)),bind(Y,$fot(X_10))]]) ).

cnf(refute_0_16,plain,
    ( big_f(X_10,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(X_10,X_10),X_10) ),
    inference(resolve,[$cnf( big_f(X_10,skolemFOFtoCNF_U(X_10)) )],[refute_0_13,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W) ),
    inference(subst,[],[refute_0_16:[bind(X_10,$fot(skolemFOFtoCNF_W))]]) ).

cnf(refute_0_18,plain,
    ( big_f(X_14,skolemFOFtoCNF_U(X_14))
    | big_f(X_14,skolemFOFtoCNF_W) ),
    inference(subst,[],[refute_0_12:[bind(X,$fot(X_14))]]) ).

cnf(refute_0_19,plain,
    ( ~ big_f(Y,skolemFOFtoCNF_U(X))
    | big_f(X,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(X,Y),skolemFOFtoCNF_U(X)) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_20,plain,
    ( ~ big_f(X_14,skolemFOFtoCNF_U(X_14))
    | big_f(X_14,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(X_14,X_14),skolemFOFtoCNF_U(X_14)) ),
    inference(subst,[],[refute_0_19:[bind(X,$fot(X_14)),bind(Y,$fot(X_14))]]) ).

cnf(refute_0_21,plain,
    ( big_f(X_14,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(X_14,X_14),skolemFOFtoCNF_U(X_14)) ),
    inference(resolve,[$cnf( big_f(X_14,skolemFOFtoCNF_U(X_14)) )],[refute_0_18,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
    inference(subst,[],[refute_0_21:[bind(X_14,$fot(skolemFOFtoCNF_W))]]) ).

cnf(refute_0_23,plain,
    ( ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
    inference(subst,[],[refute_0_19:[bind(X,$fot(skolemFOFtoCNF_W)),bind(Y,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))))]]) ).

cnf(refute_0_24,plain,
    ( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),U)
    | ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Y(U),U) ),
    inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W)))]]) ).

cnf(refute_0_25,plain,
    ( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),U)
    | big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Y(U),U) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W) )],[refute_0_17,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
    inference(subst,[],[refute_0_25:[bind(U,$fot(skolemFOFtoCNF_U(skolemFOFtoCNF_W)))]]) ).

cnf(refute_0_27,plain,
    ( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_22,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_27,refute_0_23]) ).

cnf(refute_0_29,plain,
    ( ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))) ),
    inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_W)),bind(Y,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))))]]) ).

cnf(refute_0_30,plain,
    ( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_27,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( ~ big_f(X_49,skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | ~ big_f(X_49,skolemFOFtoCNF_W)
    | ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))) ),
    inference(subst,[],[refute_0_5:[bind(U,$fot(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),bind(X,$fot(X_49)),bind(Z,$fot(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W)))))]]) ).

cnf(refute_0_32,plain,
    ( ~ big_f(X_49,skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | ~ big_f(X_49,skolemFOFtoCNF_W)
    | ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( ~ big_f(X_113,skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | ~ big_f(X_113,skolemFOFtoCNF_W)
    | ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
    inference(subst,[],[refute_0_32:[bind(X_49,$fot(X_113))]]) ).

cnf(refute_0_34,plain,
    ( ~ big_f(X_113,skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | ~ big_f(X_113,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_Y(skolemFOFtoCNF_U(skolemFOFtoCNF_W))),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_28,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W))
    | ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
    inference(subst,[],[refute_0_34:[bind(X_113,$fot(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W)))]]) ).

cnf(refute_0_36,plain,
    ( ~ big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_W)) )],[refute_0_22,refute_0_35]) ).

cnf(refute_0_37,plain,
    big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z_1(skolemFOFtoCNF_W,skolemFOFtoCNF_W),skolemFOFtoCNF_W) )],[refute_0_17,refute_0_36]) ).

cnf(refute_0_38,plain,
    big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) )],[refute_0_37,refute_0_11]) ).

cnf(refute_0_39,plain,
    ( ~ big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)))
    | ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
    | ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) )],[refute_0_38,refute_0_6]) ).

cnf(refute_0_40,plain,
    ( ~ big_f(X,skolemFOFtoCNF_Z(Y))
    | X = Y ),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_41,plain,
    ( ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
    | skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) = skolemFOFtoCNF_W ),
    inference(subst,[],[refute_0_40:[bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)))),bind(Y,$fot(skolemFOFtoCNF_W))]]) ).

cnf(refute_0_42,plain,
    skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) = skolemFOFtoCNF_W,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) )],[refute_0_38,refute_0_41]) ).

cnf(refute_0_43,plain,
    ( skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) != skolemFOFtoCNF_W
    | ~ big_f(Z,skolemFOFtoCNF_W)
    | big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))) ),
    introduced(tautology,[equality,[$cnf( ~ big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))) ),[1],$fot(skolemFOFtoCNF_W)]]) ).

cnf(refute_0_44,plain,
    ( ~ big_f(Z,skolemFOFtoCNF_W)
    | big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) )],[refute_0_42,refute_0_43]) ).

cnf(refute_0_45,plain,
    ( ~ big_f(Z,skolemFOFtoCNF_W)
    | ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
    | ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),
    inference(resolve,[$cnf( big_f(Z,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W))) )],[refute_0_44,refute_0_39]) ).

cnf(refute_0_46,plain,
    ( skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) != skolemFOFtoCNF_W
    | ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),
    introduced(tautology,[equality,[$cnf( ~ big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),[0],$fot(skolemFOFtoCNF_W)]]) ).

cnf(refute_0_47,plain,
    ( ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) )],[refute_0_42,refute_0_46]) ).

cnf(refute_0_48,plain,
    ( ~ big_f(Z,skolemFOFtoCNF_W)
    | ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W))
    | ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z(skolemFOFtoCNF_W)),skolemFOFtoCNF_W) )],[refute_0_47,refute_0_45]) ).

cnf(refute_0_49,plain,
    ( ~ big_f(Z,skolemFOFtoCNF_W)
    | ~ big_f(Z,skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) ),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) )],[refute_0_37,refute_0_48]) ).

cnf(refute_0_50,plain,
    ( ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W)
    | ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) ),
    inference(subst,[],[refute_0_49:[bind(Z,$fot(skolemFOFtoCNF_W))]]) ).

cnf(refute_0_51,plain,
    ~ big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W),
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_Z(skolemFOFtoCNF_W)) )],[refute_0_4,refute_0_50]) ).

cnf(refute_0_52,plain,
    $false,
    inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W,skolemFOFtoCNF_W) )],[refute_0_37,refute_0_51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SYN077+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.36  % Computer : n022.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Tue Jul 12 04:27:40 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.99/2.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.99/2.14  
% 1.99/2.14  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.99/2.15  
%------------------------------------------------------------------------------