TSTP Solution File: SWC001+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWC001+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n032.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 : Tue Jul 19 21:26:02 EDT 2022

% Result   : Theorem 2.88s 3.10s
% Output   : CNFRefutation 2.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  115 (  40 unt;   0 def)
%            Number of atoms       :  668 ( 110 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  834 ( 281   ~; 194   |; 324   &)
%                                         (   0 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  14 con; 0-0 aty)
%            Number of variables   :  177 (   0 sgn  75   !;  73   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X0] :
                  ( ssList(X0)
                 => ( V != X0
                    | U != W
                    | ~ duplicatefreeP(W)
                    | ? [Y] :
                        ( ssItem(Y)
                        & ( ( ~ memberP(X0,Y)
                            & memberP(W,Y) )
                          | ( ~ memberP(W,Y)
                            & memberP(X0,Y) ) ) )
                    | ( ! [Z] :
                          ( ssItem(Z)
                         => ( ( ~ memberP(V,Z)
                              & ~ memberP(U,Z) )
                            | ( memberP(V,Z)
                              & memberP(U,Z) ) ) )
                      & duplicatefreeP(U) ) ) ) ) ) ) ).

fof(subgoal_0,plain,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X0] :
                  ( ( ssList(X0)
                    & ~ ( V != X0 )
                    & ~ ( U != W )
                    & ~ ~ duplicatefreeP(W)
                    & ~ ? [Y] :
                          ( ssItem(Y)
                          & ( ( ~ memberP(X0,Y)
                              & memberP(W,Y) )
                            | ( ~ memberP(W,Y)
                              & memberP(X0,Y) ) ) ) )
                 => ! [Z] :
                      ( ( ssItem(Z)
                        & ~ ( ~ memberP(V,Z)
                            & ~ memberP(U,Z) ) )
                     => memberP(V,Z) ) ) ) ) ),
    inference(strip,[],[co1]) ).

fof(subgoal_1,plain,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X0] :
                  ( ( ssList(X0)
                    & ~ ( V != X0 )
                    & ~ ( U != W )
                    & ~ ~ duplicatefreeP(W)
                    & ~ ? [Y] :
                          ( ssItem(Y)
                          & ( ( ~ memberP(X0,Y)
                              & memberP(W,Y) )
                            | ( ~ memberP(W,Y)
                              & memberP(X0,Y) ) ) ) )
                 => ! [Z] :
                      ( ( ssItem(Z)
                        & ~ ( ~ memberP(V,Z)
                            & ~ memberP(U,Z) )
                        & memberP(V,Z) )
                     => memberP(U,Z) ) ) ) ) ),
    inference(strip,[],[co1]) ).

fof(subgoal_2,plain,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X0] :
                  ( ( ssList(X0)
                    & ~ ( V != X0 )
                    & ~ ( U != W )
                    & ~ ~ duplicatefreeP(W)
                    & ~ ? [Y] :
                          ( ssItem(Y)
                          & ( ( ~ memberP(X0,Y)
                              & memberP(W,Y) )
                            | ( ~ memberP(W,Y)
                              & memberP(X0,Y) ) ) )
                    & ! [Z] :
                        ( ssItem(Z)
                       => ( ( ~ memberP(V,Z)
                            & ~ memberP(U,Z) )
                          | ( memberP(V,Z)
                            & memberP(U,Z) ) ) ) )
                 => duplicatefreeP(U) ) ) ) ),
    inference(strip,[],[co1]) ).

fof(negate_0_0,plain,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X0] :
                    ( ( ssList(X0)
                      & ~ ( V != X0 )
                      & ~ ( U != W )
                      & ~ ~ duplicatefreeP(W)
                      & ~ ? [Y] :
                            ( ssItem(Y)
                            & ( ( ~ memberP(X0,Y)
                                & memberP(W,Y) )
                              | ( ~ memberP(W,Y)
                                & memberP(X0,Y) ) ) ) )
                   => ! [Z] :
                        ( ( ssItem(Z)
                          & ~ ( ~ memberP(V,Z)
                              & ~ memberP(U,Z) ) )
                       => memberP(V,Z) ) ) ) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X0] :
                  ( U = W
                  & V = X0
                  & duplicatefreeP(W)
                  & ssList(X0)
                  & ? [Z] :
                      ( ~ memberP(V,Z)
                      & ssItem(Z)
                      & ( memberP(U,Z)
                        | memberP(V,Z) ) )
                  & ! [Y] :
                      ( ~ ssItem(Y)
                      | ( ( ~ memberP(W,Y)
                          | memberP(X0,Y) )
                        & ( ~ memberP(X0,Y)
                          | memberP(W,Y) ) ) ) ) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ssList(skolemFOFtoCNF_U_1)
    & ? [V] :
        ( ssList(V)
        & ? [W] :
            ( ssList(W)
            & ? [X0] :
                ( V = X0
                & skolemFOFtoCNF_U_1 = W
                & duplicatefreeP(W)
                & ssList(X0)
                & ? [Z] :
                    ( ~ memberP(V,Z)
                    & ssItem(Z)
                    & ( memberP(V,Z)
                      | memberP(skolemFOFtoCNF_U_1,Z) ) )
                & ! [Y] :
                    ( ~ ssItem(Y)
                    | ( ( ~ memberP(W,Y)
                        | memberP(X0,Y) )
                      & ( ~ memberP(X0,Y)
                        | memberP(W,Y) ) ) ) ) ) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ? [V] :
      ( ssList(V)
      & ? [W] :
          ( ssList(W)
          & ? [X0] :
              ( V = X0
              & skolemFOFtoCNF_U_1 = W
              & duplicatefreeP(W)
              & ssList(X0)
              & ? [Z] :
                  ( ~ memberP(V,Z)
                  & ssItem(Z)
                  & ( memberP(V,Z)
                    | memberP(skolemFOFtoCNF_U_1,Z) ) )
              & ! [Y] :
                  ( ~ ssItem(Y)
                  | ( ( ~ memberP(W,Y)
                      | memberP(X0,Y) )
                    & ( ~ memberP(X0,Y)
                      | memberP(W,Y) ) ) ) ) ) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( ssList(skolemFOFtoCNF_V_12)
    & ? [W] :
        ( ssList(W)
        & ? [X0] :
            ( skolemFOFtoCNF_U_1 = W
            & skolemFOFtoCNF_V_12 = X0
            & duplicatefreeP(W)
            & ssList(X0)
            & ? [Z] :
                ( ~ memberP(skolemFOFtoCNF_V_12,Z)
                & ssItem(Z)
                & ( memberP(skolemFOFtoCNF_U_1,Z)
                  | memberP(skolemFOFtoCNF_V_12,Z) ) )
            & ! [Y] :
                ( ~ ssItem(Y)
                | ( ( ~ memberP(W,Y)
                    | memberP(X0,Y) )
                  & ( ~ memberP(X0,Y)
                    | memberP(W,Y) ) ) ) ) ) ),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [W] :
      ( ssList(W)
      & ? [X0] :
          ( skolemFOFtoCNF_U_1 = W
          & skolemFOFtoCNF_V_12 = X0
          & duplicatefreeP(W)
          & ssList(X0)
          & ? [Z] :
              ( ~ memberP(skolemFOFtoCNF_V_12,Z)
              & ssItem(Z)
              & ( memberP(skolemFOFtoCNF_U_1,Z)
                | memberP(skolemFOFtoCNF_V_12,Z) ) )
          & ! [Y] :
              ( ~ ssItem(Y)
              | ( ( ~ memberP(W,Y)
                  | memberP(X0,Y) )
                & ( ~ memberP(X0,Y)
                  | memberP(W,Y) ) ) ) ) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ( ssList(skolemFOFtoCNF_W_12)
    & ? [X0] :
        ( skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
        & skolemFOFtoCNF_V_12 = X0
        & duplicatefreeP(skolemFOFtoCNF_W_12)
        & ssList(X0)
        & ? [Z] :
            ( ~ memberP(skolemFOFtoCNF_V_12,Z)
            & ssItem(Z)
            & ( memberP(skolemFOFtoCNF_U_1,Z)
              | memberP(skolemFOFtoCNF_V_12,Z) ) )
        & ! [Y] :
            ( ~ ssItem(Y)
            | ( ( ~ memberP(X0,Y)
                | memberP(skolemFOFtoCNF_W_12,Y) )
              & ( ~ memberP(skolemFOFtoCNF_W_12,Y)
                | memberP(X0,Y) ) ) ) ) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ? [X0] :
      ( skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
      & skolemFOFtoCNF_V_12 = X0
      & duplicatefreeP(skolemFOFtoCNF_W_12)
      & ssList(X0)
      & ? [Z] :
          ( ~ memberP(skolemFOFtoCNF_V_12,Z)
          & ssItem(Z)
          & ( memberP(skolemFOFtoCNF_U_1,Z)
            | memberP(skolemFOFtoCNF_V_12,Z) ) )
      & ! [Y] :
          ( ~ ssItem(Y)
          | ( ( ~ memberP(X0,Y)
              | memberP(skolemFOFtoCNF_W_12,Y) )
            & ( ~ memberP(skolemFOFtoCNF_W_12,Y)
              | memberP(X0,Y) ) ) ) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ( skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
    & skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
    & duplicatefreeP(skolemFOFtoCNF_W_12)
    & ssList(skolemFOFtoCNF_X_9)
    & ? [Z] :
        ( ~ memberP(skolemFOFtoCNF_V_12,Z)
        & ssItem(Z)
        & ( memberP(skolemFOFtoCNF_U_1,Z)
          | memberP(skolemFOFtoCNF_V_12,Z) ) )
    & ! [Y] :
        ( ~ ssItem(Y)
        | ( ( ~ memberP(skolemFOFtoCNF_W_12,Y)
            | memberP(skolemFOFtoCNF_X_9,Y) )
          & ( ~ memberP(skolemFOFtoCNF_X_9,Y)
            | memberP(skolemFOFtoCNF_W_12,Y) ) ) ) ),
    inference(skolemize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ? [Z] :
      ( ~ memberP(skolemFOFtoCNF_V_12,Z)
      & ssItem(Z)
      & ( memberP(skolemFOFtoCNF_U_1,Z)
        | memberP(skolemFOFtoCNF_V_12,Z) ) ),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ( ~ memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6)
    & ssItem(skolemFOFtoCNF_Z_6)
    & ( memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6)
      | memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6) ) ),
    inference(skolemize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ( memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6)
    | memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ~ memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_12,plain,
    memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6),
    inference(simplify,[],[normalize_0_10,normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [Y] :
      ( ~ ssItem(Y)
      | ( ( ~ memberP(skolemFOFtoCNF_W_12,Y)
          | memberP(skolemFOFtoCNF_X_9,Y) )
        & ( ~ memberP(skolemFOFtoCNF_X_9,Y)
          | memberP(skolemFOFtoCNF_W_12,Y) ) ) ),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_14,plain,
    ! [Y] :
      ( ~ ssItem(Y)
      | ( ( ~ memberP(skolemFOFtoCNF_W_12,Y)
          | memberP(skolemFOFtoCNF_X_9,Y) )
        & ( ~ memberP(skolemFOFtoCNF_X_9,Y)
          | memberP(skolemFOFtoCNF_W_12,Y) ) ) ),
    inference(specialize,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [Y] :
      ( ( ~ memberP(skolemFOFtoCNF_W_12,Y)
        | ~ ssItem(Y)
        | memberP(skolemFOFtoCNF_X_9,Y) )
      & ( ~ memberP(skolemFOFtoCNF_X_9,Y)
        | ~ ssItem(Y)
        | memberP(skolemFOFtoCNF_W_12,Y) ) ),
    inference(clausify,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    ! [Y] :
      ( ~ memberP(skolemFOFtoCNF_W_12,Y)
      | ~ ssItem(Y)
      | memberP(skolemFOFtoCNF_X_9,Y) ),
    inference(conjunct,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_18,plain,
    skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_19,plain,
    ssItem(skolemFOFtoCNF_Z_6),
    inference(conjunct,[],[normalize_0_9]) ).

cnf(refute_0_0,plain,
    memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_1,plain,
    ( ~ memberP(skolemFOFtoCNF_W_12,Y)
    | ~ ssItem(Y)
    | memberP(skolemFOFtoCNF_X_9,Y) ),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_2,plain,
    skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
    inference(canonicalize,[],[normalize_0_17]) ).

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

cnf(refute_0_4,plain,
    ( X != X
    | X != Y0
    | Y0 = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).

cnf(refute_0_5,plain,
    ( X != Y0
    | Y0 = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
    | skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y0,$fot(skolemFOFtoCNF_W_12))]]) ).

cnf(refute_0_7,plain,
    skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
    | ~ memberP(skolemFOFtoCNF_U_1,Y)
    | memberP(skolemFOFtoCNF_W_12,Y) ),
    introduced(tautology,[equality,[$cnf( ~ memberP(skolemFOFtoCNF_W_12,Y) ),[0],$fot(skolemFOFtoCNF_U_1)]]) ).

cnf(refute_0_9,plain,
    ( ~ memberP(skolemFOFtoCNF_U_1,Y)
    | memberP(skolemFOFtoCNF_W_12,Y) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ memberP(skolemFOFtoCNF_U_1,Y)
    | ~ ssItem(Y)
    | memberP(skolemFOFtoCNF_X_9,Y) ),
    inference(resolve,[$cnf( memberP(skolemFOFtoCNF_W_12,Y) )],[refute_0_9,refute_0_1]) ).

cnf(refute_0_11,plain,
    skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_12,plain,
    ( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
    | skolemFOFtoCNF_X_9 = skolemFOFtoCNF_V_12 ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_V_12)),bind(Y0,$fot(skolemFOFtoCNF_X_9))]]) ).

cnf(refute_0_13,plain,
    skolemFOFtoCNF_X_9 = skolemFOFtoCNF_V_12,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( skolemFOFtoCNF_X_9 != skolemFOFtoCNF_V_12
    | ~ memberP(skolemFOFtoCNF_X_9,Y)
    | memberP(skolemFOFtoCNF_V_12,Y) ),
    introduced(tautology,[equality,[$cnf( memberP(skolemFOFtoCNF_X_9,Y) ),[0],$fot(skolemFOFtoCNF_V_12)]]) ).

cnf(refute_0_15,plain,
    ( ~ memberP(skolemFOFtoCNF_X_9,Y)
    | memberP(skolemFOFtoCNF_V_12,Y) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,skolemFOFtoCNF_V_12) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( ~ memberP(skolemFOFtoCNF_U_1,Y)
    | ~ ssItem(Y)
    | memberP(skolemFOFtoCNF_V_12,Y) ),
    inference(resolve,[$cnf( memberP(skolemFOFtoCNF_X_9,Y) )],[refute_0_10,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( ~ memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6)
    | ~ ssItem(skolemFOFtoCNF_Z_6)
    | memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6) ),
    inference(subst,[],[refute_0_16:[bind(Y,$fot(skolemFOFtoCNF_Z_6))]]) ).

cnf(refute_0_18,plain,
    ( ~ ssItem(skolemFOFtoCNF_Z_6)
    | memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6) ),
    inference(resolve,[$cnf( memberP(skolemFOFtoCNF_U_1,skolemFOFtoCNF_Z_6) )],[refute_0_0,refute_0_17]) ).

cnf(refute_0_19,plain,
    ssItem(skolemFOFtoCNF_Z_6),
    inference(canonicalize,[],[normalize_0_19]) ).

cnf(refute_0_20,plain,
    memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6),
    inference(resolve,[$cnf( ssItem(skolemFOFtoCNF_Z_6) )],[refute_0_19,refute_0_18]) ).

cnf(refute_0_21,plain,
    ~ memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_22,plain,
    $false,
    inference(resolve,[$cnf( memberP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_Z_6) )],[refute_0_20,refute_0_21]) ).

fof(negate_1_0,plain,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X0] :
                    ( ( ssList(X0)
                      & ~ ( V != X0 )
                      & ~ ( U != W )
                      & ~ ~ duplicatefreeP(W)
                      & ~ ? [Y] :
                            ( ssItem(Y)
                            & ( ( ~ memberP(X0,Y)
                                & memberP(W,Y) )
                              | ( ~ memberP(W,Y)
                                & memberP(X0,Y) ) ) ) )
                   => ! [Z] :
                        ( ( ssItem(Z)
                          & ~ ( ~ memberP(V,Z)
                              & ~ memberP(U,Z) )
                          & memberP(V,Z) )
                       => memberP(U,Z) ) ) ) ) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X0] :
                  ( U = W
                  & V = X0
                  & duplicatefreeP(W)
                  & ssList(X0)
                  & ? [Z] :
                      ( ~ memberP(U,Z)
                      & memberP(V,Z)
                      & ssItem(Z)
                      & ( memberP(U,Z)
                        | memberP(V,Z) ) )
                  & ! [Y] :
                      ( ~ ssItem(Y)
                      | ( ( ~ memberP(W,Y)
                          | memberP(X0,Y) )
                        & ( ~ memberP(X0,Y)
                          | memberP(W,Y) ) ) ) ) ) ) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_1,plain,
    ( ssList(skolemFOFtoCNF_U_2)
    & ? [V] :
        ( ssList(V)
        & ? [W] :
            ( ssList(W)
            & ? [X0] :
                ( V = X0
                & skolemFOFtoCNF_U_2 = W
                & duplicatefreeP(W)
                & ssList(X0)
                & ? [Z] :
                    ( ~ memberP(skolemFOFtoCNF_U_2,Z)
                    & memberP(V,Z)
                    & ssItem(Z)
                    & ( memberP(V,Z)
                      | memberP(skolemFOFtoCNF_U_2,Z) ) )
                & ! [Y] :
                    ( ~ ssItem(Y)
                    | ( ( ~ memberP(W,Y)
                        | memberP(X0,Y) )
                      & ( ~ memberP(X0,Y)
                        | memberP(W,Y) ) ) ) ) ) ) ),
    inference(skolemize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ? [V] :
      ( ssList(V)
      & ? [W] :
          ( ssList(W)
          & ? [X0] :
              ( V = X0
              & skolemFOFtoCNF_U_2 = W
              & duplicatefreeP(W)
              & ssList(X0)
              & ? [Z] :
                  ( ~ memberP(skolemFOFtoCNF_U_2,Z)
                  & memberP(V,Z)
                  & ssItem(Z)
                  & ( memberP(V,Z)
                    | memberP(skolemFOFtoCNF_U_2,Z) ) )
              & ! [Y] :
                  ( ~ ssItem(Y)
                  | ( ( ~ memberP(W,Y)
                      | memberP(X0,Y) )
                    & ( ~ memberP(X0,Y)
                      | memberP(W,Y) ) ) ) ) ) ),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ( ssList(skolemFOFtoCNF_V_13)
    & ? [W] :
        ( ssList(W)
        & ? [X0] :
            ( skolemFOFtoCNF_U_2 = W
            & skolemFOFtoCNF_V_13 = X0
            & duplicatefreeP(W)
            & ssList(X0)
            & ? [Z] :
                ( ~ memberP(skolemFOFtoCNF_U_2,Z)
                & memberP(skolemFOFtoCNF_V_13,Z)
                & ssItem(Z)
                & ( memberP(skolemFOFtoCNF_U_2,Z)
                  | memberP(skolemFOFtoCNF_V_13,Z) ) )
            & ! [Y] :
                ( ~ ssItem(Y)
                | ( ( ~ memberP(W,Y)
                    | memberP(X0,Y) )
                  & ( ~ memberP(X0,Y)
                    | memberP(W,Y) ) ) ) ) ) ),
    inference(skolemize,[],[normalize_1_2]) ).

fof(normalize_1_4,plain,
    ? [W] :
      ( ssList(W)
      & ? [X0] :
          ( skolemFOFtoCNF_U_2 = W
          & skolemFOFtoCNF_V_13 = X0
          & duplicatefreeP(W)
          & ssList(X0)
          & ? [Z] :
              ( ~ memberP(skolemFOFtoCNF_U_2,Z)
              & memberP(skolemFOFtoCNF_V_13,Z)
              & ssItem(Z)
              & ( memberP(skolemFOFtoCNF_U_2,Z)
                | memberP(skolemFOFtoCNF_V_13,Z) ) )
          & ! [Y] :
              ( ~ ssItem(Y)
              | ( ( ~ memberP(W,Y)
                  | memberP(X0,Y) )
                & ( ~ memberP(X0,Y)
                  | memberP(W,Y) ) ) ) ) ),
    inference(conjunct,[],[normalize_1_3]) ).

fof(normalize_1_5,plain,
    ( ssList(skolemFOFtoCNF_W_13)
    & ? [X0] :
        ( skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
        & skolemFOFtoCNF_V_13 = X0
        & duplicatefreeP(skolemFOFtoCNF_W_13)
        & ssList(X0)
        & ? [Z] :
            ( ~ memberP(skolemFOFtoCNF_U_2,Z)
            & memberP(skolemFOFtoCNF_V_13,Z)
            & ssItem(Z)
            & ( memberP(skolemFOFtoCNF_U_2,Z)
              | memberP(skolemFOFtoCNF_V_13,Z) ) )
        & ! [Y] :
            ( ~ ssItem(Y)
            | ( ( ~ memberP(X0,Y)
                | memberP(skolemFOFtoCNF_W_13,Y) )
              & ( ~ memberP(skolemFOFtoCNF_W_13,Y)
                | memberP(X0,Y) ) ) ) ) ),
    inference(skolemize,[],[normalize_1_4]) ).

fof(normalize_1_6,plain,
    ? [X0] :
      ( skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
      & skolemFOFtoCNF_V_13 = X0
      & duplicatefreeP(skolemFOFtoCNF_W_13)
      & ssList(X0)
      & ? [Z] :
          ( ~ memberP(skolemFOFtoCNF_U_2,Z)
          & memberP(skolemFOFtoCNF_V_13,Z)
          & ssItem(Z)
          & ( memberP(skolemFOFtoCNF_U_2,Z)
            | memberP(skolemFOFtoCNF_V_13,Z) ) )
      & ! [Y] :
          ( ~ ssItem(Y)
          | ( ( ~ memberP(X0,Y)
              | memberP(skolemFOFtoCNF_W_13,Y) )
            & ( ~ memberP(skolemFOFtoCNF_W_13,Y)
              | memberP(X0,Y) ) ) ) ),
    inference(conjunct,[],[normalize_1_5]) ).

fof(normalize_1_7,plain,
    ( skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13
    & skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10
    & duplicatefreeP(skolemFOFtoCNF_W_13)
    & ssList(skolemFOFtoCNF_X_10)
    & ? [Z] :
        ( ~ memberP(skolemFOFtoCNF_U_2,Z)
        & memberP(skolemFOFtoCNF_V_13,Z)
        & ssItem(Z)
        & ( memberP(skolemFOFtoCNF_U_2,Z)
          | memberP(skolemFOFtoCNF_V_13,Z) ) )
    & ! [Y] :
        ( ~ ssItem(Y)
        | ( ( ~ memberP(skolemFOFtoCNF_W_13,Y)
            | memberP(skolemFOFtoCNF_X_10,Y) )
          & ( ~ memberP(skolemFOFtoCNF_X_10,Y)
            | memberP(skolemFOFtoCNF_W_13,Y) ) ) ) ),
    inference(skolemize,[],[normalize_1_6]) ).

fof(normalize_1_8,plain,
    ? [Z] :
      ( ~ memberP(skolemFOFtoCNF_U_2,Z)
      & memberP(skolemFOFtoCNF_V_13,Z)
      & ssItem(Z)
      & ( memberP(skolemFOFtoCNF_U_2,Z)
        | memberP(skolemFOFtoCNF_V_13,Z) ) ),
    inference(conjunct,[],[normalize_1_7]) ).

fof(normalize_1_9,plain,
    ( ~ memberP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_Z_7)
    & memberP(skolemFOFtoCNF_V_13,skolemFOFtoCNF_Z_7)
    & ssItem(skolemFOFtoCNF_Z_7)
    & ( memberP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_Z_7)
      | memberP(skolemFOFtoCNF_V_13,skolemFOFtoCNF_Z_7) ) ),
    inference(skolemize,[],[normalize_1_8]) ).

fof(normalize_1_10,plain,
    memberP(skolemFOFtoCNF_V_13,skolemFOFtoCNF_Z_7),
    inference(conjunct,[],[normalize_1_9]) ).

fof(normalize_1_11,plain,
    ! [Y] :
      ( ~ ssItem(Y)
      | ( ( ~ memberP(skolemFOFtoCNF_W_13,Y)
          | memberP(skolemFOFtoCNF_X_10,Y) )
        & ( ~ memberP(skolemFOFtoCNF_X_10,Y)
          | memberP(skolemFOFtoCNF_W_13,Y) ) ) ),
    inference(conjunct,[],[normalize_1_7]) ).

fof(normalize_1_12,plain,
    ! [Y] :
      ( ~ ssItem(Y)
      | ( ( ~ memberP(skolemFOFtoCNF_W_13,Y)
          | memberP(skolemFOFtoCNF_X_10,Y) )
        & ( ~ memberP(skolemFOFtoCNF_X_10,Y)
          | memberP(skolemFOFtoCNF_W_13,Y) ) ) ),
    inference(specialize,[],[normalize_1_11]) ).

fof(normalize_1_13,plain,
    ! [Y] :
      ( ( ~ memberP(skolemFOFtoCNF_W_13,Y)
        | ~ ssItem(Y)
        | memberP(skolemFOFtoCNF_X_10,Y) )
      & ( ~ memberP(skolemFOFtoCNF_X_10,Y)
        | ~ ssItem(Y)
        | memberP(skolemFOFtoCNF_W_13,Y) ) ),
    inference(clausify,[],[normalize_1_12]) ).

fof(normalize_1_14,plain,
    ! [Y] :
      ( ~ memberP(skolemFOFtoCNF_X_10,Y)
      | ~ ssItem(Y)
      | memberP(skolemFOFtoCNF_W_13,Y) ),
    inference(conjunct,[],[normalize_1_13]) ).

fof(normalize_1_15,plain,
    skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
    inference(conjunct,[],[normalize_1_7]) ).

fof(normalize_1_16,plain,
    skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
    inference(conjunct,[],[normalize_1_7]) ).

fof(normalize_1_17,plain,
    ssItem(skolemFOFtoCNF_Z_7),
    inference(conjunct,[],[normalize_1_9]) ).

fof(normalize_1_18,plain,
    ~ memberP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_Z_7),
    inference(conjunct,[],[normalize_1_9]) ).

cnf(refute_1_0,plain,
    memberP(skolemFOFtoCNF_V_13,skolemFOFtoCNF_Z_7),
    inference(canonicalize,[],[normalize_1_10]) ).

cnf(refute_1_1,plain,
    ( ~ memberP(skolemFOFtoCNF_X_10,Y)
    | ~ ssItem(Y)
    | memberP(skolemFOFtoCNF_W_13,Y) ),
    inference(canonicalize,[],[normalize_1_14]) ).

cnf(refute_1_2,plain,
    skolemFOFtoCNF_V_13 = skolemFOFtoCNF_X_10,
    inference(canonicalize,[],[normalize_1_15]) ).

cnf(refute_1_3,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_1_4,plain,
    ( X != X
    | X != Y0
    | Y0 = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).

cnf(refute_1_5,plain,
    ( X != Y0
    | Y0 = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_1_3,refute_1_4]) ).

cnf(refute_1_6,plain,
    ( skolemFOFtoCNF_V_13 != skolemFOFtoCNF_X_10
    | skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13 ),
    inference(subst,[],[refute_1_5:[bind(X,$fot(skolemFOFtoCNF_V_13)),bind(Y0,$fot(skolemFOFtoCNF_X_10))]]) ).

cnf(refute_1_7,plain,
    skolemFOFtoCNF_X_10 = skolemFOFtoCNF_V_13,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_13,skolemFOFtoCNF_X_10) )],[refute_1_2,refute_1_6]) ).

cnf(refute_1_8,plain,
    ( skolemFOFtoCNF_X_10 != skolemFOFtoCNF_V_13
    | ~ memberP(skolemFOFtoCNF_V_13,Y)
    | memberP(skolemFOFtoCNF_X_10,Y) ),
    introduced(tautology,[equality,[$cnf( ~ memberP(skolemFOFtoCNF_X_10,Y) ),[0],$fot(skolemFOFtoCNF_V_13)]]) ).

cnf(refute_1_9,plain,
    ( ~ memberP(skolemFOFtoCNF_V_13,Y)
    | memberP(skolemFOFtoCNF_X_10,Y) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_10,skolemFOFtoCNF_V_13) )],[refute_1_7,refute_1_8]) ).

cnf(refute_1_10,plain,
    ( ~ memberP(skolemFOFtoCNF_V_13,Y)
    | ~ ssItem(Y)
    | memberP(skolemFOFtoCNF_W_13,Y) ),
    inference(resolve,[$cnf( memberP(skolemFOFtoCNF_X_10,Y) )],[refute_1_9,refute_1_1]) ).

cnf(refute_1_11,plain,
    skolemFOFtoCNF_U_2 = skolemFOFtoCNF_W_13,
    inference(canonicalize,[],[normalize_1_16]) ).

cnf(refute_1_12,plain,
    ( skolemFOFtoCNF_U_2 != skolemFOFtoCNF_W_13
    | skolemFOFtoCNF_W_13 = skolemFOFtoCNF_U_2 ),
    inference(subst,[],[refute_1_5:[bind(X,$fot(skolemFOFtoCNF_U_2)),bind(Y0,$fot(skolemFOFtoCNF_W_13))]]) ).

cnf(refute_1_13,plain,
    skolemFOFtoCNF_W_13 = skolemFOFtoCNF_U_2,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_2,skolemFOFtoCNF_W_13) )],[refute_1_11,refute_1_12]) ).

cnf(refute_1_14,plain,
    ( skolemFOFtoCNF_W_13 != skolemFOFtoCNF_U_2
    | ~ memberP(skolemFOFtoCNF_W_13,Y)
    | memberP(skolemFOFtoCNF_U_2,Y) ),
    introduced(tautology,[equality,[$cnf( memberP(skolemFOFtoCNF_W_13,Y) ),[0],$fot(skolemFOFtoCNF_U_2)]]) ).

cnf(refute_1_15,plain,
    ( ~ memberP(skolemFOFtoCNF_W_13,Y)
    | memberP(skolemFOFtoCNF_U_2,Y) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_13,skolemFOFtoCNF_U_2) )],[refute_1_13,refute_1_14]) ).

cnf(refute_1_16,plain,
    ( ~ memberP(skolemFOFtoCNF_V_13,Y)
    | ~ ssItem(Y)
    | memberP(skolemFOFtoCNF_U_2,Y) ),
    inference(resolve,[$cnf( memberP(skolemFOFtoCNF_W_13,Y) )],[refute_1_10,refute_1_15]) ).

cnf(refute_1_17,plain,
    ( ~ memberP(skolemFOFtoCNF_V_13,skolemFOFtoCNF_Z_7)
    | ~ ssItem(skolemFOFtoCNF_Z_7)
    | memberP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_Z_7) ),
    inference(subst,[],[refute_1_16:[bind(Y,$fot(skolemFOFtoCNF_Z_7))]]) ).

cnf(refute_1_18,plain,
    ( ~ ssItem(skolemFOFtoCNF_Z_7)
    | memberP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_Z_7) ),
    inference(resolve,[$cnf( memberP(skolemFOFtoCNF_V_13,skolemFOFtoCNF_Z_7) )],[refute_1_0,refute_1_17]) ).

cnf(refute_1_19,plain,
    ssItem(skolemFOFtoCNF_Z_7),
    inference(canonicalize,[],[normalize_1_17]) ).

cnf(refute_1_20,plain,
    memberP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_Z_7),
    inference(resolve,[$cnf( ssItem(skolemFOFtoCNF_Z_7) )],[refute_1_19,refute_1_18]) ).

cnf(refute_1_21,plain,
    ~ memberP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_Z_7),
    inference(canonicalize,[],[normalize_1_18]) ).

cnf(refute_1_22,plain,
    $false,
    inference(resolve,[$cnf( memberP(skolemFOFtoCNF_U_2,skolemFOFtoCNF_Z_7) )],[refute_1_20,refute_1_21]) ).

fof(negate_2_0,plain,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X0] :
                    ( ( ssList(X0)
                      & ~ ( V != X0 )
                      & ~ ( U != W )
                      & ~ ~ duplicatefreeP(W)
                      & ~ ? [Y] :
                            ( ssItem(Y)
                            & ( ( ~ memberP(X0,Y)
                                & memberP(W,Y) )
                              | ( ~ memberP(W,Y)
                                & memberP(X0,Y) ) ) )
                      & ! [Z] :
                          ( ssItem(Z)
                         => ( ( ~ memberP(V,Z)
                              & ~ memberP(U,Z) )
                            | ( memberP(V,Z)
                              & memberP(U,Z) ) ) ) )
                   => duplicatefreeP(U) ) ) ) ),
    inference(negate,[],[subgoal_2]) ).

fof(normalize_2_0,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X0] :
                  ( ~ duplicatefreeP(U)
                  & U = W
                  & V = X0
                  & duplicatefreeP(W)
                  & ssList(X0)
                  & ! [Y] :
                      ( ~ ssItem(Y)
                      | ( ( ~ memberP(W,Y)
                          | memberP(X0,Y) )
                        & ( ~ memberP(X0,Y)
                          | memberP(W,Y) ) ) )
                  & ! [Z] :
                      ( ~ ssItem(Z)
                      | ( ~ memberP(U,Z)
                        & ~ memberP(V,Z) )
                      | ( memberP(U,Z)
                        & memberP(V,Z) ) ) ) ) ) ),
    inference(canonicalize,[],[negate_2_0]) ).

fof(normalize_2_1,plain,
    ( ssList(skolemFOFtoCNF_U_3)
    & ? [V] :
        ( ssList(V)
        & ? [W] :
            ( ssList(W)
            & ? [X0] :
                ( ~ duplicatefreeP(skolemFOFtoCNF_U_3)
                & V = X0
                & skolemFOFtoCNF_U_3 = W
                & duplicatefreeP(W)
                & ssList(X0)
                & ! [Y] :
                    ( ~ ssItem(Y)
                    | ( ( ~ memberP(W,Y)
                        | memberP(X0,Y) )
                      & ( ~ memberP(X0,Y)
                        | memberP(W,Y) ) ) )
                & ! [Z] :
                    ( ~ ssItem(Z)
                    | ( ~ memberP(V,Z)
                      & ~ memberP(skolemFOFtoCNF_U_3,Z) )
                    | ( memberP(V,Z)
                      & memberP(skolemFOFtoCNF_U_3,Z) ) ) ) ) ) ),
    inference(skolemize,[],[normalize_2_0]) ).

fof(normalize_2_2,plain,
    ? [V] :
      ( ssList(V)
      & ? [W] :
          ( ssList(W)
          & ? [X0] :
              ( ~ duplicatefreeP(skolemFOFtoCNF_U_3)
              & V = X0
              & skolemFOFtoCNF_U_3 = W
              & duplicatefreeP(W)
              & ssList(X0)
              & ! [Y] :
                  ( ~ ssItem(Y)
                  | ( ( ~ memberP(W,Y)
                      | memberP(X0,Y) )
                    & ( ~ memberP(X0,Y)
                      | memberP(W,Y) ) ) )
              & ! [Z] :
                  ( ~ ssItem(Z)
                  | ( ~ memberP(V,Z)
                    & ~ memberP(skolemFOFtoCNF_U_3,Z) )
                  | ( memberP(V,Z)
                    & memberP(skolemFOFtoCNF_U_3,Z) ) ) ) ) ),
    inference(conjunct,[],[normalize_2_1]) ).

fof(normalize_2_3,plain,
    ( ssList(skolemFOFtoCNF_V_14)
    & ? [W] :
        ( ssList(W)
        & ? [X0] :
            ( ~ duplicatefreeP(skolemFOFtoCNF_U_3)
            & skolemFOFtoCNF_U_3 = W
            & skolemFOFtoCNF_V_14 = X0
            & duplicatefreeP(W)
            & ssList(X0)
            & ! [Y] :
                ( ~ ssItem(Y)
                | ( ( ~ memberP(W,Y)
                    | memberP(X0,Y) )
                  & ( ~ memberP(X0,Y)
                    | memberP(W,Y) ) ) )
            & ! [Z] :
                ( ~ ssItem(Z)
                | ( ~ memberP(skolemFOFtoCNF_U_3,Z)
                  & ~ memberP(skolemFOFtoCNF_V_14,Z) )
                | ( memberP(skolemFOFtoCNF_U_3,Z)
                  & memberP(skolemFOFtoCNF_V_14,Z) ) ) ) ) ),
    inference(skolemize,[],[normalize_2_2]) ).

fof(normalize_2_4,plain,
    ? [W] :
      ( ssList(W)
      & ? [X0] :
          ( ~ duplicatefreeP(skolemFOFtoCNF_U_3)
          & skolemFOFtoCNF_U_3 = W
          & skolemFOFtoCNF_V_14 = X0
          & duplicatefreeP(W)
          & ssList(X0)
          & ! [Y] :
              ( ~ ssItem(Y)
              | ( ( ~ memberP(W,Y)
                  | memberP(X0,Y) )
                & ( ~ memberP(X0,Y)
                  | memberP(W,Y) ) ) )
          & ! [Z] :
              ( ~ ssItem(Z)
              | ( ~ memberP(skolemFOFtoCNF_U_3,Z)
                & ~ memberP(skolemFOFtoCNF_V_14,Z) )
              | ( memberP(skolemFOFtoCNF_U_3,Z)
                & memberP(skolemFOFtoCNF_V_14,Z) ) ) ) ),
    inference(conjunct,[],[normalize_2_3]) ).

fof(normalize_2_5,plain,
    ( ssList(skolemFOFtoCNF_W_14)
    & ? [X0] :
        ( ~ duplicatefreeP(skolemFOFtoCNF_U_3)
        & skolemFOFtoCNF_U_3 = skolemFOFtoCNF_W_14
        & skolemFOFtoCNF_V_14 = X0
        & duplicatefreeP(skolemFOFtoCNF_W_14)
        & ssList(X0)
        & ! [Y] :
            ( ~ ssItem(Y)
            | ( ( ~ memberP(X0,Y)
                | memberP(skolemFOFtoCNF_W_14,Y) )
              & ( ~ memberP(skolemFOFtoCNF_W_14,Y)
                | memberP(X0,Y) ) ) )
        & ! [Z] :
            ( ~ ssItem(Z)
            | ( ~ memberP(skolemFOFtoCNF_U_3,Z)
              & ~ memberP(skolemFOFtoCNF_V_14,Z) )
            | ( memberP(skolemFOFtoCNF_U_3,Z)
              & memberP(skolemFOFtoCNF_V_14,Z) ) ) ) ),
    inference(skolemize,[],[normalize_2_4]) ).

fof(normalize_2_6,plain,
    ? [X0] :
      ( ~ duplicatefreeP(skolemFOFtoCNF_U_3)
      & skolemFOFtoCNF_U_3 = skolemFOFtoCNF_W_14
      & skolemFOFtoCNF_V_14 = X0
      & duplicatefreeP(skolemFOFtoCNF_W_14)
      & ssList(X0)
      & ! [Y] :
          ( ~ ssItem(Y)
          | ( ( ~ memberP(X0,Y)
              | memberP(skolemFOFtoCNF_W_14,Y) )
            & ( ~ memberP(skolemFOFtoCNF_W_14,Y)
              | memberP(X0,Y) ) ) )
      & ! [Z] :
          ( ~ ssItem(Z)
          | ( ~ memberP(skolemFOFtoCNF_U_3,Z)
            & ~ memberP(skolemFOFtoCNF_V_14,Z) )
          | ( memberP(skolemFOFtoCNF_U_3,Z)
            & memberP(skolemFOFtoCNF_V_14,Z) ) ) ),
    inference(conjunct,[],[normalize_2_5]) ).

fof(normalize_2_7,plain,
    ( ~ duplicatefreeP(skolemFOFtoCNF_U_3)
    & skolemFOFtoCNF_U_3 = skolemFOFtoCNF_W_14
    & skolemFOFtoCNF_V_14 = skolemFOFtoCNF_X_11
    & duplicatefreeP(skolemFOFtoCNF_W_14)
    & ssList(skolemFOFtoCNF_X_11)
    & ! [Y] :
        ( ~ ssItem(Y)
        | ( ( ~ memberP(skolemFOFtoCNF_W_14,Y)
            | memberP(skolemFOFtoCNF_X_11,Y) )
          & ( ~ memberP(skolemFOFtoCNF_X_11,Y)
            | memberP(skolemFOFtoCNF_W_14,Y) ) ) )
    & ! [Z] :
        ( ~ ssItem(Z)
        | ( ~ memberP(skolemFOFtoCNF_U_3,Z)
          & ~ memberP(skolemFOFtoCNF_V_14,Z) )
        | ( memberP(skolemFOFtoCNF_U_3,Z)
          & memberP(skolemFOFtoCNF_V_14,Z) ) ) ),
    inference(skolemize,[],[normalize_2_6]) ).

fof(normalize_2_8,plain,
    duplicatefreeP(skolemFOFtoCNF_W_14),
    inference(conjunct,[],[normalize_2_7]) ).

fof(normalize_2_9,plain,
    skolemFOFtoCNF_U_3 = skolemFOFtoCNF_W_14,
    inference(conjunct,[],[normalize_2_7]) ).

fof(normalize_2_10,plain,
    ~ duplicatefreeP(skolemFOFtoCNF_U_3),
    inference(conjunct,[],[normalize_2_7]) ).

cnf(refute_2_0,plain,
    duplicatefreeP(skolemFOFtoCNF_W_14),
    inference(canonicalize,[],[normalize_2_8]) ).

cnf(refute_2_1,plain,
    skolemFOFtoCNF_U_3 = skolemFOFtoCNF_W_14,
    inference(canonicalize,[],[normalize_2_9]) ).

cnf(refute_2_2,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_2_3,plain,
    ( X != X
    | X != Y0
    | Y0 = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).

cnf(refute_2_4,plain,
    ( X != Y0
    | Y0 = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_2_2,refute_2_3]) ).

cnf(refute_2_5,plain,
    ( skolemFOFtoCNF_U_3 != skolemFOFtoCNF_W_14
    | skolemFOFtoCNF_W_14 = skolemFOFtoCNF_U_3 ),
    inference(subst,[],[refute_2_4:[bind(X,$fot(skolemFOFtoCNF_U_3)),bind(Y0,$fot(skolemFOFtoCNF_W_14))]]) ).

cnf(refute_2_6,plain,
    skolemFOFtoCNF_W_14 = skolemFOFtoCNF_U_3,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_3,skolemFOFtoCNF_W_14) )],[refute_2_1,refute_2_5]) ).

cnf(refute_2_7,plain,
    ( skolemFOFtoCNF_W_14 != skolemFOFtoCNF_U_3
    | ~ duplicatefreeP(skolemFOFtoCNF_W_14)
    | duplicatefreeP(skolemFOFtoCNF_U_3) ),
    introduced(tautology,[equality,[$cnf( duplicatefreeP(skolemFOFtoCNF_W_14) ),[0],$fot(skolemFOFtoCNF_U_3)]]) ).

cnf(refute_2_8,plain,
    ( ~ duplicatefreeP(skolemFOFtoCNF_W_14)
    | duplicatefreeP(skolemFOFtoCNF_U_3) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_14,skolemFOFtoCNF_U_3) )],[refute_2_6,refute_2_7]) ).

cnf(refute_2_9,plain,
    duplicatefreeP(skolemFOFtoCNF_U_3),
    inference(resolve,[$cnf( duplicatefreeP(skolemFOFtoCNF_W_14) )],[refute_2_0,refute_2_8]) ).

cnf(refute_2_10,plain,
    ~ duplicatefreeP(skolemFOFtoCNF_U_3),
    inference(canonicalize,[],[normalize_2_10]) ).

cnf(refute_2_11,plain,
    $false,
    inference(resolve,[$cnf( duplicatefreeP(skolemFOFtoCNF_U_3) )],[refute_2_9,refute_2_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SWC001+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.11  % Command  : metis --show proof --show saturation %s
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 600
% 0.11/0.31  % DateTime : Sun Jun 12 08:30:10 EDT 2022
% 0.11/0.31  % CPUTime  : 
% 0.11/0.31  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.88/3.10  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.88/3.10  
% 2.88/3.10  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.88/3.11  
%------------------------------------------------------------------------------