TSTP Solution File: SWC035+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWC035+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 21:26:12 EDT 2022

% Result   : Theorem 0.19s 0.40s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   46 (  20 unt;   0 def)
%            Number of atoms       :  142 ( 109 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  148 (  52   ~;  24   |;  60   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   33 (   0 sgn  12   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X0] :
                  ( ssList(X0)
                 => ( nil != V
                    | V != X0
                    | U != W
                    | X0 != W
                    | nil = U ) ) ) ) ) ).

fof(subgoal_0,plain,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X0] :
                  ( ( ssList(X0)
                    & ~ ( nil != V )
                    & ~ ( V != X0 )
                    & ~ ( U != W )
                    & ~ ( X0 != W ) )
                 => nil = U ) ) ) ),
    inference(strip,[],[co1]) ).

fof(negate_0_0,plain,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X0] :
                    ( ( ssList(X0)
                      & ~ ( nil != V )
                      & ~ ( V != X0 )
                      & ~ ( U != W )
                      & ~ ( X0 != W ) )
                   => nil = U ) ) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X0] :
                  ( nil != U
                  & U = W
                  & V = X0
                  & X0 = W
                  & nil = V
                  & ssList(X0) ) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ssList(skolemFOFtoCNF_U_1)
    & ? [V] :
        ( ssList(V)
        & ? [W] :
            ( ssList(W)
            & ? [X0] :
                ( nil != skolemFOFtoCNF_U_1
                & V = X0
                & X0 = W
                & nil = V
                & skolemFOFtoCNF_U_1 = W
                & ssList(X0) ) ) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ? [V] :
      ( ssList(V)
      & ? [W] :
          ( ssList(W)
          & ? [X0] :
              ( nil != skolemFOFtoCNF_U_1
              & V = X0
              & X0 = W
              & nil = V
              & skolemFOFtoCNF_U_1 = W
              & ssList(X0) ) ) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( ssList(skolemFOFtoCNF_V_12)
    & ? [W] :
        ( ssList(W)
        & ? [X0] :
            ( nil != skolemFOFtoCNF_U_1
            & X0 = W
            & nil = skolemFOFtoCNF_V_12
            & skolemFOFtoCNF_U_1 = W
            & skolemFOFtoCNF_V_12 = X0
            & ssList(X0) ) ) ),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [W] :
      ( ssList(W)
      & ? [X0] :
          ( nil != skolemFOFtoCNF_U_1
          & X0 = W
          & nil = skolemFOFtoCNF_V_12
          & skolemFOFtoCNF_U_1 = W
          & skolemFOFtoCNF_V_12 = X0
          & ssList(X0) ) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ( ssList(skolemFOFtoCNF_W_12)
    & ? [X0] :
        ( nil != skolemFOFtoCNF_U_1
        & X0 = skolemFOFtoCNF_W_12
        & nil = skolemFOFtoCNF_V_12
        & skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
        & skolemFOFtoCNF_V_12 = X0
        & ssList(X0) ) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ? [X0] :
      ( nil != skolemFOFtoCNF_U_1
      & X0 = skolemFOFtoCNF_W_12
      & nil = skolemFOFtoCNF_V_12
      & skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
      & skolemFOFtoCNF_V_12 = X0
      & ssList(X0) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ( nil != skolemFOFtoCNF_U_1
    & nil = skolemFOFtoCNF_V_12
    & skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
    & skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
    & skolemFOFtoCNF_X_9 = skolemFOFtoCNF_W_12
    & ssList(skolemFOFtoCNF_X_9) ),
    inference(skolemize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    nil != skolemFOFtoCNF_U_1,
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    skolemFOFtoCNF_X_9 = skolemFOFtoCNF_W_12,
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_10,plain,
    skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_11,plain,
    nil = skolemFOFtoCNF_V_12,
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_12,plain,
    skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
    inference(conjunct,[],[normalize_0_7]) ).

cnf(refute_0_0,plain,
    nil != skolemFOFtoCNF_U_1,
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_1,plain,
    skolemFOFtoCNF_X_9 = skolemFOFtoCNF_W_12,
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_2,plain,
    skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9,
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_3,plain,
    nil = skolemFOFtoCNF_V_12,
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_4,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_5,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_6,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( nil != skolemFOFtoCNF_V_12
    | skolemFOFtoCNF_V_12 = nil ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_V_12))]]) ).

cnf(refute_0_8,plain,
    skolemFOFtoCNF_V_12 = nil,
    inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_V_12) )],[refute_0_3,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( skolemFOFtoCNF_V_12 != nil
    | skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
    | nil = skolemFOFtoCNF_X_9 ),
    introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) ),[0],$fot(nil)]]) ).

cnf(refute_0_10,plain,
    ( skolemFOFtoCNF_V_12 != skolemFOFtoCNF_X_9
    | nil = skolemFOFtoCNF_X_9 ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,nil) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    nil = skolemFOFtoCNF_X_9,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V_12,skolemFOFtoCNF_X_9) )],[refute_0_2,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( nil != skolemFOFtoCNF_X_9
    | skolemFOFtoCNF_X_9 = nil ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_X_9))]]) ).

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

cnf(refute_0_14,plain,
    ( skolemFOFtoCNF_X_9 != nil
    | skolemFOFtoCNF_X_9 != skolemFOFtoCNF_W_12
    | nil = skolemFOFtoCNF_W_12 ),
    introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12) ),[0],$fot(nil)]]) ).

cnf(refute_0_15,plain,
    ( skolemFOFtoCNF_X_9 != skolemFOFtoCNF_W_12
    | nil = skolemFOFtoCNF_W_12 ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,nil) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_17,plain,
    ( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
    | skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1 ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y,$fot(skolemFOFtoCNF_W_12))]]) ).

cnf(refute_0_18,plain,
    skolemFOFtoCNF_W_12 = skolemFOFtoCNF_U_1,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( nil != skolemFOFtoCNF_W_12
    | skolemFOFtoCNF_W_12 != skolemFOFtoCNF_U_1
    | nil = skolemFOFtoCNF_U_1 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_U_1) ),[0],$fot(skolemFOFtoCNF_W_12)]]) ).

cnf(refute_0_20,plain,
    ( nil != skolemFOFtoCNF_W_12
    | nil = skolemFOFtoCNF_U_1 ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,skolemFOFtoCNF_U_1) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( skolemFOFtoCNF_X_9 != skolemFOFtoCNF_W_12
    | nil = skolemFOFtoCNF_U_1 ),
    inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_12) )],[refute_0_15,refute_0_20]) ).

cnf(refute_0_22,plain,
    nil = skolemFOFtoCNF_U_1,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X_9,skolemFOFtoCNF_W_12) )],[refute_0_1,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( nil != skolemFOFtoCNF_U_1
    | skolemFOFtoCNF_U_1 = nil ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_U_1))]]) ).

cnf(refute_0_24,plain,
    skolemFOFtoCNF_U_1 = nil,
    inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_1) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( nil != nil
    | skolemFOFtoCNF_U_1 != nil
    | nil = skolemFOFtoCNF_U_1 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(nil,skolemFOFtoCNF_U_1) ),[1],$fot(nil)]]) ).

cnf(refute_0_26,plain,
    ( nil != nil
    | nil = skolemFOFtoCNF_U_1 ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,nil) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    nil != nil,
    inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_U_1) )],[refute_0_26,refute_0_0]) ).

cnf(refute_0_28,plain,
    nil = nil,
    introduced(tautology,[refl,[$fot(nil)]]) ).

cnf(refute_0_29,plain,
    $false,
    inference(resolve,[$cnf( $equal(nil,nil) )],[refute_0_28,refute_0_27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWC035+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jun 12 23:25:48 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.40  
% 0.19/0.40  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.40  
%------------------------------------------------------------------------------