TSTP Solution File: SWC349+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWC349+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 21:27:51 EDT 2022

% Result   : Theorem 0.16s 0.40s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   37 (  14 unt;   0 def)
%            Number of atoms       :  128 (  53 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  137 (  46   ~;  18   |;  60   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   37 (   0 sgn  15   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ax45,axiom,
    ! [U] :
      ( ssList(U)
     => frontsegP(U,nil) ) ).

fof(co1,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X0] :
                  ( ssList(X0)
                 => ( nil != W
                    | V != X0
                    | U != W
                    | ~ neq(V,nil)
                    | frontsegP(V,U) ) ) ) ) ) ).

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

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

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

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

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

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

fof(normalize_0_4,plain,
    ssList(skolemFOFtoCNF_V_12),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [U] :
      ( ~ ssList(U)
      | frontsegP(U,nil) ),
    inference(canonicalize,[],[ax45]) ).

fof(normalize_0_6,plain,
    ! [U] :
      ( ~ ssList(U)
      | frontsegP(U,nil) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ? [W] :
      ( ssList(W)
      & ? [X0] :
          ( ~ frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1)
          & nil = W
          & skolemFOFtoCNF_U_1 = W
          & skolemFOFtoCNF_V_12 = X0
          & neq(skolemFOFtoCNF_V_12,nil)
          & ssList(X0) ) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_8,plain,
    ( ssList(skolemFOFtoCNF_W_12)
    & ? [X0] :
        ( ~ frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1)
        & nil = skolemFOFtoCNF_W_12
        & skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
        & skolemFOFtoCNF_V_12 = X0
        & neq(skolemFOFtoCNF_V_12,nil)
        & ssList(X0) ) ),
    inference(skolemize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ? [X0] :
      ( ~ frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1)
      & nil = skolemFOFtoCNF_W_12
      & skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
      & skolemFOFtoCNF_V_12 = X0
      & neq(skolemFOFtoCNF_V_12,nil)
      & ssList(X0) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ( ~ frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1)
    & nil = skolemFOFtoCNF_W_12
    & skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12
    & skolemFOFtoCNF_V_12 = skolemFOFtoCNF_X_9
    & neq(skolemFOFtoCNF_V_12,nil)
    & ssList(skolemFOFtoCNF_X_9) ),
    inference(skolemize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ~ frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_13,plain,
    nil = skolemFOFtoCNF_W_12,
    inference(conjunct,[],[normalize_0_10]) ).

cnf(refute_0_0,plain,
    ssList(skolemFOFtoCNF_V_12),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_1,plain,
    ( ~ ssList(U)
    | frontsegP(U,nil) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    ( ~ ssList(skolemFOFtoCNF_V_12)
    | frontsegP(skolemFOFtoCNF_V_12,nil) ),
    inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_V_12))]]) ).

cnf(refute_0_3,plain,
    frontsegP(skolemFOFtoCNF_V_12,nil),
    inference(resolve,[$cnf( ssList(skolemFOFtoCNF_V_12) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ~ frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_5,plain,
    skolemFOFtoCNF_U_1 = skolemFOFtoCNF_W_12,
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_6,plain,
    nil = skolemFOFtoCNF_W_12,
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_7,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_8,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_9,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( nil != skolemFOFtoCNF_W_12
    | skolemFOFtoCNF_W_12 = nil ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(nil)),bind(Y,$fot(skolemFOFtoCNF_W_12))]]) ).

cnf(refute_0_11,plain,
    skolemFOFtoCNF_W_12 = nil,
    inference(resolve,[$cnf( $equal(nil,skolemFOFtoCNF_W_12) )],[refute_0_6,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
    | skolemFOFtoCNF_W_12 != nil
    | skolemFOFtoCNF_U_1 = nil ),
    introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_U_1,nil) ),[0],$fot(skolemFOFtoCNF_W_12)]]) ).

cnf(refute_0_13,plain,
    ( skolemFOFtoCNF_U_1 != skolemFOFtoCNF_W_12
    | skolemFOFtoCNF_U_1 = nil ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W_12,nil) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    skolemFOFtoCNF_U_1 = nil,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,skolemFOFtoCNF_W_12) )],[refute_0_5,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( skolemFOFtoCNF_U_1 != nil
    | ~ frontsegP(skolemFOFtoCNF_V_12,nil)
    | frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1) ),
    introduced(tautology,[equality,[$cnf( ~ frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1) ),[1],$fot(nil)]]) ).

cnf(refute_0_16,plain,
    ( ~ frontsegP(skolemFOFtoCNF_V_12,nil)
    | frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U_1,nil) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    ~ frontsegP(skolemFOFtoCNF_V_12,nil),
    inference(resolve,[$cnf( frontsegP(skolemFOFtoCNF_V_12,skolemFOFtoCNF_U_1) )],[refute_0_16,refute_0_4]) ).

cnf(refute_0_18,plain,
    $false,
    inference(resolve,[$cnf( frontsegP(skolemFOFtoCNF_V_12,nil) )],[refute_0_3,refute_0_17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SWC349+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.11  % Command  : metis --show proof --show saturation %s
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 600
% 0.11/0.31  % DateTime : Sun Jun 12 22:32:26 EDT 2022
% 0.11/0.31  % CPUTime  : 
% 0.16/0.31  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.16/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.40  
% 0.16/0.40  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.16/0.40  
%------------------------------------------------------------------------------