TSTP Solution File: SWC018+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC018+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n012.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  : 300s
% DateTime : Wed Aug 31 18:38:14 EDT 2022

% Result   : Theorem 0.15s 0.47s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  105 (  14 unt;   0 def)
%            Number of atoms       :  617 ( 193 equ)
%            Maximal formula atoms :   46 (   5 avg)
%            Number of connectives :  827 ( 315   ~; 286   |; 185   &)
%                                         (  15 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   16 (  14 usr;  10 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  175 ( 122   !;  53   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f429,plain,
    $false,
    inference(avatar_sat_refutation,[],[f256,f269,f275,f281,f284,f296,f308,f311,f339,f401,f404,f428]) ).

fof(f428,plain,
    ( ~ spl14_1
    | ~ spl14_6
    | spl14_11 ),
    inference(avatar_contradiction_clause,[],[f427]) ).

fof(f427,plain,
    ( $false
    | ~ spl14_1
    | ~ spl14_6
    | spl14_11 ),
    inference(subsumption_resolution,[],[f425,f307]) ).

fof(f307,plain,
    ( ~ neq(nil,nil)
    | spl14_11 ),
    inference(avatar_component_clause,[],[f305]) ).

fof(f305,plain,
    ( spl14_11
  <=> neq(nil,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_11])]) ).

fof(f425,plain,
    ( neq(nil,nil)
    | ~ spl14_1
    | ~ spl14_6 ),
    inference(backward_demodulation,[],[f251,f273]) ).

fof(f273,plain,
    ( nil = sK4
    | ~ spl14_6 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f271,plain,
    ( spl14_6
  <=> nil = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_6])]) ).

fof(f251,plain,
    ( neq(sK4,nil)
    | ~ spl14_1 ),
    inference(avatar_component_clause,[],[f249]) ).

fof(f249,plain,
    ( spl14_1
  <=> neq(sK4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).

fof(f404,plain,
    ( ~ spl14_6
    | spl14_2 ),
    inference(avatar_split_clause,[],[f403,f253,f271]) ).

fof(f253,plain,
    ( spl14_2
  <=> nil = sK5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).

fof(f403,plain,
    ( nil = sK5
    | nil != sK4 ),
    inference(subsumption_resolution,[],[f402,f176]) ).

fof(f176,plain,
    ssList(sK5),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,plain,
    ( ssList(sK3)
    & ssList(sK4)
    & ( ( nil = sK4
        & nil != sK3 )
      | ( ! [X4] :
            ( ~ ssList(X4)
            | ~ frontsegP(sK4,X4)
            | ~ frontsegP(sK3,X4)
            | ~ neq(X4,nil) )
        & neq(sK4,nil) ) )
    & ( nil = sK6
      | nil != sK5 )
    & equalelemsP(sK5)
    & app(sK5,sK7) = sK6
    & ! [X6] :
        ( ! [X7] :
            ( sK7 != app(cons(X6,nil),X7)
            | ! [X8] :
                ( ~ ssList(X8)
                | app(X8,cons(X6,nil)) != sK5 )
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & ssList(sK7)
    & sK6 = sK4
    & ssList(sK6)
    & sK3 = sK5
    & ssList(sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f141,f146,f145,f144,f143,f142]) ).

fof(f142,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X1
                        & nil != X0 )
                      | ( ! [X4] :
                            ( ~ ssList(X4)
                            | ~ frontsegP(X1,X4)
                            | ~ frontsegP(X0,X4)
                            | ~ neq(X4,nil) )
                        & neq(X1,nil) ) )
                    & ( nil = X3
                      | nil != X2 )
                    & ? [X5] :
                        ( equalelemsP(X2)
                        & app(X2,X5) = X3
                        & ! [X6] :
                            ( ! [X7] :
                                ( app(cons(X6,nil),X7) != X5
                                | ! [X8] :
                                    ( ~ ssList(X8)
                                    | app(X8,cons(X6,nil)) != X2 )
                                | ~ ssList(X7) )
                            | ~ ssItem(X6) )
                        & ssList(X5) )
                    & X1 = X3
                    & ssList(X3)
                    & X0 = X2 )
                & ssList(X2) ) ) )
   => ( ssList(sK3)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X1
                      & nil != sK3 )
                    | ( ! [X4] :
                          ( ~ ssList(X4)
                          | ~ frontsegP(X1,X4)
                          | ~ frontsegP(sK3,X4)
                          | ~ neq(X4,nil) )
                      & neq(X1,nil) ) )
                  & ( nil = X3
                    | nil != X2 )
                  & ? [X5] :
                      ( equalelemsP(X2)
                      & app(X2,X5) = X3
                      & ! [X6] :
                          ( ! [X7] :
                              ( app(cons(X6,nil),X7) != X5
                              | ! [X8] :
                                  ( ~ ssList(X8)
                                  | app(X8,cons(X6,nil)) != X2 )
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & ssList(X5) )
                  & X1 = X3
                  & ssList(X3)
                  & sK3 = X2 )
              & ssList(X2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X1
                    & nil != sK3 )
                  | ( ! [X4] :
                        ( ~ ssList(X4)
                        | ~ frontsegP(X1,X4)
                        | ~ frontsegP(sK3,X4)
                        | ~ neq(X4,nil) )
                    & neq(X1,nil) ) )
                & ( nil = X3
                  | nil != X2 )
                & ? [X5] :
                    ( equalelemsP(X2)
                    & app(X2,X5) = X3
                    & ! [X6] :
                        ( ! [X7] :
                            ( app(cons(X6,nil),X7) != X5
                            | ! [X8] :
                                ( ~ ssList(X8)
                                | app(X8,cons(X6,nil)) != X2 )
                            | ~ ssList(X7) )
                        | ~ ssItem(X6) )
                    & ssList(X5) )
                & X1 = X3
                & ssList(X3)
                & sK3 = X2 )
            & ssList(X2) ) )
   => ( ssList(sK4)
      & ? [X2] :
          ( ? [X3] :
              ( ( ( nil = sK4
                  & nil != sK3 )
                | ( ! [X4] :
                      ( ~ ssList(X4)
                      | ~ frontsegP(sK4,X4)
                      | ~ frontsegP(sK3,X4)
                      | ~ neq(X4,nil) )
                  & neq(sK4,nil) ) )
              & ( nil = X3
                | nil != X2 )
              & ? [X5] :
                  ( equalelemsP(X2)
                  & app(X2,X5) = X3
                  & ! [X6] :
                      ( ! [X7] :
                          ( app(cons(X6,nil),X7) != X5
                          | ! [X8] :
                              ( ~ ssList(X8)
                              | app(X8,cons(X6,nil)) != X2 )
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & ssList(X5) )
              & sK4 = X3
              & ssList(X3)
              & sK3 = X2 )
          & ssList(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f144,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = sK4
                & nil != sK3 )
              | ( ! [X4] :
                    ( ~ ssList(X4)
                    | ~ frontsegP(sK4,X4)
                    | ~ frontsegP(sK3,X4)
                    | ~ neq(X4,nil) )
                & neq(sK4,nil) ) )
            & ( nil = X3
              | nil != X2 )
            & ? [X5] :
                ( equalelemsP(X2)
                & app(X2,X5) = X3
                & ! [X6] :
                    ( ! [X7] :
                        ( app(cons(X6,nil),X7) != X5
                        | ! [X8] :
                            ( ~ ssList(X8)
                            | app(X8,cons(X6,nil)) != X2 )
                        | ~ ssList(X7) )
                    | ~ ssItem(X6) )
                & ssList(X5) )
            & sK4 = X3
            & ssList(X3)
            & sK3 = X2 )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK4
              & nil != sK3 )
            | ( ! [X4] :
                  ( ~ ssList(X4)
                  | ~ frontsegP(sK4,X4)
                  | ~ frontsegP(sK3,X4)
                  | ~ neq(X4,nil) )
              & neq(sK4,nil) ) )
          & ( nil = X3
            | nil != sK5 )
          & ? [X5] :
              ( equalelemsP(sK5)
              & app(sK5,X5) = X3
              & ! [X6] :
                  ( ! [X7] :
                      ( app(cons(X6,nil),X7) != X5
                      | ! [X8] :
                          ( ~ ssList(X8)
                          | app(X8,cons(X6,nil)) != sK5 )
                      | ~ ssList(X7) )
                  | ~ ssItem(X6) )
              & ssList(X5) )
          & sK4 = X3
          & ssList(X3)
          & sK3 = sK5 )
      & ssList(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f145,plain,
    ( ? [X3] :
        ( ( ( nil = sK4
            & nil != sK3 )
          | ( ! [X4] :
                ( ~ ssList(X4)
                | ~ frontsegP(sK4,X4)
                | ~ frontsegP(sK3,X4)
                | ~ neq(X4,nil) )
            & neq(sK4,nil) ) )
        & ( nil = X3
          | nil != sK5 )
        & ? [X5] :
            ( equalelemsP(sK5)
            & app(sK5,X5) = X3
            & ! [X6] :
                ( ! [X7] :
                    ( app(cons(X6,nil),X7) != X5
                    | ! [X8] :
                        ( ~ ssList(X8)
                        | app(X8,cons(X6,nil)) != sK5 )
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            & ssList(X5) )
        & sK4 = X3
        & ssList(X3)
        & sK3 = sK5 )
   => ( ( ( nil = sK4
          & nil != sK3 )
        | ( ! [X4] :
              ( ~ ssList(X4)
              | ~ frontsegP(sK4,X4)
              | ~ frontsegP(sK3,X4)
              | ~ neq(X4,nil) )
          & neq(sK4,nil) ) )
      & ( nil = sK6
        | nil != sK5 )
      & ? [X5] :
          ( equalelemsP(sK5)
          & app(sK5,X5) = sK6
          & ! [X6] :
              ( ! [X7] :
                  ( app(cons(X6,nil),X7) != X5
                  | ! [X8] :
                      ( ~ ssList(X8)
                      | app(X8,cons(X6,nil)) != sK5 )
                  | ~ ssList(X7) )
              | ~ ssItem(X6) )
          & ssList(X5) )
      & sK6 = sK4
      & ssList(sK6)
      & sK3 = sK5 ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ( ? [X5] :
        ( equalelemsP(sK5)
        & app(sK5,X5) = sK6
        & ! [X6] :
            ( ! [X7] :
                ( app(cons(X6,nil),X7) != X5
                | ! [X8] :
                    ( ~ ssList(X8)
                    | app(X8,cons(X6,nil)) != sK5 )
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & ssList(X5) )
   => ( equalelemsP(sK5)
      & app(sK5,sK7) = sK6
      & ! [X6] :
          ( ! [X7] :
              ( sK7 != app(cons(X6,nil),X7)
              | ! [X8] :
                  ( ~ ssList(X8)
                  | app(X8,cons(X6,nil)) != sK5 )
              | ~ ssList(X7) )
          | ~ ssItem(X6) )
      & ssList(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f141,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X1
                      & nil != X0 )
                    | ( ! [X4] :
                          ( ~ ssList(X4)
                          | ~ frontsegP(X1,X4)
                          | ~ frontsegP(X0,X4)
                          | ~ neq(X4,nil) )
                      & neq(X1,nil) ) )
                  & ( nil = X3
                    | nil != X2 )
                  & ? [X5] :
                      ( equalelemsP(X2)
                      & app(X2,X5) = X3
                      & ! [X6] :
                          ( ! [X7] :
                              ( app(cons(X6,nil),X7) != X5
                              | ! [X8] :
                                  ( ~ ssList(X8)
                                  | app(X8,cons(X6,nil)) != X2 )
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & ssList(X5) )
                  & X1 = X3
                  & ssList(X3)
                  & X0 = X2 )
              & ssList(X2) ) ) ),
    inference(rectify,[],[f104]) ).

fof(f104,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X1
                      & nil != X0 )
                    | ( ! [X8] :
                          ( ~ ssList(X8)
                          | ~ frontsegP(X1,X8)
                          | ~ frontsegP(X0,X8)
                          | ~ neq(X8,nil) )
                      & neq(X1,nil) ) )
                  & ( nil = X3
                    | nil != X2 )
                  & ? [X4] :
                      ( equalelemsP(X2)
                      & app(X2,X4) = X3
                      & ! [X5] :
                          ( ! [X6] :
                              ( app(cons(X5,nil),X6) != X4
                              | ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(X7,cons(X5,nil)) != X2 )
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & ssList(X4) )
                  & X1 = X3
                  & ssList(X3)
                  & X0 = X2 )
              & ssList(X2) ) ) ),
    inference(flattening,[],[f103]) ).

fof(f103,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil = X3
                    | nil != X2 )
                  & X1 = X3
                  & ? [X4] :
                      ( app(X2,X4) = X3
                      & ! [X5] :
                          ( ! [X6] :
                              ( app(cons(X5,nil),X6) != X4
                              | ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(X7,cons(X5,nil)) != X2 )
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & equalelemsP(X2)
                      & ssList(X4) )
                  & ( ( nil = X1
                      & nil != X0 )
                    | ( ! [X8] :
                          ( ~ ssList(X8)
                          | ~ frontsegP(X1,X8)
                          | ~ frontsegP(X0,X8)
                          | ~ neq(X8,nil) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( nil != X3
                        & nil = X2 )
                      | X1 != X3
                      | ! [X4] :
                          ( ssList(X4)
                         => ( app(X2,X4) != X3
                            | ? [X5] :
                                ( ? [X6] :
                                    ( app(cons(X5,nil),X6) = X4
                                    & ssList(X6)
                                    & ? [X7] :
                                        ( app(X7,cons(X5,nil)) = X2
                                        & ssList(X7) ) )
                                & ssItem(X5) )
                            | ~ equalelemsP(X2) ) )
                      | ( ( ? [X8] :
                              ( frontsegP(X0,X8)
                              & neq(X8,nil)
                              & ssList(X8)
                              & frontsegP(X1,X8) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | X0 != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( nil != X3
                      & nil = X2 )
                    | X1 != X3
                    | ! [X4] :
                        ( ssList(X4)
                       => ( app(X2,X4) != X3
                          | ? [X5] :
                              ( ? [X6] :
                                  ( app(cons(X5,nil),X6) = X4
                                  & ssList(X6)
                                  & ? [X7] :
                                      ( app(X7,cons(X5,nil)) = X2
                                      & ssList(X7) ) )
                              & ssItem(X5) )
                          | ~ equalelemsP(X2) ) )
                    | ( ( ? [X8] :
                            ( frontsegP(X0,X8)
                            & neq(X8,nil)
                            & ssList(X8)
                            & frontsegP(X1,X8) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | X0 != X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f402,plain,
    ( nil != sK4
    | nil = sK5
    | ~ ssList(sK5) ),
    inference(subsumption_resolution,[],[f356,f180]) ).

fof(f180,plain,
    ssList(sK7),
    inference(cnf_transformation,[],[f147]) ).

fof(f356,plain,
    ( ~ ssList(sK7)
    | nil = sK5
    | nil != sK4
    | ~ ssList(sK5) ),
    inference(superposition,[],[f193,f234]) ).

fof(f234,plain,
    app(sK5,sK7) = sK4,
    inference(definition_unfolding,[],[f182,f179]) ).

fof(f179,plain,
    sK6 = sK4,
    inference(cnf_transformation,[],[f147]) ).

fof(f182,plain,
    app(sK5,sK7) = sK6,
    inference(cnf_transformation,[],[f147]) ).

fof(f193,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | ~ ssList(X0)
      | nil = X0
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) )
            & ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 ) )
          | ~ ssList(X1) ) ),
    inference(flattening,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) )
            & ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 ) )
          | ~ ssList(X1) ) ),
    inference(nnf_transformation,[],[f128]) ).

fof(f128,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( nil = X0
              & nil = X1 )
          <=> nil = app(X0,X1) )
          | ~ ssList(X1) ) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( nil = X0
              & nil = X1 )
          <=> nil = app(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).

fof(f401,plain,
    spl14_9,
    inference(avatar_split_clause,[],[f397,f293]) ).

fof(f293,plain,
    ( spl14_9
  <=> frontsegP(sK4,sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_9])]) ).

fof(f397,plain,
    frontsegP(sK4,sK5),
    inference(subsumption_resolution,[],[f396,f176]) ).

fof(f396,plain,
    ( ~ ssList(sK5)
    | frontsegP(sK4,sK5) ),
    inference(subsumption_resolution,[],[f390,f180]) ).

fof(f390,plain,
    ( ~ ssList(sK7)
    | frontsegP(sK4,sK5)
    | ~ ssList(sK5) ),
    inference(superposition,[],[f384,f234]) ).

fof(f384,plain,
    ! [X3,X1] :
      ( frontsegP(app(X1,X3),X1)
      | ~ ssList(X1)
      | ~ ssList(X3) ),
    inference(subsumption_resolution,[],[f236,f228]) ).

fof(f228,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X0)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ssList(app(X0,X1)) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f236,plain,
    ! [X3,X1] :
      ( ~ ssList(X3)
      | ~ ssList(app(X1,X3))
      | frontsegP(app(X1,X3),X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f173]) ).

fof(f173,plain,
    ! [X3,X0,X1] :
      ( ~ ssList(X1)
      | frontsegP(X0,X1)
      | app(X1,X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( ( app(X1,sK2(X0,X1)) = X0
                & ssList(sK2(X0,X1)) )
              | ~ frontsegP(X0,X1) )
            & ( frontsegP(X0,X1)
              | ! [X3] :
                  ( app(X1,X3) != X0
                  | ~ ssList(X3) ) ) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f138,f139]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( app(X1,X2) = X0
          & ssList(X2) )
     => ( app(X1,sK2(X0,X1)) = X0
        & ssList(sK2(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f138,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( ? [X2] :
                  ( app(X1,X2) = X0
                  & ssList(X2) )
              | ~ frontsegP(X0,X1) )
            & ( frontsegP(X0,X1)
              | ! [X3] :
                  ( app(X1,X3) != X0
                  | ~ ssList(X3) ) ) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f137]) ).

fof(f137,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( ? [X2] :
                  ( app(X1,X2) = X0
                  & ssList(X2) )
              | ~ frontsegP(X0,X1) )
            & ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) )
          <=> frontsegP(X0,X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) )
          <=> frontsegP(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

fof(f339,plain,
    ( spl14_2
    | ~ spl14_3
    | spl14_8 ),
    inference(avatar_contradiction_clause,[],[f338]) ).

fof(f338,plain,
    ( $false
    | spl14_2
    | ~ spl14_3
    | spl14_8 ),
    inference(subsumption_resolution,[],[f337,f176]) ).

fof(f337,plain,
    ( ~ ssList(sK5)
    | spl14_2
    | ~ spl14_3
    | spl14_8 ),
    inference(subsumption_resolution,[],[f336,f259]) ).

fof(f259,plain,
    ( ssList(nil)
    | ~ spl14_3 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f258,plain,
    ( spl14_3
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).

fof(f336,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK5)
    | spl14_2
    | spl14_8 ),
    inference(subsumption_resolution,[],[f329,f255]) ).

fof(f255,plain,
    ( nil != sK5
    | spl14_2 ),
    inference(avatar_component_clause,[],[f253]) ).

fof(f329,plain,
    ( nil = sK5
    | ~ ssList(nil)
    | ~ ssList(sK5)
    | spl14_8 ),
    inference(resolution,[],[f206,f291]) ).

fof(f291,plain,
    ( ~ neq(sK5,nil)
    | spl14_8 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f289,plain,
    ( spl14_8
  <=> neq(sK5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_8])]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f157]) ).

fof(f157,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) ) ) ),
    inference(nnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( X0 != X1
          <=> neq(X0,X1) ) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( X0 != X1
          <=> neq(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f311,plain,
    spl14_10,
    inference(avatar_contradiction_clause,[],[f310]) ).

fof(f310,plain,
    ( $false
    | spl14_10 ),
    inference(subsumption_resolution,[],[f309,f189]) ).

fof(f189,plain,
    ssList(sK4),
    inference(cnf_transformation,[],[f147]) ).

fof(f309,plain,
    ( ~ ssList(sK4)
    | spl14_10 ),
    inference(resolution,[],[f303,f211]) ).

fof(f211,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).

fof(f303,plain,
    ( ~ frontsegP(sK4,nil)
    | spl14_10 ),
    inference(avatar_component_clause,[],[f301]) ).

fof(f301,plain,
    ( spl14_10
  <=> frontsegP(sK4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_10])]) ).

fof(f308,plain,
    ( ~ spl14_10
    | ~ spl14_11
    | ~ spl14_3
    | ~ spl14_5 ),
    inference(avatar_split_clause,[],[f299,f267,f258,f305,f301]) ).

fof(f267,plain,
    ( spl14_5
  <=> ! [X4] :
        ( ~ neq(X4,nil)
        | ~ frontsegP(sK4,X4)
        | ~ frontsegP(sK5,X4)
        | ~ ssList(X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_5])]) ).

fof(f299,plain,
    ( ~ neq(nil,nil)
    | ~ frontsegP(sK4,nil)
    | ~ spl14_3
    | ~ spl14_5 ),
    inference(subsumption_resolution,[],[f298,f176]) ).

fof(f298,plain,
    ( ~ ssList(sK5)
    | ~ frontsegP(sK4,nil)
    | ~ neq(nil,nil)
    | ~ spl14_3
    | ~ spl14_5 ),
    inference(subsumption_resolution,[],[f297,f259]) ).

fof(f297,plain,
    ( ~ frontsegP(sK4,nil)
    | ~ neq(nil,nil)
    | ~ ssList(nil)
    | ~ ssList(sK5)
    | ~ spl14_5 ),
    inference(resolution,[],[f211,f268]) ).

fof(f268,plain,
    ( ! [X4] :
        ( ~ frontsegP(sK5,X4)
        | ~ frontsegP(sK4,X4)
        | ~ neq(X4,nil)
        | ~ ssList(X4) )
    | ~ spl14_5 ),
    inference(avatar_component_clause,[],[f267]) ).

fof(f296,plain,
    ( ~ spl14_8
    | ~ spl14_9
    | ~ spl14_5 ),
    inference(avatar_split_clause,[],[f287,f267,f293,f289]) ).

fof(f287,plain,
    ( ~ frontsegP(sK4,sK5)
    | ~ neq(sK5,nil)
    | ~ spl14_5 ),
    inference(subsumption_resolution,[],[f286,f176]) ).

fof(f286,plain,
    ( ~ ssList(sK5)
    | ~ neq(sK5,nil)
    | ~ frontsegP(sK4,sK5)
    | ~ spl14_5 ),
    inference(duplicate_literal_removal,[],[f285]) ).

fof(f285,plain,
    ( ~ neq(sK5,nil)
    | ~ ssList(sK5)
    | ~ frontsegP(sK4,sK5)
    | ~ ssList(sK5)
    | ~ spl14_5 ),
    inference(resolution,[],[f172,f268]) ).

fof(f172,plain,
    ! [X0] :
      ( frontsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f114,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | frontsegP(X0,X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).

fof(f284,plain,
    spl14_3,
    inference(avatar_split_clause,[],[f168,f258]) ).

fof(f168,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f281,plain,
    ( ~ spl14_2
    | spl14_6 ),
    inference(avatar_split_clause,[],[f233,f271,f253]) ).

fof(f233,plain,
    ( nil = sK4
    | nil != sK5 ),
    inference(definition_unfolding,[],[f184,f179]) ).

fof(f184,plain,
    ( nil = sK6
    | nil != sK5 ),
    inference(cnf_transformation,[],[f147]) ).

fof(f275,plain,
    ( spl14_5
    | spl14_6 ),
    inference(avatar_split_clause,[],[f230,f271,f267]) ).

fof(f230,plain,
    ! [X4] :
      ( nil = sK4
      | ~ frontsegP(sK4,X4)
      | ~ frontsegP(sK5,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f188,f177]) ).

fof(f177,plain,
    sK3 = sK5,
    inference(cnf_transformation,[],[f147]) ).

fof(f188,plain,
    ! [X4] :
      ( nil = sK4
      | ~ ssList(X4)
      | ~ frontsegP(sK4,X4)
      | ~ frontsegP(sK3,X4)
      | ~ neq(X4,nil) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f269,plain,
    ( ~ spl14_2
    | spl14_5 ),
    inference(avatar_split_clause,[],[f231,f267,f253]) ).

fof(f231,plain,
    ! [X4] :
      ( ~ neq(X4,nil)
      | nil != sK5
      | ~ ssList(X4)
      | ~ frontsegP(sK5,X4)
      | ~ frontsegP(sK4,X4) ),
    inference(definition_unfolding,[],[f186,f177,f177]) ).

fof(f186,plain,
    ! [X4] :
      ( nil != sK3
      | ~ ssList(X4)
      | ~ frontsegP(sK4,X4)
      | ~ frontsegP(sK3,X4)
      | ~ neq(X4,nil) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f256,plain,
    ( spl14_1
    | ~ spl14_2 ),
    inference(avatar_split_clause,[],[f232,f253,f249]) ).

fof(f232,plain,
    ( nil != sK5
    | neq(sK4,nil) ),
    inference(definition_unfolding,[],[f185,f177]) ).

fof(f185,plain,
    ( nil != sK3
    | neq(sK4,nil) ),
    inference(cnf_transformation,[],[f147]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : SWC018+1 : TPTP v8.1.0. Released v2.4.0.
% 0.05/0.10  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.30  % Computer : n012.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Tue Aug 30 17:56:05 EDT 2022
% 0.10/0.30  % CPUTime    : 
% 0.15/0.45  % (30693)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.15/0.46  % (30710)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.15/0.46  % (30702)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.46  % (30693)First to succeed.
% 0.15/0.46  % (30701)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.46  % (30709)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.15/0.47  % (30691)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.15/0.47  % (30689)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.47  % (30689)Instruction limit reached!
% 0.15/0.47  % (30689)------------------------------
% 0.15/0.47  % (30689)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.47  % (30689)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.47  % (30689)Termination reason: Unknown
% 0.15/0.47  % (30689)Termination phase: shuffling
% 0.15/0.47  
% 0.15/0.47  % (30689)Memory used [KB]: 1535
% 0.15/0.47  % (30689)Time elapsed: 0.003 s
% 0.15/0.47  % (30689)Instructions burned: 3 (million)
% 0.15/0.47  % (30689)------------------------------
% 0.15/0.47  % (30689)------------------------------
% 0.15/0.47  % (30695)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.15/0.47  % (30701)Instruction limit reached!
% 0.15/0.47  % (30701)------------------------------
% 0.15/0.47  % (30701)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.47  % (30701)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.47  % (30701)Termination reason: Unknown
% 0.15/0.47  % (30701)Termination phase: shuffling
% 0.15/0.47  
% 0.15/0.47  % (30701)Memory used [KB]: 1535
% 0.15/0.47  % (30701)Time elapsed: 0.005 s
% 0.15/0.47  % (30701)Instructions burned: 3 (million)
% 0.15/0.47  % (30701)------------------------------
% 0.15/0.47  % (30701)------------------------------
% 0.15/0.47  % (30694)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.15/0.47  % (30693)Refutation found. Thanks to Tanya!
% 0.15/0.47  % SZS status Theorem for theBenchmark
% 0.15/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47  % (30693)------------------------------
% 0.15/0.47  % (30693)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.47  % (30693)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.47  % (30693)Termination reason: Refutation
% 0.15/0.47  
% 0.15/0.47  % (30693)Memory used [KB]: 6268
% 0.15/0.47  % (30693)Time elapsed: 0.111 s
% 0.15/0.47  % (30693)Instructions burned: 10 (million)
% 0.15/0.47  % (30693)------------------------------
% 0.15/0.47  % (30693)------------------------------
% 0.15/0.47  % (30686)Success in time 0.167 s
%------------------------------------------------------------------------------