TSTP Solution File: SWC029+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC029+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 18:38:18 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   86 (   7 unt;   0 def)
%            Number of atoms       :  436 ( 197 equ)
%            Maximal formula atoms :   34 (   5 avg)
%            Number of connectives :  520 ( 170   ~; 157   |; 154   &)
%                                         (  13 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;  10 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   90 (  42   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f297,plain,
    $false,
    inference(avatar_sat_refutation,[],[f201,f206,f215,f221,f226,f236,f239,f254,f278,f282,f296]) ).

fof(f296,plain,
    ( ~ spl10_3
    | ~ spl10_9
    | ~ spl10_10 ),
    inference(avatar_contradiction_clause,[],[f295]) ).

fof(f295,plain,
    ( $false
    | ~ spl10_3
    | ~ spl10_9
    | ~ spl10_10 ),
    inference(subsumption_resolution,[],[f294,f233]) ).

fof(f233,plain,
    ( ssList(nil)
    | ~ spl10_9 ),
    inference(avatar_component_clause,[],[f232]) ).

fof(f232,plain,
    ( spl10_9
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_9])]) ).

fof(f294,plain,
    ( ~ ssList(nil)
    | ~ spl10_3
    | ~ spl10_10 ),
    inference(subsumption_resolution,[],[f289,f205]) ).

fof(f205,plain,
    ( ssItem(sK4)
    | ~ spl10_3 ),
    inference(avatar_component_clause,[],[f203]) ).

fof(f203,plain,
    ( spl10_3
  <=> ssItem(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).

fof(f289,plain,
    ( ~ ssItem(sK4)
    | ~ ssList(nil)
    | ~ spl10_10 ),
    inference(trivial_inequality_removal,[],[f287]) ).

fof(f287,plain,
    ( ~ ssItem(sK4)
    | ~ ssList(nil)
    | nil != nil
    | ~ spl10_10 ),
    inference(superposition,[],[f142,f273]) ).

fof(f273,plain,
    ( nil = cons(sK4,nil)
    | ~ spl10_10 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f271,plain,
    ( spl10_10
  <=> nil = cons(sK4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_10])]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssList(X0)
      | ~ ssItem(X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | nil != cons(X1,X0) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f282,plain,
    ( ~ spl10_3
    | ~ spl10_9
    | spl10_11 ),
    inference(avatar_contradiction_clause,[],[f281]) ).

fof(f281,plain,
    ( $false
    | ~ spl10_3
    | ~ spl10_9
    | spl10_11 ),
    inference(subsumption_resolution,[],[f280,f233]) ).

fof(f280,plain,
    ( ~ ssList(nil)
    | ~ spl10_3
    | spl10_11 ),
    inference(subsumption_resolution,[],[f279,f205]) ).

fof(f279,plain,
    ( ~ ssItem(sK4)
    | ~ ssList(nil)
    | spl10_11 ),
    inference(resolution,[],[f277,f168]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssList(X0)
      | ~ ssItem(X1) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) ) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

fof(f277,plain,
    ( ~ ssList(cons(sK4,nil))
    | spl10_11 ),
    inference(avatar_component_clause,[],[f275]) ).

fof(f275,plain,
    ( spl10_11
  <=> ssList(cons(sK4,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_11])]) ).

fof(f278,plain,
    ( spl10_10
    | ~ spl10_11
    | ~ spl10_1
    | ~ spl10_4
    | ~ spl10_7 ),
    inference(avatar_split_clause,[],[f269,f223,f208,f194,f275,f271]) ).

fof(f194,plain,
    ( spl10_1
  <=> sK0 = app(sK5,cons(sK4,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).

fof(f208,plain,
    ( spl10_4
  <=> nil = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).

fof(f223,plain,
    ( spl10_7
  <=> ssList(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).

fof(f269,plain,
    ( ~ ssList(cons(sK4,nil))
    | nil = cons(sK4,nil)
    | ~ spl10_1
    | ~ spl10_4
    | ~ spl10_7 ),
    inference(subsumption_resolution,[],[f268,f225]) ).

fof(f225,plain,
    ( ssList(sK5)
    | ~ spl10_7 ),
    inference(avatar_component_clause,[],[f223]) ).

fof(f268,plain,
    ( ~ ssList(cons(sK4,nil))
    | nil = cons(sK4,nil)
    | ~ ssList(sK5)
    | ~ spl10_1
    | ~ spl10_4 ),
    inference(trivial_inequality_removal,[],[f263]) ).

fof(f263,plain,
    ( ~ ssList(cons(sK4,nil))
    | nil = cons(sK4,nil)
    | ~ ssList(sK5)
    | nil != nil
    | ~ spl10_1
    | ~ spl10_4 ),
    inference(superposition,[],[f164,f255]) ).

fof(f255,plain,
    ( nil = app(sK5,cons(sK4,nil))
    | ~ spl10_1
    | ~ spl10_4 ),
    inference(forward_demodulation,[],[f196,f209]) ).

fof(f209,plain,
    ( nil = sK0
    | ~ spl10_4 ),
    inference(avatar_component_clause,[],[f208]) ).

fof(f196,plain,
    ( sK0 = app(sK5,cons(sK4,nil))
    | ~ spl10_1 ),
    inference(avatar_component_clause,[],[f194]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | nil = X1
      | ~ ssList(X0)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) )
            & ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 ) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f128]) ).

fof(f128,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) )
            & ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( nil = X0
              & nil = X1 )
          <=> nil = app(X0,X1) ) )
      | ~ ssList(X0) ),
    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(f254,plain,
    ( spl10_2
    | spl10_5
    | ~ spl10_9 ),
    inference(avatar_contradiction_clause,[],[f253]) ).

fof(f253,plain,
    ( $false
    | spl10_2
    | spl10_5
    | ~ spl10_9 ),
    inference(subsumption_resolution,[],[f252,f233]) ).

fof(f252,plain,
    ( ~ ssList(nil)
    | spl10_2
    | spl10_5 ),
    inference(subsumption_resolution,[],[f251,f145]) ).

fof(f145,plain,
    ssList(sK3),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ( ssList(sK0)
    & ssList(sK1)
    & ssList(sK2)
    & ( ~ neq(sK3,nil)
      | ( ssList(sK5)
        & sK2 = app(sK5,cons(sK4,nil))
        & app(cons(sK4,nil),sK5) = sK3
        & ssItem(sK4) ) )
    & sK2 = sK0
    & ( nil = sK2
      | nil != sK3 )
    & sK1 = sK3
    & ( ( nil = sK1
        & nil != sK0 )
      | ( nil = sK0
        & nil != sK1 ) )
    & ssList(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f108,f125,f124,f123,f122,f121,f120]) ).

fof(f120,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ( ~ neq(X3,nil)
                      | ? [X4] :
                          ( ? [X5] :
                              ( ssList(X5)
                              & app(X5,cons(X4,nil)) = X2
                              & app(cons(X4,nil),X5) = X3 )
                          & ssItem(X4) ) )
                    & X0 = X2
                    & ( nil = X2
                      | nil != X3 )
                    & X1 = X3
                    & ( ( nil = X1
                        & nil != X0 )
                      | ( nil = X0
                        & nil != X1 ) )
                    & ssList(X3) ) ) ) )
   => ( ssList(sK0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ? [X5] :
                            ( ssList(X5)
                            & app(X5,cons(X4,nil)) = X2
                            & app(cons(X4,nil),X5) = X3 )
                        & ssItem(X4) ) )
                  & sK0 = X2
                  & ( nil = X2
                    | nil != X3 )
                  & X1 = X3
                  & ( ( nil = X1
                      & nil != sK0 )
                    | ( nil = sK0
                      & nil != X1 ) )
                  & ssList(X3) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f121,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ( ~ neq(X3,nil)
                  | ? [X4] :
                      ( ? [X5] :
                          ( ssList(X5)
                          & app(X5,cons(X4,nil)) = X2
                          & app(cons(X4,nil),X5) = X3 )
                      & ssItem(X4) ) )
                & sK0 = X2
                & ( nil = X2
                  | nil != X3 )
                & X1 = X3
                & ( ( nil = X1
                    & nil != sK0 )
                  | ( nil = sK0
                    & nil != X1 ) )
                & ssList(X3) ) ) )
   => ( ssList(sK1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ( ~ neq(X3,nil)
                | ? [X4] :
                    ( ? [X5] :
                        ( ssList(X5)
                        & app(X5,cons(X4,nil)) = X2
                        & app(cons(X4,nil),X5) = X3 )
                    & ssItem(X4) ) )
              & sK0 = X2
              & ( nil = X2
                | nil != X3 )
              & sK1 = X3
              & ( ( nil = sK1
                  & nil != sK0 )
                | ( nil = sK0
                  & nil != sK1 ) )
              & ssList(X3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ( ~ neq(X3,nil)
              | ? [X4] :
                  ( ? [X5] :
                      ( ssList(X5)
                      & app(X5,cons(X4,nil)) = X2
                      & app(cons(X4,nil),X5) = X3 )
                  & ssItem(X4) ) )
            & sK0 = X2
            & ( nil = X2
              | nil != X3 )
            & sK1 = X3
            & ( ( nil = sK1
                & nil != sK0 )
              | ( nil = sK0
                & nil != sK1 ) )
            & ssList(X3) ) )
   => ( ssList(sK2)
      & ? [X3] :
          ( ( ~ neq(X3,nil)
            | ? [X4] :
                ( ? [X5] :
                    ( ssList(X5)
                    & app(X5,cons(X4,nil)) = sK2
                    & app(cons(X4,nil),X5) = X3 )
                & ssItem(X4) ) )
          & sK2 = sK0
          & ( nil = sK2
            | nil != X3 )
          & sK1 = X3
          & ( ( nil = sK1
              & nil != sK0 )
            | ( nil = sK0
              & nil != sK1 ) )
          & ssList(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ( ? [X3] :
        ( ( ~ neq(X3,nil)
          | ? [X4] :
              ( ? [X5] :
                  ( ssList(X5)
                  & app(X5,cons(X4,nil)) = sK2
                  & app(cons(X4,nil),X5) = X3 )
              & ssItem(X4) ) )
        & sK2 = sK0
        & ( nil = sK2
          | nil != X3 )
        & sK1 = X3
        & ( ( nil = sK1
            & nil != sK0 )
          | ( nil = sK0
            & nil != sK1 ) )
        & ssList(X3) )
   => ( ( ~ neq(sK3,nil)
        | ? [X4] :
            ( ? [X5] :
                ( ssList(X5)
                & app(X5,cons(X4,nil)) = sK2
                & app(cons(X4,nil),X5) = sK3 )
            & ssItem(X4) ) )
      & sK2 = sK0
      & ( nil = sK2
        | nil != sK3 )
      & sK1 = sK3
      & ( ( nil = sK1
          & nil != sK0 )
        | ( nil = sK0
          & nil != sK1 ) )
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( ssList(X5)
            & app(X5,cons(X4,nil)) = sK2
            & app(cons(X4,nil),X5) = sK3 )
        & ssItem(X4) )
   => ( ? [X5] :
          ( ssList(X5)
          & app(X5,cons(sK4,nil)) = sK2
          & app(cons(sK4,nil),X5) = sK3 )
      & ssItem(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ( ? [X5] :
        ( ssList(X5)
        & app(X5,cons(sK4,nil)) = sK2
        & app(cons(sK4,nil),X5) = sK3 )
   => ( ssList(sK5)
      & sK2 = app(sK5,cons(sK4,nil))
      & app(cons(sK4,nil),sK5) = sK3 ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ? [X5] :
                            ( ssList(X5)
                            & app(X5,cons(X4,nil)) = X2
                            & app(cons(X4,nil),X5) = X3 )
                        & ssItem(X4) ) )
                  & X0 = X2
                  & ( nil = X2
                    | nil != X3 )
                  & X1 = X3
                  & ( ( nil = X1
                      & nil != X0 )
                    | ( nil = X0
                      & nil != X1 ) )
                  & ssList(X3) ) ) ) ),
    inference(flattening,[],[f107]) ).

fof(f107,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil = X2
                    | nil != X3 )
                  & ( ( nil = X1
                      & nil != X0 )
                    | ( nil = X0
                      & nil != X1 ) )
                  & X1 = X3
                  & ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ? [X5] :
                            ( app(X5,cons(X4,nil)) = X2
                            & app(cons(X4,nil),X5) = X3
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & 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 != X2
                        & nil = X3 )
                      | ( ( nil != X0
                          | nil = X1 )
                        & ( nil != X1
                          | nil = X0 ) )
                      | X1 != X3
                      | ( neq(X3,nil)
                        & ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( ssList(X5)
                               => ( app(X5,cons(X4,nil)) != X2
                                  | app(cons(X4,nil),X5) != X3 ) ) ) )
                      | X0 != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f251,plain,
    ( ~ ssList(sK3)
    | ~ ssList(nil)
    | spl10_2
    | spl10_5 ),
    inference(subsumption_resolution,[],[f246,f214]) ).

fof(f214,plain,
    ( nil != sK3
    | spl10_5 ),
    inference(avatar_component_clause,[],[f212]) ).

fof(f212,plain,
    ( spl10_5
  <=> nil = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_5])]) ).

fof(f246,plain,
    ( nil = sK3
    | ~ ssList(nil)
    | ~ ssList(sK3)
    | spl10_2 ),
    inference(resolution,[],[f161,f200]) ).

fof(f200,plain,
    ( ~ neq(sK3,nil)
    | spl10_2 ),
    inference(avatar_component_clause,[],[f198]) ).

fof(f198,plain,
    ( spl10_2
  <=> neq(sK3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X1)
      | X0 = X1
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( X0 != X1
          <=> neq(X0,X1) ) )
      | ~ ssList(X0) ),
    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(f239,plain,
    spl10_9,
    inference(avatar_split_clause,[],[f160,f232]) ).

fof(f160,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f236,plain,
    ( spl10_4
    | ~ spl10_5 ),
    inference(avatar_split_clause,[],[f182,f212,f208]) ).

fof(f182,plain,
    ( nil != sK3
    | nil = sK0 ),
    inference(definition_unfolding,[],[f151,f152]) ).

fof(f152,plain,
    sK2 = sK0,
    inference(cnf_transformation,[],[f126]) ).

fof(f151,plain,
    ( nil = sK2
    | nil != sK3 ),
    inference(cnf_transformation,[],[f126]) ).

fof(f226,plain,
    ( spl10_7
    | ~ spl10_2 ),
    inference(avatar_split_clause,[],[f156,f198,f223]) ).

fof(f156,plain,
    ( ~ neq(sK3,nil)
    | ssList(sK5) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f221,plain,
    ( spl10_4
    | spl10_5 ),
    inference(avatar_split_clause,[],[f183,f212,f208]) ).

fof(f183,plain,
    ( nil = sK3
    | nil = sK0 ),
    inference(definition_unfolding,[],[f149,f150]) ).

fof(f150,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f126]) ).

fof(f149,plain,
    ( nil = sK1
    | nil = sK0 ),
    inference(cnf_transformation,[],[f126]) ).

fof(f215,plain,
    ( ~ spl10_4
    | ~ spl10_5 ),
    inference(avatar_split_clause,[],[f185,f212,f208]) ).

fof(f185,plain,
    ( nil != sK3
    | nil != sK0 ),
    inference(definition_unfolding,[],[f146,f150]) ).

fof(f146,plain,
    ( nil != sK0
    | nil != sK1 ),
    inference(cnf_transformation,[],[f126]) ).

fof(f206,plain,
    ( spl10_3
    | ~ spl10_2 ),
    inference(avatar_split_clause,[],[f153,f198,f203]) ).

fof(f153,plain,
    ( ~ neq(sK3,nil)
    | ssItem(sK4) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f201,plain,
    ( spl10_1
    | ~ spl10_2 ),
    inference(avatar_split_clause,[],[f181,f198,f194]) ).

fof(f181,plain,
    ( ~ neq(sK3,nil)
    | sK0 = app(sK5,cons(sK4,nil)) ),
    inference(definition_unfolding,[],[f155,f152]) ).

fof(f155,plain,
    ( ~ neq(sK3,nil)
    | sK2 = app(sK5,cons(sK4,nil)) ),
    inference(cnf_transformation,[],[f126]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SWC029+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n012.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
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 17:58:20 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.48  % (3811)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.49  % (3835)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)
% 0.19/0.49  % (3823)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.49  % (3823)Instruction limit reached!
% 0.19/0.49  % (3823)------------------------------
% 0.19/0.49  % (3823)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (3823)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (3823)Termination reason: Unknown
% 0.19/0.49  % (3823)Termination phase: Saturation
% 0.19/0.49  
% 0.19/0.49  % (3823)Memory used [KB]: 6140
% 0.19/0.49  % (3823)Time elapsed: 0.099 s
% 0.19/0.49  % (3823)Instructions burned: 8 (million)
% 0.19/0.49  % (3823)------------------------------
% 0.19/0.49  % (3823)------------------------------
% 0.19/0.50  % (3817)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)
% 0.19/0.50  % (3832)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.50  % (3827)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)
% 0.19/0.50  % (3827)Instruction limit reached!
% 0.19/0.50  % (3827)------------------------------
% 0.19/0.50  % (3827)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (3827)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (3827)Termination reason: Unknown
% 0.19/0.50  % (3827)Termination phase: Property scanning
% 0.19/0.50  
% 0.19/0.50  % (3827)Memory used [KB]: 1791
% 0.19/0.50  % (3827)Time elapsed: 0.005 s
% 0.19/0.50  % (3827)Instructions burned: 9 (million)
% 0.19/0.50  % (3827)------------------------------
% 0.19/0.50  % (3827)------------------------------
% 0.19/0.50  % (3817)First to succeed.
% 0.19/0.50  % (3815)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)
% 0.19/0.50  % (3841)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.51  % (3816)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.51  % (3817)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (3817)------------------------------
% 0.19/0.51  % (3817)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (3817)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (3817)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (3817)Memory used [KB]: 6140
% 0.19/0.51  % (3817)Time elapsed: 0.111 s
% 0.19/0.51  % (3817)Instructions burned: 6 (million)
% 0.19/0.51  % (3817)------------------------------
% 0.19/0.51  % (3817)------------------------------
% 0.19/0.51  % (3807)Success in time 0.165 s
%------------------------------------------------------------------------------