TSTP Solution File: SWC419+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC419+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 : n015.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 18:41:05 EDT 2022

% Result   : Theorem 0.20s 0.56s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   70 (  11 unt;   0 def)
%            Number of atoms       :  391 ( 146 equ)
%            Maximal formula atoms :   38 (   5 avg)
%            Number of connectives :  495 ( 174   ~; 154   |; 136   &)
%                                         (   9 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Maximal term depth    :    4 (   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   :  120 (  69   !;  51   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f754,plain,
    $false,
    inference(avatar_sat_refutation,[],[f604,f605,f610,f624,f644,f645,f656,f697,f703,f753]) ).

fof(f753,plain,
    ( ~ spl53_4
    | ~ spl53_2
    | spl53_22 ),
    inference(avatar_split_clause,[],[f752,f694,f588,f597]) ).

fof(f597,plain,
    ( spl53_4
  <=> ssItem(sK31) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_4])]) ).

fof(f588,plain,
    ( spl53_2
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_2])]) ).

fof(f694,plain,
    ( spl53_22
  <=> ssList(cons(sK31,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_22])]) ).

fof(f752,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sK31)
    | spl53_22 ),
    inference(resolution,[],[f358,f696]) ).

fof(f696,plain,
    ( ~ ssList(cons(sK31,nil))
    | spl53_22 ),
    inference(avatar_component_clause,[],[f694]) ).

fof(f358,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssList(X0)
      | ~ ssItem(X1) ),
    inference(cnf_transformation,[],[f214]) ).

fof(f214,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    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(f703,plain,
    spl53_21,
    inference(avatar_contradiction_clause,[],[f700]) ).

fof(f700,plain,
    ( $false
    | spl53_21 ),
    inference(resolution,[],[f699,f541]) ).

fof(f541,plain,
    ssList(sK29),
    inference(definition_unfolding,[],[f476,f469]) ).

fof(f469,plain,
    sK27 = sK29,
    inference(cnf_transformation,[],[f296]) ).

fof(f296,plain,
    ( ssList(sK27)
    & ( ( sK30 = app(cons(sK31,nil),sK32)
        & ssList(sK32)
        & sK29 = app(sK32,cons(sK31,nil))
        & ssItem(sK31) )
      | ~ neq(sK30,nil) )
    & ! [X6] :
        ( ~ ssItem(X6)
        | ! [X7] :
            ( ~ ssList(X7)
            | ! [X8] :
                ( ~ ssList(X8)
                | app(app(X7,cons(X6,nil)),X8) != sK28
                | sK27 != app(app(X8,cons(X6,nil)),X7) ) ) )
    & ssList(sK30)
    & sK27 = sK29
    & ( nil != sK30
      | nil = sK29 )
    & neq(sK28,nil)
    & sK30 = sK28
    & ssList(sK29)
    & ssList(sK28) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30,sK31,sK32])],[f181,f295,f294,f293,f292,f291,f290]) ).

fof(f290,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ? [X4] :
                          ( ? [X5] :
                              ( app(cons(X4,nil),X5) = X3
                              & ssList(X5)
                              & app(X5,cons(X4,nil)) = X2 )
                          & ssItem(X4) )
                      | ~ neq(X3,nil) )
                    & ! [X6] :
                        ( ~ ssItem(X6)
                        | ! [X7] :
                            ( ~ ssList(X7)
                            | ! [X8] :
                                ( ~ ssList(X8)
                                | app(app(X7,cons(X6,nil)),X8) != X1
                                | app(app(X8,cons(X6,nil)),X7) != X0 ) ) )
                    & ssList(X3)
                    & X0 = X2
                    & ( nil != X3
                      | nil = X2 )
                    & neq(X1,nil)
                    & X1 = X3 )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK27)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ? [X4] :
                        ( ? [X5] :
                            ( app(cons(X4,nil),X5) = X3
                            & ssList(X5)
                            & app(X5,cons(X4,nil)) = X2 )
                        & ssItem(X4) )
                    | ~ neq(X3,nil) )
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( ~ ssList(X7)
                          | ! [X8] :
                              ( ~ ssList(X8)
                              | app(app(X7,cons(X6,nil)),X8) != X1
                              | sK27 != app(app(X8,cons(X6,nil)),X7) ) ) )
                  & ssList(X3)
                  & sK27 = X2
                  & ( nil != X3
                    | nil = X2 )
                  & neq(X1,nil)
                  & X1 = X3 )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f291,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ? [X4] :
                      ( ? [X5] :
                          ( app(cons(X4,nil),X5) = X3
                          & ssList(X5)
                          & app(X5,cons(X4,nil)) = X2 )
                      & ssItem(X4) )
                  | ~ neq(X3,nil) )
                & ! [X6] :
                    ( ~ ssItem(X6)
                    | ! [X7] :
                        ( ~ ssList(X7)
                        | ! [X8] :
                            ( ~ ssList(X8)
                            | app(app(X7,cons(X6,nil)),X8) != X1
                            | sK27 != app(app(X8,cons(X6,nil)),X7) ) ) )
                & ssList(X3)
                & sK27 = X2
                & ( nil != X3
                  | nil = X2 )
                & neq(X1,nil)
                & X1 = X3 )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ? [X4] :
                    ( ? [X5] :
                        ( app(cons(X4,nil),X5) = X3
                        & ssList(X5)
                        & app(X5,cons(X4,nil)) = X2 )
                    & ssItem(X4) )
                | ~ neq(X3,nil) )
              & ! [X6] :
                  ( ~ ssItem(X6)
                  | ! [X7] :
                      ( ~ ssList(X7)
                      | ! [X8] :
                          ( ~ ssList(X8)
                          | app(app(X7,cons(X6,nil)),X8) != sK28
                          | sK27 != app(app(X8,cons(X6,nil)),X7) ) ) )
              & ssList(X3)
              & sK27 = X2
              & ( nil != X3
                | nil = X2 )
              & neq(sK28,nil)
              & sK28 = X3 )
          & ssList(X2) )
      & ssList(sK28) ) ),
    introduced(choice_axiom,[]) ).

fof(f292,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ? [X4] :
                  ( ? [X5] :
                      ( app(cons(X4,nil),X5) = X3
                      & ssList(X5)
                      & app(X5,cons(X4,nil)) = X2 )
                  & ssItem(X4) )
              | ~ neq(X3,nil) )
            & ! [X6] :
                ( ~ ssItem(X6)
                | ! [X7] :
                    ( ~ ssList(X7)
                    | ! [X8] :
                        ( ~ ssList(X8)
                        | app(app(X7,cons(X6,nil)),X8) != sK28
                        | sK27 != app(app(X8,cons(X6,nil)),X7) ) ) )
            & ssList(X3)
            & sK27 = X2
            & ( nil != X3
              | nil = X2 )
            & neq(sK28,nil)
            & sK28 = X3 )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ? [X4] :
                ( ? [X5] :
                    ( app(cons(X4,nil),X5) = X3
                    & ssList(X5)
                    & app(X5,cons(X4,nil)) = sK29 )
                & ssItem(X4) )
            | ~ neq(X3,nil) )
          & ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( ~ ssList(X7)
                  | ! [X8] :
                      ( ~ ssList(X8)
                      | app(app(X7,cons(X6,nil)),X8) != sK28
                      | sK27 != app(app(X8,cons(X6,nil)),X7) ) ) )
          & ssList(X3)
          & sK27 = sK29
          & ( nil != X3
            | nil = sK29 )
          & neq(sK28,nil)
          & sK28 = X3 )
      & ssList(sK29) ) ),
    introduced(choice_axiom,[]) ).

fof(f293,plain,
    ( ? [X3] :
        ( ( ? [X4] :
              ( ? [X5] :
                  ( app(cons(X4,nil),X5) = X3
                  & ssList(X5)
                  & app(X5,cons(X4,nil)) = sK29 )
              & ssItem(X4) )
          | ~ neq(X3,nil) )
        & ! [X6] :
            ( ~ ssItem(X6)
            | ! [X7] :
                ( ~ ssList(X7)
                | ! [X8] :
                    ( ~ ssList(X8)
                    | app(app(X7,cons(X6,nil)),X8) != sK28
                    | sK27 != app(app(X8,cons(X6,nil)),X7) ) ) )
        & ssList(X3)
        & sK27 = sK29
        & ( nil != X3
          | nil = sK29 )
        & neq(sK28,nil)
        & sK28 = X3 )
   => ( ( ? [X4] :
            ( ? [X5] :
                ( sK30 = app(cons(X4,nil),X5)
                & ssList(X5)
                & app(X5,cons(X4,nil)) = sK29 )
            & ssItem(X4) )
        | ~ neq(sK30,nil) )
      & ! [X6] :
          ( ~ ssItem(X6)
          | ! [X7] :
              ( ~ ssList(X7)
              | ! [X8] :
                  ( ~ ssList(X8)
                  | app(app(X7,cons(X6,nil)),X8) != sK28
                  | sK27 != app(app(X8,cons(X6,nil)),X7) ) ) )
      & ssList(sK30)
      & sK27 = sK29
      & ( nil != sK30
        | nil = sK29 )
      & neq(sK28,nil)
      & sK30 = sK28 ) ),
    introduced(choice_axiom,[]) ).

fof(f294,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( sK30 = app(cons(X4,nil),X5)
            & ssList(X5)
            & app(X5,cons(X4,nil)) = sK29 )
        & ssItem(X4) )
   => ( ? [X5] :
          ( app(cons(sK31,nil),X5) = sK30
          & ssList(X5)
          & sK29 = app(X5,cons(sK31,nil)) )
      & ssItem(sK31) ) ),
    introduced(choice_axiom,[]) ).

fof(f295,plain,
    ( ? [X5] :
        ( app(cons(sK31,nil),X5) = sK30
        & ssList(X5)
        & sK29 = app(X5,cons(sK31,nil)) )
   => ( sK30 = app(cons(sK31,nil),sK32)
      & ssList(sK32)
      & sK29 = app(sK32,cons(sK31,nil)) ) ),
    introduced(choice_axiom,[]) ).

fof(f181,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ? [X4] :
                        ( ? [X5] :
                            ( app(cons(X4,nil),X5) = X3
                            & ssList(X5)
                            & app(X5,cons(X4,nil)) = X2 )
                        & ssItem(X4) )
                    | ~ neq(X3,nil) )
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( ~ ssList(X7)
                          | ! [X8] :
                              ( ~ ssList(X8)
                              | app(app(X7,cons(X6,nil)),X8) != X1
                              | app(app(X8,cons(X6,nil)),X7) != X0 ) ) )
                  & ssList(X3)
                  & X0 = X2
                  & ( nil != X3
                    | nil = X2 )
                  & neq(X1,nil)
                  & X1 = X3 )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( X1 != X3
                    | ( ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( app(X5,cons(X4,nil)) != X2
                              | app(cons(X4,nil),X5) != X3
                              | ~ ssList(X5) ) )
                      & neq(X3,nil) )
                    | ( nil != X2
                      & nil = X3 )
                    | ~ neq(X1,nil)
                    | ? [X6] :
                        ( ? [X7] :
                            ( ? [X8] :
                                ( app(app(X7,cons(X6,nil)),X8) = X1
                                & app(app(X8,cons(X6,nil)),X7) = X0
                                & ssList(X8) )
                            & ssList(X7) )
                        & ssItem(X6) )
                    | X0 != X2
                    | ~ ssList(X3) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

fof(f476,plain,
    ssList(sK27),
    inference(cnf_transformation,[],[f296]) ).

fof(f699,plain,
    ( ~ ssList(sK29)
    | spl53_21 ),
    inference(trivial_inequality_removal,[],[f698]) ).

fof(f698,plain,
    ( ~ ssList(sK29)
    | sK29 != sK29
    | spl53_21 ),
    inference(superposition,[],[f692,f353]) ).

fof(f353,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).

fof(f692,plain,
    ( sK29 != app(sK29,nil)
    | spl53_21 ),
    inference(avatar_component_clause,[],[f690]) ).

fof(f690,plain,
    ( spl53_21
  <=> sK29 = app(sK29,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_21])]) ).

fof(f697,plain,
    ( ~ spl53_21
    | ~ spl53_2
    | ~ spl53_22
    | ~ spl53_6
    | ~ spl53_15 ),
    inference(avatar_split_clause,[],[f688,f654,f607,f694,f588,f690]) ).

fof(f607,plain,
    ( spl53_6
  <=> app(cons(sK31,nil),sK32) = sK28 ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_6])]) ).

fof(f654,plain,
    ( spl53_15
  <=> ! [X0] :
        ( app(app(X0,cons(sK31,nil)),sK32) != sK28
        | ~ ssList(X0)
        | sK29 != app(sK29,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_15])]) ).

fof(f688,plain,
    ( ~ ssList(cons(sK31,nil))
    | ~ ssList(nil)
    | sK29 != app(sK29,nil)
    | ~ spl53_6
    | ~ spl53_15 ),
    inference(trivial_inequality_removal,[],[f687]) ).

fof(f687,plain,
    ( ~ ssList(cons(sK31,nil))
    | sK29 != app(sK29,nil)
    | sK28 != sK28
    | ~ ssList(nil)
    | ~ spl53_6
    | ~ spl53_15 ),
    inference(forward_demodulation,[],[f681,f609]) ).

fof(f609,plain,
    ( app(cons(sK31,nil),sK32) = sK28
    | ~ spl53_6 ),
    inference(avatar_component_clause,[],[f607]) ).

fof(f681,plain,
    ( sK29 != app(sK29,nil)
    | app(cons(sK31,nil),sK32) != sK28
    | ~ ssList(cons(sK31,nil))
    | ~ ssList(nil)
    | ~ spl53_15 ),
    inference(superposition,[],[f655,f422]) ).

fof(f422,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f655,plain,
    ( ! [X0] :
        ( app(app(X0,cons(sK31,nil)),sK32) != sK28
        | ~ ssList(X0)
        | sK29 != app(sK29,X0) )
    | ~ spl53_15 ),
    inference(avatar_component_clause,[],[f654]) ).

fof(f656,plain,
    ( ~ spl53_4
    | ~ spl53_13
    | spl53_15
    | ~ spl53_9 ),
    inference(avatar_split_clause,[],[f652,f621,f654,f641,f597]) ).

fof(f641,plain,
    ( spl53_13
  <=> ssList(sK32) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_13])]) ).

fof(f621,plain,
    ( spl53_9
  <=> sK29 = app(sK32,cons(sK31,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_9])]) ).

fof(f652,plain,
    ( ! [X0] :
        ( app(app(X0,cons(sK31,nil)),sK32) != sK28
        | sK29 != app(sK29,X0)
        | ~ ssList(sK32)
        | ~ ssList(X0)
        | ~ ssItem(sK31) )
    | ~ spl53_9 ),
    inference(superposition,[],[f546,f623]) ).

fof(f623,plain,
    ( sK29 = app(sK32,cons(sK31,nil))
    | ~ spl53_9 ),
    inference(avatar_component_clause,[],[f621]) ).

fof(f546,plain,
    ! [X8,X6,X7] :
      ( sK29 != app(app(X8,cons(X6,nil)),X7)
      | ~ ssItem(X6)
      | app(app(X7,cons(X6,nil)),X8) != sK28
      | ~ ssList(X7)
      | ~ ssList(X8) ),
    inference(definition_unfolding,[],[f471,f469]) ).

fof(f471,plain,
    ! [X8,X6,X7] :
      ( ~ ssItem(X6)
      | ~ ssList(X7)
      | ~ ssList(X8)
      | app(app(X7,cons(X6,nil)),X8) != sK28
      | sK27 != app(app(X8,cons(X6,nil)),X7) ),
    inference(cnf_transformation,[],[f296]) ).

fof(f645,plain,
    spl53_2,
    inference(avatar_split_clause,[],[f452,f588]) ).

fof(f452,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f644,plain,
    ( ~ spl53_5
    | spl53_13 ),
    inference(avatar_split_clause,[],[f543,f641,f601]) ).

fof(f601,plain,
    ( spl53_5
  <=> neq(sK28,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_5])]) ).

fof(f543,plain,
    ( ssList(sK32)
    | ~ neq(sK28,nil) ),
    inference(definition_unfolding,[],[f474,f466]) ).

fof(f466,plain,
    sK30 = sK28,
    inference(cnf_transformation,[],[f296]) ).

fof(f474,plain,
    ( ssList(sK32)
    | ~ neq(sK30,nil) ),
    inference(cnf_transformation,[],[f296]) ).

fof(f624,plain,
    ( ~ spl53_5
    | spl53_9 ),
    inference(avatar_split_clause,[],[f544,f621,f601]) ).

fof(f544,plain,
    ( sK29 = app(sK32,cons(sK31,nil))
    | ~ neq(sK28,nil) ),
    inference(definition_unfolding,[],[f473,f466]) ).

fof(f473,plain,
    ( sK29 = app(sK32,cons(sK31,nil))
    | ~ neq(sK30,nil) ),
    inference(cnf_transformation,[],[f296]) ).

fof(f610,plain,
    ( ~ spl53_5
    | spl53_6 ),
    inference(avatar_split_clause,[],[f542,f607,f601]) ).

fof(f542,plain,
    ( app(cons(sK31,nil),sK32) = sK28
    | ~ neq(sK28,nil) ),
    inference(definition_unfolding,[],[f475,f466,f466]) ).

fof(f475,plain,
    ( sK30 = app(cons(sK31,nil),sK32)
    | ~ neq(sK30,nil) ),
    inference(cnf_transformation,[],[f296]) ).

fof(f605,plain,
    spl53_5,
    inference(avatar_split_clause,[],[f467,f601]) ).

fof(f467,plain,
    neq(sK28,nil),
    inference(cnf_transformation,[],[f296]) ).

fof(f604,plain,
    ( spl53_4
    | ~ spl53_5 ),
    inference(avatar_split_clause,[],[f545,f601,f597]) ).

fof(f545,plain,
    ( ~ neq(sK28,nil)
    | ssItem(sK31) ),
    inference(definition_unfolding,[],[f472,f466]) ).

fof(f472,plain,
    ( ssItem(sK31)
    | ~ neq(sK30,nil) ),
    inference(cnf_transformation,[],[f296]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SWC419+1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 19:06:36 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.50  % (6666)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50  % (6653)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.51  % (6676)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)
% 0.20/0.51  % (6682)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)
% 0.20/0.51  % (6660)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)
% 0.20/0.51  % (6658)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)
% 0.20/0.52  % (6665)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.52  % (6674)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52  % (6664)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)
% 0.20/0.53  % (6681)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.20/0.53  % (6654)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.53  % (6673)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)
% 0.20/0.54  % (6675)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)
% 0.20/0.54  % (6657)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)
% 0.20/0.54  % (6656)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (6655)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)
% 0.20/0.54  % (6667)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)
% 0.20/0.54  % (6655)Instruction limit reached!
% 0.20/0.54  % (6655)------------------------------
% 0.20/0.54  % (6655)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (6655)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (6655)Termination reason: Unknown
% 0.20/0.54  % (6655)Termination phase: Preprocessing 3
% 0.20/0.54  
% 0.20/0.54  % (6655)Memory used [KB]: 1663
% 0.20/0.54  % (6655)Time elapsed: 0.003 s
% 0.20/0.54  % (6655)Instructions burned: 4 (million)
% 0.20/0.54  % (6655)------------------------------
% 0.20/0.54  % (6655)------------------------------
% 0.20/0.54  % (6663)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.54  % (6662)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.54  % (6663)Refutation not found, incomplete strategy% (6663)------------------------------
% 0.20/0.54  % (6663)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (6663)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (6663)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.54  
% 0.20/0.54  % (6663)Memory used [KB]: 6140
% 0.20/0.54  % (6663)Time elapsed: 0.133 s
% 0.20/0.54  % (6663)Instructions burned: 6 (million)
% 0.20/0.54  % (6663)------------------------------
% 0.20/0.54  % (6663)------------------------------
% 0.20/0.54  % (6664)Instruction limit reached!
% 0.20/0.54  % (6664)------------------------------
% 0.20/0.54  % (6664)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (6665)Instruction limit reached!
% 0.20/0.54  % (6665)------------------------------
% 0.20/0.54  % (6665)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (6665)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (6665)Termination reason: Unknown
% 0.20/0.54  % (6665)Termination phase: Saturation
% 0.20/0.54  
% 0.20/0.54  % (6665)Memory used [KB]: 2046
% 0.20/0.54  % (6665)Time elapsed: 0.137 s
% 0.20/0.54  % (6665)Instructions burned: 17 (million)
% 0.20/0.54  % (6665)------------------------------
% 0.20/0.54  % (6665)------------------------------
% 0.20/0.55  % (6669)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.55  % (6675)First to succeed.
% 0.20/0.55  % (6681)Instruction limit reached!
% 0.20/0.55  % (6681)------------------------------
% 0.20/0.55  % (6681)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (6679)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.55  % (6680)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.55  % (6664)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (6664)Termination reason: Unknown
% 0.20/0.55  % (6664)Termination phase: Saturation
% 0.20/0.55  
% 0.20/0.55  % (6664)Memory used [KB]: 6140
% 0.20/0.55  % (6664)Time elapsed: 0.135 s
% 0.20/0.55  % (6664)Instructions burned: 8 (million)
% 0.20/0.55  % (6664)------------------------------
% 0.20/0.55  % (6664)------------------------------
% 0.20/0.55  % (6659)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)
% 0.20/0.55  % (6671)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.55  % (6668)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)
% 0.20/0.55  % (6661)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)
% 0.20/0.55  % (6667)Instruction limit reached!
% 0.20/0.55  % (6667)------------------------------
% 0.20/0.55  % (6667)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (6667)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (6667)Termination reason: Unknown
% 0.20/0.55  % (6667)Termination phase: Preprocessing 2
% 0.20/0.55  
% 0.20/0.55  % (6667)Memory used [KB]: 1535
% 0.20/0.55  % (6667)Time elapsed: 0.003 s
% 0.20/0.55  % (6667)Instructions burned: 3 (million)
% 0.20/0.55  % (6667)------------------------------
% 0.20/0.55  % (6667)------------------------------
% 0.20/0.55  % (6672)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.55  % (6668)Instruction limit reached!
% 0.20/0.55  % (6668)------------------------------
% 0.20/0.55  % (6668)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (6658)Instruction limit reached!
% 0.20/0.55  % (6658)------------------------------
% 0.20/0.55  % (6658)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (6658)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (6658)Termination reason: Unknown
% 0.20/0.55  % (6658)Termination phase: Saturation
% 0.20/0.55  
% 0.20/0.55  % (6658)Memory used [KB]: 1663
% 0.20/0.55  % (6658)Time elapsed: 0.134 s
% 0.20/0.55  % (6658)Instructions burned: 16 (million)
% 0.20/0.55  % (6658)------------------------------
% 0.20/0.55  % (6658)------------------------------
% 0.20/0.56  % (6657)Instruction limit reached!
% 0.20/0.56  % (6657)------------------------------
% 0.20/0.56  % (6657)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (6681)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (6681)Termination reason: Unknown
% 0.20/0.56  % (6681)Termination phase: Property scanning
% 0.20/0.56  
% 0.20/0.56  % (6681)Memory used [KB]: 1791
% 0.20/0.56  % (6681)Time elapsed: 0.005 s
% 0.20/0.56  % (6681)Instructions burned: 9 (million)
% 0.20/0.56  % (6681)------------------------------
% 0.20/0.56  % (6681)------------------------------
% 0.20/0.56  % (6682)Instruction limit reached!
% 0.20/0.56  % (6682)------------------------------
% 0.20/0.56  % (6682)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (6678)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.20/0.56  % (6654)Instruction limit reached!
% 0.20/0.56  % (6654)------------------------------
% 0.20/0.56  % (6654)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (6654)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (6654)Termination reason: Unknown
% 0.20/0.56  % (6654)Termination phase: Saturation
% 0.20/0.56  
% 0.20/0.56  % (6654)Memory used [KB]: 6396
% 0.20/0.56  % (6654)Time elapsed: 0.141 s
% 0.20/0.56  % (6654)Instructions burned: 14 (million)
% 0.20/0.56  % (6654)------------------------------
% 0.20/0.56  % (6654)------------------------------
% 0.20/0.56  % (6677)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.56  % (6668)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (6668)Termination reason: Unknown
% 0.20/0.56  % (6668)Termination phase: Property scanning
% 0.20/0.56  
% 0.20/0.56  % (6668)Memory used [KB]: 1791
% 0.20/0.56  % (6668)Time elapsed: 0.006 s
% 0.20/0.56  % (6668)Instructions burned: 9 (million)
% 0.20/0.56  % (6668)------------------------------
% 0.20/0.56  % (6668)------------------------------
% 0.20/0.56  % (6659)Also succeeded, but the first one will report.
% 0.20/0.56  % (6670)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.56  % (6675)Refutation found. Thanks to Tanya!
% 0.20/0.56  % SZS status Theorem for theBenchmark
% 0.20/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.56  % (6675)------------------------------
% 0.20/0.56  % (6675)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (6675)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (6675)Termination reason: Refutation
% 0.20/0.56  
% 0.20/0.56  % (6675)Memory used [KB]: 6524
% 0.20/0.56  % (6675)Time elapsed: 0.101 s
% 0.20/0.56  % (6675)Instructions burned: 15 (million)
% 0.20/0.56  % (6675)------------------------------
% 0.20/0.56  % (6675)------------------------------
% 0.20/0.56  % (6652)Success in time 0.202 s
%------------------------------------------------------------------------------