TSTP Solution File: SWC314+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC314+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 : n027.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 18:40:21 EDT 2022

% Result   : Theorem 0.20s 0.56s
% Output   : Refutation 1.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  175 (   7 unt;   0 def)
%            Number of atoms       :  860 ( 301 equ)
%            Maximal formula atoms :   52 (   4 avg)
%            Number of connectives : 1145 ( 460   ~; 480   |; 151   &)
%                                         (  20 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   21 (  19 usr;  17 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  178 ( 128   !;  50   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f649,plain,
    $false,
    inference(avatar_sat_refutation,[],[f262,f271,f276,f285,f286,f287,f292,f293,f294,f304,f312,f360,f364,f379,f383,f387,f390,f394,f410,f416,f648]) ).

fof(f648,plain,
    ( ~ spl12_1
    | ~ spl12_9
    | ~ spl12_10
    | spl12_12
    | ~ spl12_13 ),
    inference(avatar_contradiction_clause,[],[f647]) ).

fof(f647,plain,
    ( $false
    | ~ spl12_1
    | ~ spl12_9
    | ~ spl12_10
    | spl12_12
    | ~ spl12_13 ),
    inference(subsumption_resolution,[],[f646,f284]) ).

fof(f284,plain,
    ( app(sK6,cons(sK5,nil)) != sK1
    | spl12_12 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f282,plain,
    ( spl12_12
  <=> app(sK6,cons(sK5,nil)) = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).

fof(f646,plain,
    ( app(sK6,cons(sK5,nil)) = sK1
    | ~ spl12_1
    | ~ spl12_9
    | ~ spl12_10
    | ~ spl12_13 ),
    inference(forward_demodulation,[],[f528,f527]) ).

fof(f527,plain,
    ( tl(sK4) = sK6
    | ~ spl12_9
    | ~ spl12_10
    | ~ spl12_13 ),
    inference(subsumption_resolution,[],[f526,f275]) ).

fof(f275,plain,
    ( ssItem(sK5)
    | ~ spl12_10 ),
    inference(avatar_component_clause,[],[f273]) ).

fof(f273,plain,
    ( spl12_10
  <=> ssItem(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).

fof(f526,plain,
    ( tl(sK4) = sK6
    | ~ ssItem(sK5)
    | ~ spl12_9
    | ~ spl12_10
    | ~ spl12_13 ),
    inference(subsumption_resolution,[],[f518,f291]) ).

fof(f291,plain,
    ( ssList(sK6)
    | ~ spl12_13 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f289,plain,
    ( spl12_13
  <=> ssList(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_13])]) ).

fof(f518,plain,
    ( ~ ssList(sK6)
    | ~ ssItem(sK5)
    | tl(sK4) = sK6
    | ~ spl12_9
    | ~ spl12_10
    | ~ spl12_13 ),
    inference(superposition,[],[f194,f514]) ).

fof(f514,plain,
    ( cons(sK5,sK6) = sK4
    | ~ spl12_9
    | ~ spl12_10
    | ~ spl12_13 ),
    inference(subsumption_resolution,[],[f513,f275]) ).

fof(f513,plain,
    ( ~ ssItem(sK5)
    | cons(sK5,sK6) = sK4
    | ~ spl12_9
    | ~ spl12_13 ),
    inference(subsumption_resolution,[],[f506,f291]) ).

fof(f506,plain,
    ( ~ ssList(sK6)
    | ~ ssItem(sK5)
    | cons(sK5,sK6) = sK4
    | ~ spl12_9 ),
    inference(superposition,[],[f270,f199]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssList(X0)
      | ~ ssItem(X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).

fof(f270,plain,
    ( app(cons(sK5,nil),sK6) = sK4
    | ~ spl12_9 ),
    inference(avatar_component_clause,[],[f268]) ).

fof(f268,plain,
    ( spl12_9
  <=> app(cons(sK5,nil),sK6) = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_9])]) ).

fof(f194,plain,
    ! [X0,X1] :
      ( tl(cons(X1,X0)) = X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssItem(X1)
          | tl(cons(X1,X0)) = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => tl(cons(X1,X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).

fof(f528,plain,
    ( sK1 = app(tl(sK4),cons(sK5,nil))
    | ~ spl12_1
    | ~ spl12_9
    | ~ spl12_10
    | ~ spl12_13 ),
    inference(backward_demodulation,[],[f237,f523]) ).

fof(f523,plain,
    ( sK5 = hd(sK4)
    | ~ spl12_9
    | ~ spl12_10
    | ~ spl12_13 ),
    inference(subsumption_resolution,[],[f522,f275]) ).

fof(f522,plain,
    ( ~ ssItem(sK5)
    | sK5 = hd(sK4)
    | ~ spl12_9
    | ~ spl12_10
    | ~ spl12_13 ),
    inference(subsumption_resolution,[],[f517,f291]) ).

fof(f517,plain,
    ( sK5 = hd(sK4)
    | ~ ssList(sK6)
    | ~ ssItem(sK5)
    | ~ spl12_9
    | ~ spl12_10
    | ~ spl12_13 ),
    inference(superposition,[],[f209,f514]) ).

fof(f209,plain,
    ! [X0,X1] :
      ( hd(cons(X1,X0)) = X1
      | ~ ssList(X0)
      | ~ ssItem(X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | hd(cons(X1,X0)) = X1 ) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => hd(cons(X1,X0)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

fof(f237,plain,
    ( app(tl(sK4),cons(hd(sK4),nil)) = sK1
    | ~ spl12_1 ),
    inference(avatar_component_clause,[],[f235]) ).

fof(f235,plain,
    ( spl12_1
  <=> app(tl(sK4),cons(hd(sK4),nil)) = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f416,plain,
    ( spl12_4
    | spl12_8
    | ~ spl12_14 ),
    inference(avatar_contradiction_clause,[],[f415]) ).

fof(f415,plain,
    ( $false
    | spl12_4
    | spl12_8
    | ~ spl12_14 ),
    inference(subsumption_resolution,[],[f414,f265]) ).

fof(f265,plain,
    ( nil != sK4
    | spl12_8 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f264,plain,
    ( spl12_8
  <=> nil = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).

fof(f414,plain,
    ( nil = sK4
    | spl12_4
    | ~ spl12_14 ),
    inference(subsumption_resolution,[],[f413,f297]) ).

fof(f297,plain,
    ( ssList(nil)
    | ~ spl12_14 ),
    inference(avatar_component_clause,[],[f296]) ).

fof(f296,plain,
    ( spl12_14
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).

fof(f413,plain,
    ( ~ ssList(nil)
    | nil = sK4
    | spl12_4 ),
    inference(subsumption_resolution,[],[f411,f177]) ).

fof(f177,plain,
    ssList(sK4),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ( ssList(sK1)
    & ssList(sK4)
    & ( ~ neq(sK4,nil)
      | ! [X4] :
          ( ! [X5] :
              ( ! [X6] :
                  ( ~ neq(nil,sK4)
                  | ! [X7] :
                      ( ~ ssItem(X7)
                      | ~ neq(nil,sK4)
                      | cons(X7,nil) != X6
                      | hd(sK4) != X7 )
                  | ~ ssList(X6)
                  | tl(sK4) != X5
                  | app(X5,X6) != X4 )
              | ~ ssList(X5) )
          | sK3 = X4
          | ~ ssList(X4) ) )
    & sK3 = sK1
    & sK2 = sK4
    & ( nil != sK4
      | nil = sK3 )
    & ( ( nil = sK2
        & nil != sK1 )
      | ( ssItem(sK5)
        & sK2 = app(cons(sK5,nil),sK6)
        & app(sK6,cons(sK5,nil)) != sK1
        & ssList(sK6) ) )
    & ssList(sK3)
    & ssList(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f101,f145,f144,f143,f142,f141,f140]) ).

fof(f140,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ssList(X3)
                    & ( ~ neq(X3,nil)
                      | ! [X4] :
                          ( ! [X5] :
                              ( ! [X6] :
                                  ( ~ neq(nil,X3)
                                  | ! [X7] :
                                      ( ~ ssItem(X7)
                                      | ~ neq(nil,X3)
                                      | cons(X7,nil) != X6
                                      | hd(X3) != X7 )
                                  | ~ ssList(X6)
                                  | tl(X3) != X5
                                  | app(X5,X6) != X4 )
                              | ~ ssList(X5) )
                          | X2 = X4
                          | ~ ssList(X4) ) )
                    & X0 = X2
                    & X1 = X3
                    & ( nil != X3
                      | nil = X2 )
                    & ( ( nil = X1
                        & nil != X0 )
                      | ? [X8] :
                          ( ssItem(X8)
                          & ? [X9] :
                              ( app(cons(X8,nil),X9) = X1
                              & app(X9,cons(X8,nil)) != X0
                              & ssList(X9) ) ) ) )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK1)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & ( ~ neq(X3,nil)
                    | ! [X4] :
                        ( ! [X5] :
                            ( ! [X6] :
                                ( ~ neq(nil,X3)
                                | ! [X7] :
                                    ( ~ ssItem(X7)
                                    | ~ neq(nil,X3)
                                    | cons(X7,nil) != X6
                                    | hd(X3) != X7 )
                                | ~ ssList(X6)
                                | tl(X3) != X5
                                | app(X5,X6) != X4 )
                            | ~ ssList(X5) )
                        | X2 = X4
                        | ~ ssList(X4) ) )
                  & sK1 = X2
                  & X1 = X3
                  & ( nil != X3
                    | nil = X2 )
                  & ( ( nil = X1
                      & nil != sK1 )
                    | ? [X8] :
                        ( ssItem(X8)
                        & ? [X9] :
                            ( app(cons(X8,nil),X9) = X1
                            & app(X9,cons(X8,nil)) != sK1
                            & ssList(X9) ) ) ) )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f141,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ssList(X3)
                & ( ~ neq(X3,nil)
                  | ! [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ~ neq(nil,X3)
                              | ! [X7] :
                                  ( ~ ssItem(X7)
                                  | ~ neq(nil,X3)
                                  | cons(X7,nil) != X6
                                  | hd(X3) != X7 )
                              | ~ ssList(X6)
                              | tl(X3) != X5
                              | app(X5,X6) != X4 )
                          | ~ ssList(X5) )
                      | X2 = X4
                      | ~ ssList(X4) ) )
                & sK1 = X2
                & X1 = X3
                & ( nil != X3
                  | nil = X2 )
                & ( ( nil = X1
                    & nil != sK1 )
                  | ? [X8] :
                      ( ssItem(X8)
                      & ? [X9] :
                          ( app(cons(X8,nil),X9) = X1
                          & app(X9,cons(X8,nil)) != sK1
                          & ssList(X9) ) ) ) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ssList(X3)
              & ( ~ neq(X3,nil)
                | ! [X4] :
                    ( ! [X5] :
                        ( ! [X6] :
                            ( ~ neq(nil,X3)
                            | ! [X7] :
                                ( ~ ssItem(X7)
                                | ~ neq(nil,X3)
                                | cons(X7,nil) != X6
                                | hd(X3) != X7 )
                            | ~ ssList(X6)
                            | tl(X3) != X5
                            | app(X5,X6) != X4 )
                        | ~ ssList(X5) )
                    | X2 = X4
                    | ~ ssList(X4) ) )
              & sK1 = X2
              & sK2 = X3
              & ( nil != X3
                | nil = X2 )
              & ( ( nil = sK2
                  & nil != sK1 )
                | ? [X8] :
                    ( ssItem(X8)
                    & ? [X9] :
                        ( app(cons(X8,nil),X9) = sK2
                        & app(X9,cons(X8,nil)) != sK1
                        & ssList(X9) ) ) ) )
          & ssList(X2) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f142,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ssList(X3)
            & ( ~ neq(X3,nil)
              | ! [X4] :
                  ( ! [X5] :
                      ( ! [X6] :
                          ( ~ neq(nil,X3)
                          | ! [X7] :
                              ( ~ ssItem(X7)
                              | ~ neq(nil,X3)
                              | cons(X7,nil) != X6
                              | hd(X3) != X7 )
                          | ~ ssList(X6)
                          | tl(X3) != X5
                          | app(X5,X6) != X4 )
                      | ~ ssList(X5) )
                  | X2 = X4
                  | ~ ssList(X4) ) )
            & sK1 = X2
            & sK2 = X3
            & ( nil != X3
              | nil = X2 )
            & ( ( nil = sK2
                & nil != sK1 )
              | ? [X8] :
                  ( ssItem(X8)
                  & ? [X9] :
                      ( app(cons(X8,nil),X9) = sK2
                      & app(X9,cons(X8,nil)) != sK1
                      & ssList(X9) ) ) ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ssList(X3)
          & ( ~ neq(X3,nil)
            | ! [X4] :
                ( ! [X5] :
                    ( ! [X6] :
                        ( ~ neq(nil,X3)
                        | ! [X7] :
                            ( ~ ssItem(X7)
                            | ~ neq(nil,X3)
                            | cons(X7,nil) != X6
                            | hd(X3) != X7 )
                        | ~ ssList(X6)
                        | tl(X3) != X5
                        | app(X5,X6) != X4 )
                    | ~ ssList(X5) )
                | sK3 = X4
                | ~ ssList(X4) ) )
          & sK3 = sK1
          & sK2 = X3
          & ( nil != X3
            | nil = sK3 )
          & ( ( nil = sK2
              & nil != sK1 )
            | ? [X8] :
                ( ssItem(X8)
                & ? [X9] :
                    ( app(cons(X8,nil),X9) = sK2
                    & app(X9,cons(X8,nil)) != sK1
                    & ssList(X9) ) ) ) )
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ( ? [X3] :
        ( ssList(X3)
        & ( ~ neq(X3,nil)
          | ! [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ~ neq(nil,X3)
                      | ! [X7] :
                          ( ~ ssItem(X7)
                          | ~ neq(nil,X3)
                          | cons(X7,nil) != X6
                          | hd(X3) != X7 )
                      | ~ ssList(X6)
                      | tl(X3) != X5
                      | app(X5,X6) != X4 )
                  | ~ ssList(X5) )
              | sK3 = X4
              | ~ ssList(X4) ) )
        & sK3 = sK1
        & sK2 = X3
        & ( nil != X3
          | nil = sK3 )
        & ( ( nil = sK2
            & nil != sK1 )
          | ? [X8] :
              ( ssItem(X8)
              & ? [X9] :
                  ( app(cons(X8,nil),X9) = sK2
                  & app(X9,cons(X8,nil)) != sK1
                  & ssList(X9) ) ) ) )
   => ( ssList(sK4)
      & ( ~ neq(sK4,nil)
        | ! [X4] :
            ( ! [X5] :
                ( ! [X6] :
                    ( ~ neq(nil,sK4)
                    | ! [X7] :
                        ( ~ ssItem(X7)
                        | ~ neq(nil,sK4)
                        | cons(X7,nil) != X6
                        | hd(sK4) != X7 )
                    | ~ ssList(X6)
                    | tl(sK4) != X5
                    | app(X5,X6) != X4 )
                | ~ ssList(X5) )
            | sK3 = X4
            | ~ ssList(X4) ) )
      & sK3 = sK1
      & sK2 = sK4
      & ( nil != sK4
        | nil = sK3 )
      & ( ( nil = sK2
          & nil != sK1 )
        | ? [X8] :
            ( ssItem(X8)
            & ? [X9] :
                ( app(cons(X8,nil),X9) = sK2
                & app(X9,cons(X8,nil)) != sK1
                & ssList(X9) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f144,plain,
    ( ? [X8] :
        ( ssItem(X8)
        & ? [X9] :
            ( app(cons(X8,nil),X9) = sK2
            & app(X9,cons(X8,nil)) != sK1
            & ssList(X9) ) )
   => ( ssItem(sK5)
      & ? [X9] :
          ( sK2 = app(cons(sK5,nil),X9)
          & app(X9,cons(sK5,nil)) != sK1
          & ssList(X9) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f145,plain,
    ( ? [X9] :
        ( sK2 = app(cons(sK5,nil),X9)
        & app(X9,cons(sK5,nil)) != sK1
        & ssList(X9) )
   => ( sK2 = app(cons(sK5,nil),sK6)
      & app(sK6,cons(sK5,nil)) != sK1
      & ssList(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & ( ~ neq(X3,nil)
                    | ! [X4] :
                        ( ! [X5] :
                            ( ! [X6] :
                                ( ~ neq(nil,X3)
                                | ! [X7] :
                                    ( ~ ssItem(X7)
                                    | ~ neq(nil,X3)
                                    | cons(X7,nil) != X6
                                    | hd(X3) != X7 )
                                | ~ ssList(X6)
                                | tl(X3) != X5
                                | app(X5,X6) != X4 )
                            | ~ ssList(X5) )
                        | X2 = X4
                        | ~ ssList(X4) ) )
                  & X0 = X2
                  & X1 = X3
                  & ( nil != X3
                    | nil = X2 )
                  & ( ( nil = X1
                      & nil != X0 )
                    | ? [X8] :
                        ( ssItem(X8)
                        & ? [X9] :
                            ( app(cons(X8,nil),X9) = X1
                            & app(X9,cons(X8,nil)) != X0
                            & ssList(X9) ) ) ) )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( X1 != X3
                    | ( ! [X8] :
                          ( ssItem(X8)
                         => ! [X9] :
                              ( ~ ssList(X9)
                              | app(cons(X8,nil),X9) != X1
                              | app(X9,cons(X8,nil)) = X0 ) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | ~ ssList(X3)
                    | ( nil = X3
                      & nil != X2 )
                    | ( ? [X4] :
                          ( ssList(X4)
                          & X2 != X4
                          & ? [X5] :
                              ( ? [X6] :
                                  ( ssList(X6)
                                  & ? [X7] :
                                      ( ssItem(X7)
                                      & hd(X3) = X7
                                      & cons(X7,nil) = X6
                                      & neq(nil,X3) )
                                  & tl(X3) = X5
                                  & neq(nil,X3)
                                  & app(X5,X6) = X4 )
                              & ssList(X5) ) )
                      & neq(X3,nil) )
                    | X0 != X2 ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( X1 != X3
                  | ( ! [X8] :
                        ( ssItem(X8)
                       => ! [X9] :
                            ( ~ ssList(X9)
                            | app(cons(X8,nil),X9) != X1
                            | app(X9,cons(X8,nil)) = X0 ) )
                    & ( nil = X0
                      | nil != X1 ) )
                  | ~ ssList(X3)
                  | ( nil = X3
                    & nil != X2 )
                  | ( ? [X4] :
                        ( ssList(X4)
                        & X2 != X4
                        & ? [X5] :
                            ( ? [X6] :
                                ( ssList(X6)
                                & ? [X7] :
                                    ( ssItem(X7)
                                    & hd(X3) = X7
                                    & cons(X7,nil) = X6
                                    & neq(nil,X3) )
                                & tl(X3) = X5
                                & neq(nil,X3)
                                & app(X5,X6) = X4 )
                            & ssList(X5) ) )
                    & neq(X3,nil) )
                  | X0 != X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f411,plain,
    ( ~ ssList(sK4)
    | ~ ssList(nil)
    | nil = sK4
    | spl12_4 ),
    inference(resolution,[],[f249,f203]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X1)
      | X0 = X1
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( neq(X0,X1)
          <=> X0 != X1 ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

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

fof(f249,plain,
    ( ~ neq(nil,sK4)
    | spl12_4 ),
    inference(avatar_component_clause,[],[f247]) ).

fof(f247,plain,
    ( spl12_4
  <=> neq(nil,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).

fof(f410,plain,
    ( spl12_2
    | spl12_8
    | ~ spl12_14 ),
    inference(avatar_contradiction_clause,[],[f409]) ).

fof(f409,plain,
    ( $false
    | spl12_2
    | spl12_8
    | ~ spl12_14 ),
    inference(subsumption_resolution,[],[f408,f177]) ).

fof(f408,plain,
    ( ~ ssList(sK4)
    | spl12_2
    | spl12_8
    | ~ spl12_14 ),
    inference(subsumption_resolution,[],[f407,f297]) ).

fof(f407,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK4)
    | spl12_2
    | spl12_8 ),
    inference(subsumption_resolution,[],[f395,f265]) ).

fof(f395,plain,
    ( nil = sK4
    | ~ ssList(nil)
    | ~ ssList(sK4)
    | spl12_2 ),
    inference(resolution,[],[f241,f203]) ).

fof(f241,plain,
    ( ~ neq(sK4,nil)
    | spl12_2 ),
    inference(avatar_component_clause,[],[f239]) ).

fof(f239,plain,
    ( spl12_2
  <=> neq(sK4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).

fof(f394,plain,
    ( spl12_5
    | spl12_8 ),
    inference(avatar_contradiction_clause,[],[f393]) ).

fof(f393,plain,
    ( $false
    | spl12_5
    | spl12_8 ),
    inference(subsumption_resolution,[],[f392,f177]) ).

fof(f392,plain,
    ( ~ ssList(sK4)
    | spl12_5
    | spl12_8 ),
    inference(subsumption_resolution,[],[f391,f265]) ).

fof(f391,plain,
    ( nil = sK4
    | ~ ssList(sK4)
    | spl12_5 ),
    inference(resolution,[],[f253,f186]) ).

fof(f186,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssItem(hd(X0))
      | nil = X0 ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f253,plain,
    ( ~ ssItem(hd(sK4))
    | spl12_5 ),
    inference(avatar_component_clause,[],[f251]) ).

fof(f251,plain,
    ( spl12_5
  <=> ssItem(hd(sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).

fof(f390,plain,
    ( ~ spl12_5
    | spl12_7
    | ~ spl12_14 ),
    inference(avatar_split_clause,[],[f389,f296,f259,f251]) ).

fof(f259,plain,
    ( spl12_7
  <=> ssList(cons(hd(sK4),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).

fof(f389,plain,
    ( ~ ssItem(hd(sK4))
    | spl12_7
    | ~ spl12_14 ),
    inference(subsumption_resolution,[],[f388,f297]) ).

fof(f388,plain,
    ( ~ ssItem(hd(sK4))
    | ~ ssList(nil)
    | spl12_7 ),
    inference(resolution,[],[f261,f185]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssList(X0)
      | ~ ssItem(X1) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssItem(X1)
          | ssList(cons(X1,X0)) )
      | ~ 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(f261,plain,
    ( ~ ssList(cons(hd(sK4),nil))
    | spl12_7 ),
    inference(avatar_component_clause,[],[f259]) ).

fof(f387,plain,
    ( spl12_3
    | spl12_8 ),
    inference(avatar_contradiction_clause,[],[f386]) ).

fof(f386,plain,
    ( $false
    | spl12_3
    | spl12_8 ),
    inference(subsumption_resolution,[],[f385,f265]) ).

fof(f385,plain,
    ( nil = sK4
    | spl12_3 ),
    inference(subsumption_resolution,[],[f384,f177]) ).

fof(f384,plain,
    ( ~ ssList(sK4)
    | nil = sK4
    | spl12_3 ),
    inference(resolution,[],[f245,f192]) ).

fof(f192,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    inference(flattening,[],[f129]) ).

fof(f129,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

fof(f245,plain,
    ( ~ ssList(tl(sK4))
    | spl12_3 ),
    inference(avatar_component_clause,[],[f243]) ).

fof(f243,plain,
    ( spl12_3
  <=> ssList(tl(sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).

fof(f383,plain,
    ( ~ spl12_3
    | ~ spl12_7
    | spl12_6 ),
    inference(avatar_split_clause,[],[f382,f255,f259,f243]) ).

fof(f255,plain,
    ( spl12_6
  <=> ssList(app(tl(sK4),cons(hd(sK4),nil))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).

fof(f382,plain,
    ( ~ ssList(cons(hd(sK4),nil))
    | ~ ssList(tl(sK4))
    | spl12_6 ),
    inference(resolution,[],[f257,f197]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ssList(app(X0,X1)) ) ),
    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(f257,plain,
    ( ~ ssList(app(tl(sK4),cons(hd(sK4),nil)))
    | spl12_6 ),
    inference(avatar_component_clause,[],[f255]) ).

fof(f379,plain,
    ( ~ spl12_8
    | ~ spl12_9
    | ~ spl12_11
    | spl12_12
    | ~ spl12_18
    | ~ spl12_19 ),
    inference(avatar_contradiction_clause,[],[f378]) ).

fof(f378,plain,
    ( $false
    | ~ spl12_8
    | ~ spl12_9
    | ~ spl12_11
    | spl12_12
    | ~ spl12_18
    | ~ spl12_19 ),
    inference(subsumption_resolution,[],[f377,f358]) ).

fof(f358,plain,
    ( ssList(cons(sK5,nil))
    | ~ spl12_19 ),
    inference(avatar_component_clause,[],[f357]) ).

fof(f357,plain,
    ( spl12_19
  <=> ssList(cons(sK5,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_19])]) ).

fof(f377,plain,
    ( ~ ssList(cons(sK5,nil))
    | ~ spl12_8
    | ~ spl12_9
    | ~ spl12_11
    | spl12_12
    | ~ spl12_18
    | ~ spl12_19 ),
    inference(subsumption_resolution,[],[f370,f369]) ).

fof(f369,plain,
    ( nil != cons(sK5,nil)
    | ~ spl12_11
    | spl12_12
    | ~ spl12_18
    | ~ spl12_19 ),
    inference(subsumption_resolution,[],[f368,f358]) ).

fof(f368,plain,
    ( ~ ssList(cons(sK5,nil))
    | nil != cons(sK5,nil)
    | ~ spl12_11
    | spl12_12
    | ~ spl12_18 ),
    inference(superposition,[],[f365,f158]) ).

fof(f158,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

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

fof(f365,plain,
    ( nil != app(nil,cons(sK5,nil))
    | ~ spl12_11
    | spl12_12
    | ~ spl12_18 ),
    inference(backward_demodulation,[],[f310,f355]) ).

fof(f355,plain,
    ( nil = sK6
    | ~ spl12_18 ),
    inference(avatar_component_clause,[],[f353]) ).

fof(f353,plain,
    ( spl12_18
  <=> nil = sK6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_18])]) ).

fof(f310,plain,
    ( nil != app(sK6,cons(sK5,nil))
    | ~ spl12_11
    | spl12_12 ),
    inference(forward_demodulation,[],[f284,f279]) ).

fof(f279,plain,
    ( nil = sK1
    | ~ spl12_11 ),
    inference(avatar_component_clause,[],[f278]) ).

fof(f278,plain,
    ( spl12_11
  <=> nil = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).

fof(f370,plain,
    ( nil = cons(sK5,nil)
    | ~ ssList(cons(sK5,nil))
    | ~ spl12_8
    | ~ spl12_9
    | ~ spl12_18 ),
    inference(superposition,[],[f366,f195]) ).

fof(f195,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

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

fof(f366,plain,
    ( nil = app(cons(sK5,nil),nil)
    | ~ spl12_8
    | ~ spl12_9
    | ~ spl12_18 ),
    inference(backward_demodulation,[],[f309,f355]) ).

fof(f309,plain,
    ( nil = app(cons(sK5,nil),sK6)
    | ~ spl12_8
    | ~ spl12_9 ),
    inference(forward_demodulation,[],[f270,f266]) ).

fof(f266,plain,
    ( nil = sK4
    | ~ spl12_8 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f364,plain,
    ( ~ spl12_10
    | ~ spl12_14
    | spl12_19 ),
    inference(avatar_contradiction_clause,[],[f363]) ).

fof(f363,plain,
    ( $false
    | ~ spl12_10
    | ~ spl12_14
    | spl12_19 ),
    inference(subsumption_resolution,[],[f362,f297]) ).

fof(f362,plain,
    ( ~ ssList(nil)
    | ~ spl12_10
    | spl12_19 ),
    inference(subsumption_resolution,[],[f361,f275]) ).

fof(f361,plain,
    ( ~ ssItem(sK5)
    | ~ ssList(nil)
    | spl12_19 ),
    inference(resolution,[],[f359,f185]) ).

fof(f359,plain,
    ( ~ ssList(cons(sK5,nil))
    | spl12_19 ),
    inference(avatar_component_clause,[],[f357]) ).

fof(f360,plain,
    ( spl12_18
    | ~ spl12_19
    | ~ spl12_8
    | ~ spl12_9
    | ~ spl12_13 ),
    inference(avatar_split_clause,[],[f351,f289,f268,f264,f357,f353]) ).

fof(f351,plain,
    ( ~ ssList(cons(sK5,nil))
    | nil = sK6
    | ~ spl12_8
    | ~ spl12_9
    | ~ spl12_13 ),
    inference(subsumption_resolution,[],[f350,f291]) ).

fof(f350,plain,
    ( ~ ssList(cons(sK5,nil))
    | nil = sK6
    | ~ ssList(sK6)
    | ~ spl12_8
    | ~ spl12_9 ),
    inference(trivial_inequality_removal,[],[f345]) ).

fof(f345,plain,
    ( ~ ssList(sK6)
    | nil != nil
    | nil = sK6
    | ~ ssList(cons(sK5,nil))
    | ~ spl12_8
    | ~ spl12_9 ),
    inference(superposition,[],[f183,f309]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) )
            & ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f147]) ).

fof(f147,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) )
            & ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = X0
              & nil = X1 )
          <=> nil = app(X0,X1) )
          | ~ ssList(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(f312,plain,
    spl12_14,
    inference(avatar_split_clause,[],[f189,f296]) ).

fof(f189,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f304,plain,
    ( spl12_9
    | ~ spl12_11 ),
    inference(avatar_split_clause,[],[f219,f278,f268]) ).

fof(f219,plain,
    ( nil != sK1
    | app(cons(sK5,nil),sK6) = sK4 ),
    inference(definition_unfolding,[],[f167,f174]) ).

fof(f174,plain,
    sK2 = sK4,
    inference(cnf_transformation,[],[f146]) ).

fof(f167,plain,
    ( nil != sK1
    | sK2 = app(cons(sK5,nil),sK6) ),
    inference(cnf_transformation,[],[f146]) ).

fof(f294,plain,
    ( spl12_8
    | spl12_13 ),
    inference(avatar_split_clause,[],[f218,f289,f264]) ).

fof(f218,plain,
    ( ssList(sK6)
    | nil = sK4 ),
    inference(definition_unfolding,[],[f169,f174]) ).

fof(f169,plain,
    ( nil = sK2
    | ssList(sK6) ),
    inference(cnf_transformation,[],[f146]) ).

fof(f293,plain,
    ( ~ spl12_11
    | spl12_10 ),
    inference(avatar_split_clause,[],[f168,f273,f278]) ).

fof(f168,plain,
    ( ssItem(sK5)
    | nil != sK1 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f292,plain,
    ( ~ spl12_11
    | spl12_13 ),
    inference(avatar_split_clause,[],[f165,f289,f278]) ).

fof(f165,plain,
    ( ssList(sK6)
    | nil != sK1 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f287,plain,
    ( ~ spl12_12
    | spl12_8 ),
    inference(avatar_split_clause,[],[f217,f264,f282]) ).

fof(f217,plain,
    ( nil = sK4
    | app(sK6,cons(sK5,nil)) != sK1 ),
    inference(definition_unfolding,[],[f170,f174]) ).

fof(f170,plain,
    ( nil = sK2
    | app(sK6,cons(sK5,nil)) != sK1 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f286,plain,
    ( ~ spl12_8
    | spl12_11 ),
    inference(avatar_split_clause,[],[f214,f278,f264]) ).

fof(f214,plain,
    ( nil = sK1
    | nil != sK4 ),
    inference(definition_unfolding,[],[f173,f175]) ).

fof(f175,plain,
    sK3 = sK1,
    inference(cnf_transformation,[],[f146]) ).

fof(f173,plain,
    ( nil != sK4
    | nil = sK3 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f285,plain,
    ( ~ spl12_11
    | ~ spl12_12 ),
    inference(avatar_split_clause,[],[f166,f282,f278]) ).

fof(f166,plain,
    ( app(sK6,cons(sK5,nil)) != sK1
    | nil != sK1 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f276,plain,
    ( spl12_8
    | spl12_10 ),
    inference(avatar_split_clause,[],[f215,f273,f264]) ).

fof(f215,plain,
    ( ssItem(sK5)
    | nil = sK4 ),
    inference(definition_unfolding,[],[f172,f174]) ).

fof(f172,plain,
    ( nil = sK2
    | ssItem(sK5) ),
    inference(cnf_transformation,[],[f146]) ).

fof(f271,plain,
    ( spl12_8
    | spl12_9 ),
    inference(avatar_split_clause,[],[f216,f268,f264]) ).

fof(f216,plain,
    ( app(cons(sK5,nil),sK6) = sK4
    | nil = sK4 ),
    inference(definition_unfolding,[],[f171,f174,f174]) ).

fof(f171,plain,
    ( nil = sK2
    | sK2 = app(cons(sK5,nil),sK6) ),
    inference(cnf_transformation,[],[f146]) ).

fof(f262,plain,
    ( spl12_1
    | ~ spl12_2
    | ~ spl12_3
    | ~ spl12_4
    | ~ spl12_5
    | ~ spl12_6
    | ~ spl12_7 ),
    inference(avatar_split_clause,[],[f233,f259,f255,f251,f247,f243,f239,f235]) ).

fof(f233,plain,
    ( ~ ssList(cons(hd(sK4),nil))
    | ~ ssList(app(tl(sK4),cons(hd(sK4),nil)))
    | ~ ssItem(hd(sK4))
    | ~ neq(nil,sK4)
    | ~ ssList(tl(sK4))
    | ~ neq(sK4,nil)
    | app(tl(sK4),cons(hd(sK4),nil)) = sK1 ),
    inference(duplicate_literal_removal,[],[f226]) ).

fof(f226,plain,
    ( ~ ssList(tl(sK4))
    | app(tl(sK4),cons(hd(sK4),nil)) = sK1
    | ~ neq(nil,sK4)
    | ~ ssList(cons(hd(sK4),nil))
    | ~ neq(sK4,nil)
    | ~ ssItem(hd(sK4))
    | ~ neq(nil,sK4)
    | ~ ssList(app(tl(sK4),cons(hd(sK4),nil))) ),
    inference(equality_resolution,[],[f225]) ).

fof(f225,plain,
    ! [X4] :
      ( ~ neq(sK4,nil)
      | ~ neq(nil,sK4)
      | ~ ssItem(hd(sK4))
      | ~ neq(nil,sK4)
      | ~ ssList(cons(hd(sK4),nil))
      | app(tl(sK4),cons(hd(sK4),nil)) != X4
      | ~ ssList(tl(sK4))
      | sK1 = X4
      | ~ ssList(X4) ),
    inference(equality_resolution,[],[f224]) ).

fof(f224,plain,
    ! [X4,X5] :
      ( ~ neq(sK4,nil)
      | ~ neq(nil,sK4)
      | ~ ssItem(hd(sK4))
      | ~ neq(nil,sK4)
      | ~ ssList(cons(hd(sK4),nil))
      | tl(sK4) != X5
      | app(X5,cons(hd(sK4),nil)) != X4
      | ~ ssList(X5)
      | sK1 = X4
      | ~ ssList(X4) ),
    inference(equality_resolution,[],[f223]) ).

fof(f223,plain,
    ! [X7,X4,X5] :
      ( ~ neq(sK4,nil)
      | ~ neq(nil,sK4)
      | ~ ssItem(X7)
      | ~ neq(nil,sK4)
      | hd(sK4) != X7
      | ~ ssList(cons(X7,nil))
      | tl(sK4) != X5
      | app(X5,cons(X7,nil)) != X4
      | ~ ssList(X5)
      | sK1 = X4
      | ~ ssList(X4) ),
    inference(equality_resolution,[],[f213]) ).

fof(f213,plain,
    ! [X6,X7,X4,X5] :
      ( ~ neq(sK4,nil)
      | ~ neq(nil,sK4)
      | ~ ssItem(X7)
      | ~ neq(nil,sK4)
      | cons(X7,nil) != X6
      | hd(sK4) != X7
      | ~ ssList(X6)
      | tl(sK4) != X5
      | app(X5,X6) != X4
      | ~ ssList(X5)
      | sK1 = X4
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f176,f175]) ).

fof(f176,plain,
    ! [X6,X7,X4,X5] :
      ( ~ neq(sK4,nil)
      | ~ neq(nil,sK4)
      | ~ ssItem(X7)
      | ~ neq(nil,sK4)
      | cons(X7,nil) != X6
      | hd(sK4) != X7
      | ~ ssList(X6)
      | tl(sK4) != X5
      | app(X5,X6) != X4
      | ~ ssList(X5)
      | sK3 = X4
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f146]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC314+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34  % CPULimit   : 300
% 0.19/0.34  % WCLimit    : 300
% 0.19/0.34  % DateTime   : Tue Aug 30 19:00:46 EDT 2022
% 0.19/0.34  % CPUTime    : 
% 0.20/0.47  % (18021)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)
% 0.20/0.48  % (18030)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)
% 0.20/0.48  % (18030)Instruction limit reached!
% 0.20/0.48  % (18030)------------------------------
% 0.20/0.48  % (18030)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48  % (18030)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48  % (18030)Termination reason: Unknown
% 0.20/0.48  % (18030)Termination phase: Preprocessing 2
% 0.20/0.48  
% 0.20/0.48  % (18030)Memory used [KB]: 1535
% 0.20/0.48  % (18030)Time elapsed: 0.004 s
% 0.20/0.48  % (18030)Instructions burned: 2 (million)
% 0.20/0.48  % (18030)------------------------------
% 0.20/0.48  % (18030)------------------------------
% 0.20/0.49  % (18021)Instruction limit reached!
% 0.20/0.49  % (18021)------------------------------
% 0.20/0.49  % (18021)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (18021)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (18021)Termination reason: Unknown
% 0.20/0.49  % (18021)Termination phase: Saturation
% 0.20/0.49  
% 0.20/0.49  % (18021)Memory used [KB]: 6652
% 0.20/0.49  % (18021)Time elapsed: 0.095 s
% 0.20/0.49  % (18021)Instructions burned: 34 (million)
% 0.20/0.49  % (18021)------------------------------
% 0.20/0.49  % (18021)------------------------------
% 0.20/0.50  % (18012)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  % (18038)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)
% 0.20/0.51  % (18026)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)
% 0.20/0.51  % (18019)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  % (18026)Instruction limit reached!
% 0.20/0.51  % (18026)------------------------------
% 0.20/0.51  % (18026)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (18026)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (18026)Termination reason: Unknown
% 0.20/0.51  % (18026)Termination phase: Preprocessing 3
% 0.20/0.51  
% 0.20/0.51  % (18026)Memory used [KB]: 1663
% 0.20/0.51  % (18026)Time elapsed: 0.003 s
% 0.20/0.51  % (18026)Instructions burned: 4 (million)
% 0.20/0.51  % (18026)------------------------------
% 0.20/0.51  % (18026)------------------------------
% 0.20/0.52  % (18034)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)
% 0.20/0.52  % (18027)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)
% 0.20/0.52  % (18027)Instruction limit reached!
% 0.20/0.52  % (18027)------------------------------
% 0.20/0.52  % (18027)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (18027)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (18027)Termination reason: Unknown
% 0.20/0.52  % (18027)Termination phase: Property scanning
% 0.20/0.52  
% 0.20/0.52  % (18027)Memory used [KB]: 1791
% 0.20/0.52  % (18027)Time elapsed: 0.004 s
% 0.20/0.52  % (18027)Instructions burned: 8 (million)
% 0.20/0.52  % (18027)------------------------------
% 0.20/0.52  % (18027)------------------------------
% 0.20/0.52  % (18016)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)
% 0.20/0.53  % (18013)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  % (18022)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)
% 0.20/0.53  % (18041)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)
% 0.20/0.53  % (18037)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)
% 0.20/0.53  % (18015)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)
% 0.20/0.53  % (18022)Refutation not found, incomplete strategy% (18022)------------------------------
% 0.20/0.53  % (18022)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (18022)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (18022)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53  
% 0.20/0.53  % (18022)Memory used [KB]: 6268
% 0.20/0.53  % (18022)Time elapsed: 0.135 s
% 0.20/0.53  % (18022)Instructions burned: 9 (million)
% 0.20/0.53  % (18022)------------------------------
% 0.20/0.53  % (18022)------------------------------
% 0.20/0.53  % (18017)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)
% 0.20/0.53  % (18018)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)
% 0.20/0.54  % (18036)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)
% 0.20/0.54  % (18014)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  % (18014)Instruction limit reached!
% 0.20/0.54  % (18014)------------------------------
% 0.20/0.54  % (18014)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (18014)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (18014)Termination reason: Unknown
% 0.20/0.54  % (18014)Termination phase: Preprocessing 3
% 0.20/0.54  
% 0.20/0.54  % (18014)Memory used [KB]: 1663
% 0.20/0.54  % (18014)Time elapsed: 0.004 s
% 0.20/0.54  % (18014)Instructions burned: 4 (million)
% 0.20/0.54  % (18014)------------------------------
% 0.20/0.54  % (18014)------------------------------
% 0.20/0.54  % (18029)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.54  % (18020)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)
% 0.20/0.54  % (18029)Instruction limit reached!
% 0.20/0.54  % (18029)------------------------------
% 0.20/0.54  % (18029)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (18029)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (18029)Termination reason: Unknown
% 0.20/0.54  % (18029)Termination phase: Preprocessing 2
% 0.20/0.54  
% 0.20/0.54  % (18029)Memory used [KB]: 1535
% 0.20/0.54  % (18029)Time elapsed: 0.002 s
% 0.20/0.54  % (18029)Instructions burned: 3 (million)
% 0.20/0.54  % (18029)------------------------------
% 0.20/0.54  % (18029)------------------------------
% 0.20/0.54  % (18033)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)
% 0.20/0.54  % (18039)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)
% 0.20/0.54  % (18032)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)
% 0.20/0.55  % (18023)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)
% 0.20/0.55  % (18028)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  % (18031)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  % (18025)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)
% 0.20/0.55  % (18035)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)
% 0.20/0.55  % (18013)Instruction limit reached!
% 0.20/0.55  % (18013)------------------------------
% 0.20/0.55  % (18013)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (18013)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (18013)Termination reason: Unknown
% 0.20/0.55  % (18013)Termination phase: Saturation
% 0.20/0.55  
% 0.20/0.55  % (18013)Memory used [KB]: 6396
% 0.20/0.55  % (18013)Time elapsed: 0.132 s
% 0.20/0.55  % (18013)Instructions burned: 13 (million)
% 0.20/0.55  % (18013)------------------------------
% 0.20/0.55  % (18013)------------------------------
% 0.20/0.55  % (18016)Instruction limit reached!
% 0.20/0.55  % (18016)------------------------------
% 0.20/0.55  % (18016)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (18016)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (18016)Termination reason: Unknown
% 0.20/0.55  % (18016)Termination phase: Saturation
% 0.20/0.55  
% 0.20/0.55  % (18016)Memory used [KB]: 6268
% 0.20/0.55  % (18016)Time elapsed: 0.159 s
% 0.20/0.55  % (18016)Instructions burned: 13 (million)
% 0.20/0.55  % (18016)------------------------------
% 0.20/0.55  % (18016)------------------------------
% 0.20/0.55  % (18040)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)
% 0.20/0.56  % (18040)Instruction limit reached!
% 0.20/0.56  % (18040)------------------------------
% 0.20/0.56  % (18040)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (18040)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (18040)Termination reason: Unknown
% 0.20/0.56  % (18040)Termination phase: Function definition elimination
% 0.20/0.56  
% 0.20/0.56  % (18040)Memory used [KB]: 1791
% 0.20/0.56  % (18040)Time elapsed: 0.006 s
% 0.20/0.56  % (18040)Instructions burned: 8 (million)
% 0.20/0.56  % (18040)------------------------------
% 0.20/0.56  % (18040)------------------------------
% 0.20/0.56  % (18024)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)
% 0.20/0.56  % (18017)Instruction limit reached!
% 0.20/0.56  % (18017)------------------------------
% 0.20/0.56  % (18017)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (18017)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (18017)Termination reason: Unknown
% 0.20/0.56  % (18017)Termination phase: Saturation
% 0.20/0.56  
% 0.20/0.56  % (18017)Memory used [KB]: 1663
% 0.20/0.56  % (18017)Time elapsed: 0.138 s
% 0.20/0.56  % (18017)Instructions burned: 15 (million)
% 0.20/0.56  % (18017)------------------------------
% 0.20/0.56  % (18017)------------------------------
% 0.20/0.56  % (18018)First to succeed.
% 0.20/0.56  % (18018)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
% 1.71/0.56  % (18018)------------------------------
% 1.71/0.56  % (18018)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.71/0.56  % (18018)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.71/0.56  % (18018)Termination reason: Refutation
% 1.71/0.56  
% 1.71/0.56  % (18018)Memory used [KB]: 6268
% 1.71/0.56  % (18018)Time elapsed: 0.138 s
% 1.71/0.56  % (18018)Instructions burned: 15 (million)
% 1.71/0.56  % (18018)------------------------------
% 1.71/0.56  % (18018)------------------------------
% 1.71/0.56  % (18011)Success in time 0.209 s
%------------------------------------------------------------------------------