TSTP Solution File: SWC239+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC239+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 : n014.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 18:39:49 EDT 2022

% Result   : Theorem 1.56s 0.55s
% Output   : Refutation 1.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   59 (   9 unt;   0 def)
%            Number of atoms       :  474 ( 139 equ)
%            Maximal formula atoms :   50 (   8 avg)
%            Number of connectives :  627 ( 212   ~; 197   |; 194   &)
%                                         (   3 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   4 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :  142 (  88   !;  54   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f315,plain,
    $false,
    inference(avatar_sat_refutation,[],[f268,f275,f277,f314]) ).

fof(f314,plain,
    ( ~ spl12_1
    | ~ spl12_5 ),
    inference(avatar_contradiction_clause,[],[f313]) ).

fof(f313,plain,
    ( $false
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f312,f308]) ).

fof(f308,plain,
    ( ssItem(sK4(sK5,nil,nil))
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f307,f227]) ).

fof(f227,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f307,plain,
    ( ~ ssList(nil)
    | ssItem(sK4(sK5,nil,nil))
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(trivial_inequality_removal,[],[f306]) ).

fof(f306,plain,
    ( ssItem(sK4(sK5,nil,nil))
    | ~ ssList(nil)
    | sK0 != sK0
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(superposition,[],[f303,f290]) ).

fof(f290,plain,
    sK0 = app(sK0,nil),
    inference(resolution,[],[f163,f197]) ).

fof(f197,plain,
    ssList(sK0),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ( ssList(sK0)
    & ! [X4] :
        ( ! [X5] :
            ( ~ ssList(X5)
            | ! [X6] :
                ( ~ ssList(X6)
                | ( memberP(X5,sK4(X4,X5,X6))
                  & ~ leq(X4,sK4(X4,X5,X6))
                  & lt(X4,sK4(X4,X5,X6))
                  & memberP(X6,sK4(X4,X5,X6))
                  & ssItem(sK4(X4,X5,X6)) )
                | app(app(X5,cons(X4,nil)),X6) != sK0 ) )
        | ~ ssItem(X4) )
    & ssList(sK3)
    & sK2 = sK0
    & ( ( memberP(sK3,sK5)
        & ! [X9] :
            ( ~ leq(sK5,X9)
            | ~ memberP(sK3,X9)
            | sK5 = X9
            | ~ ssItem(X9) )
        & sK2 = cons(sK5,nil)
        & ssItem(sK5) )
      | ( nil = sK2
        & nil = sK3 ) )
    & nil != sK0
    & sK3 = sK1
    & ssList(sK2)
    & ssList(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f124,f148,f147,f146,f145,f144,f143]) ).

fof(f143,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( ~ ssList(X5)
                            | ! [X6] :
                                ( ~ ssList(X6)
                                | ? [X7] :
                                    ( memberP(X5,X7)
                                    & ~ leq(X4,X7)
                                    & lt(X4,X7)
                                    & memberP(X6,X7)
                                    & ssItem(X7) )
                                | app(app(X5,cons(X4,nil)),X6) != X0 ) )
                        | ~ ssItem(X4) )
                    & ssList(X3)
                    & X0 = X2
                    & ( ? [X8] :
                          ( memberP(X3,X8)
                          & ! [X9] :
                              ( ~ leq(X8,X9)
                              | ~ memberP(X3,X9)
                              | X8 = X9
                              | ~ ssItem(X9) )
                          & cons(X8,nil) = X2
                          & ssItem(X8) )
                      | ( nil = X2
                        & nil = X3 ) )
                    & nil != X0
                    & X1 = X3 )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | ? [X7] :
                                  ( memberP(X5,X7)
                                  & ~ leq(X4,X7)
                                  & lt(X4,X7)
                                  & memberP(X6,X7)
                                  & ssItem(X7) )
                              | app(app(X5,cons(X4,nil)),X6) != sK0 ) )
                      | ~ ssItem(X4) )
                  & ssList(X3)
                  & sK0 = X2
                  & ( ? [X8] :
                        ( memberP(X3,X8)
                        & ! [X9] :
                            ( ~ leq(X8,X9)
                            | ~ memberP(X3,X9)
                            | X8 = X9
                            | ~ ssItem(X9) )
                        & cons(X8,nil) = X2
                        & ssItem(X8) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & nil != sK0
                  & X1 = X3 )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f144,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ! [X4] :
                    ( ! [X5] :
                        ( ~ ssList(X5)
                        | ! [X6] :
                            ( ~ ssList(X6)
                            | ? [X7] :
                                ( memberP(X5,X7)
                                & ~ leq(X4,X7)
                                & lt(X4,X7)
                                & memberP(X6,X7)
                                & ssItem(X7) )
                            | app(app(X5,cons(X4,nil)),X6) != sK0 ) )
                    | ~ ssItem(X4) )
                & ssList(X3)
                & sK0 = X2
                & ( ? [X8] :
                      ( memberP(X3,X8)
                      & ! [X9] :
                          ( ~ leq(X8,X9)
                          | ~ memberP(X3,X9)
                          | X8 = X9
                          | ~ ssItem(X9) )
                      & cons(X8,nil) = X2
                      & ssItem(X8) )
                  | ( nil = X2
                    & nil = X3 ) )
                & nil != sK0
                & X1 = X3 )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ! [X4] :
                  ( ! [X5] :
                      ( ~ ssList(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | ? [X7] :
                              ( memberP(X5,X7)
                              & ~ leq(X4,X7)
                              & lt(X4,X7)
                              & memberP(X6,X7)
                              & ssItem(X7) )
                          | app(app(X5,cons(X4,nil)),X6) != sK0 ) )
                  | ~ ssItem(X4) )
              & ssList(X3)
              & sK0 = X2
              & ( ? [X8] :
                    ( memberP(X3,X8)
                    & ! [X9] :
                        ( ~ leq(X8,X9)
                        | ~ memberP(X3,X9)
                        | X8 = X9
                        | ~ ssItem(X9) )
                    & cons(X8,nil) = X2
                    & ssItem(X8) )
                | ( nil = X2
                  & nil = X3 ) )
              & nil != sK0
              & sK1 = X3 )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f145,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ! [X4] :
                ( ! [X5] :
                    ( ~ ssList(X5)
                    | ! [X6] :
                        ( ~ ssList(X6)
                        | ? [X7] :
                            ( memberP(X5,X7)
                            & ~ leq(X4,X7)
                            & lt(X4,X7)
                            & memberP(X6,X7)
                            & ssItem(X7) )
                        | app(app(X5,cons(X4,nil)),X6) != sK0 ) )
                | ~ ssItem(X4) )
            & ssList(X3)
            & sK0 = X2
            & ( ? [X8] :
                  ( memberP(X3,X8)
                  & ! [X9] :
                      ( ~ leq(X8,X9)
                      | ~ memberP(X3,X9)
                      | X8 = X9
                      | ~ ssItem(X9) )
                  & cons(X8,nil) = X2
                  & ssItem(X8) )
              | ( nil = X2
                & nil = X3 ) )
            & nil != sK0
            & sK1 = X3 )
        & ssList(X2) )
   => ( ? [X3] :
          ( ! [X4] :
              ( ! [X5] :
                  ( ~ ssList(X5)
                  | ! [X6] :
                      ( ~ ssList(X6)
                      | ? [X7] :
                          ( memberP(X5,X7)
                          & ~ leq(X4,X7)
                          & lt(X4,X7)
                          & memberP(X6,X7)
                          & ssItem(X7) )
                      | app(app(X5,cons(X4,nil)),X6) != sK0 ) )
              | ~ ssItem(X4) )
          & ssList(X3)
          & sK2 = sK0
          & ( ? [X8] :
                ( memberP(X3,X8)
                & ! [X9] :
                    ( ~ leq(X8,X9)
                    | ~ memberP(X3,X9)
                    | X8 = X9
                    | ~ ssItem(X9) )
                & cons(X8,nil) = sK2
                & ssItem(X8) )
            | ( nil = sK2
              & nil = X3 ) )
          & nil != sK0
          & sK1 = X3 )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ( ? [X3] :
        ( ! [X4] :
            ( ! [X5] :
                ( ~ ssList(X5)
                | ! [X6] :
                    ( ~ ssList(X6)
                    | ? [X7] :
                        ( memberP(X5,X7)
                        & ~ leq(X4,X7)
                        & lt(X4,X7)
                        & memberP(X6,X7)
                        & ssItem(X7) )
                    | app(app(X5,cons(X4,nil)),X6) != sK0 ) )
            | ~ ssItem(X4) )
        & ssList(X3)
        & sK2 = sK0
        & ( ? [X8] :
              ( memberP(X3,X8)
              & ! [X9] :
                  ( ~ leq(X8,X9)
                  | ~ memberP(X3,X9)
                  | X8 = X9
                  | ~ ssItem(X9) )
              & cons(X8,nil) = sK2
              & ssItem(X8) )
          | ( nil = sK2
            & nil = X3 ) )
        & nil != sK0
        & sK1 = X3 )
   => ( ! [X4] :
          ( ! [X5] :
              ( ~ ssList(X5)
              | ! [X6] :
                  ( ~ ssList(X6)
                  | ? [X7] :
                      ( memberP(X5,X7)
                      & ~ leq(X4,X7)
                      & lt(X4,X7)
                      & memberP(X6,X7)
                      & ssItem(X7) )
                  | app(app(X5,cons(X4,nil)),X6) != sK0 ) )
          | ~ ssItem(X4) )
      & ssList(sK3)
      & sK2 = sK0
      & ( ? [X8] :
            ( memberP(sK3,X8)
            & ! [X9] :
                ( ~ leq(X8,X9)
                | ~ memberP(sK3,X9)
                | X8 = X9
                | ~ ssItem(X9) )
            & cons(X8,nil) = sK2
            & ssItem(X8) )
        | ( nil = sK2
          & nil = sK3 ) )
      & nil != sK0
      & sK3 = sK1 ) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ! [X4,X5,X6] :
      ( ? [X7] :
          ( memberP(X5,X7)
          & ~ leq(X4,X7)
          & lt(X4,X7)
          & memberP(X6,X7)
          & ssItem(X7) )
     => ( memberP(X5,sK4(X4,X5,X6))
        & ~ leq(X4,sK4(X4,X5,X6))
        & lt(X4,sK4(X4,X5,X6))
        & memberP(X6,sK4(X4,X5,X6))
        & ssItem(sK4(X4,X5,X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f148,plain,
    ( ? [X8] :
        ( memberP(sK3,X8)
        & ! [X9] :
            ( ~ leq(X8,X9)
            | ~ memberP(sK3,X9)
            | X8 = X9
            | ~ ssItem(X9) )
        & cons(X8,nil) = sK2
        & ssItem(X8) )
   => ( memberP(sK3,sK5)
      & ! [X9] :
          ( ~ leq(sK5,X9)
          | ~ memberP(sK3,X9)
          | sK5 = X9
          | ~ ssItem(X9) )
      & sK2 = cons(sK5,nil)
      & ssItem(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | ? [X7] :
                                  ( memberP(X5,X7)
                                  & ~ leq(X4,X7)
                                  & lt(X4,X7)
                                  & memberP(X6,X7)
                                  & ssItem(X7) )
                              | app(app(X5,cons(X4,nil)),X6) != X0 ) )
                      | ~ ssItem(X4) )
                  & ssList(X3)
                  & X0 = X2
                  & ( ? [X8] :
                        ( memberP(X3,X8)
                        & ! [X9] :
                            ( ~ leq(X8,X9)
                            | ~ memberP(X3,X9)
                            | X8 = X9
                            | ~ ssItem(X9) )
                        & cons(X8,nil) = X2
                        & ssItem(X8) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & nil != X0
                  & X1 = X3 )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(flattening,[],[f123]) ).

fof(f123,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X8] :
                        ( memberP(X3,X8)
                        & ! [X9] :
                            ( ~ leq(X8,X9)
                            | ~ memberP(X3,X9)
                            | X8 = X9
                            | ~ ssItem(X9) )
                        & cons(X8,nil) = X2
                        & ssItem(X8) ) )
                  & X1 = X3
                  & nil != X0
                  & X0 = X2
                  & ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( app(app(X5,cons(X4,nil)),X6) != X0
                              | ? [X7] :
                                  ( memberP(X6,X7)
                                  & ~ leq(X4,X7)
                                  & memberP(X5,X7)
                                  & lt(X4,X7)
                                  & ssItem(X7) )
                              | ~ ssList(X6) ) )
                      | ~ ssItem(X4) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

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

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

fof(f163,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,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/sandbox/benchmark/theBenchmark.p',ax84) ).

fof(f303,plain,
    ( ! [X4] :
        ( sK0 != app(sK0,X4)
        | ssItem(sK4(sK5,nil,X4))
        | ~ ssList(X4) )
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f300,f227]) ).

fof(f300,plain,
    ( ! [X4] :
        ( ~ ssList(nil)
        | ~ ssList(X4)
        | sK0 != app(sK0,X4)
        | ssItem(sK4(sK5,nil,X4)) )
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(superposition,[],[f279,f293]) ).

fof(f293,plain,
    app(nil,sK0) = sK0,
    inference(resolution,[],[f207,f197]) ).

fof(f207,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,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/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f279,plain,
    ( ! [X0,X1] :
        ( app(app(X0,sK0),X1) != sK0
        | ssItem(sK4(sK5,X0,X1))
        | ~ ssList(X0)
        | ~ ssList(X1) )
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f278,f267]) ).

fof(f267,plain,
    ( ssItem(sK5)
    | ~ spl12_5 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f265,plain,
    ( spl12_5
  <=> ssItem(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).

fof(f278,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(sK5)
        | ~ ssList(X1)
        | ~ ssList(X0)
        | app(app(X0,sK0),X1) != sK0
        | ssItem(sK4(sK5,X0,X1)) )
    | ~ spl12_1 ),
    inference(superposition,[],[f192,f249]) ).

fof(f249,plain,
    ( sK0 = cons(sK5,nil)
    | ~ spl12_1 ),
    inference(avatar_component_clause,[],[f247]) ).

fof(f247,plain,
    ( spl12_1
  <=> sK0 = cons(sK5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f192,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK0
      | ssItem(sK4(X4,X5,X6))
      | ~ ssList(X6)
      | ~ ssItem(X4)
      | ~ ssList(X5) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f312,plain,
    ( ~ ssItem(sK4(sK5,nil,nil))
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(resolution,[],[f311,f218]) ).

fof(f218,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).

fof(f311,plain,
    ( memberP(nil,sK4(sK5,nil,nil))
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f310,f227]) ).

fof(f310,plain,
    ( memberP(nil,sK4(sK5,nil,nil))
    | ~ ssList(nil)
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(trivial_inequality_removal,[],[f309]) ).

fof(f309,plain,
    ( ~ ssList(nil)
    | sK0 != sK0
    | memberP(nil,sK4(sK5,nil,nil))
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(superposition,[],[f301,f290]) ).

fof(f301,plain,
    ( ! [X0] :
        ( app(sK0,X0) != sK0
        | memberP(nil,sK4(sK5,nil,X0))
        | ~ ssList(X0) )
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f296,f227]) ).

fof(f296,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(sK0,X0) != sK0
        | ~ ssList(nil)
        | memberP(nil,sK4(sK5,nil,X0)) )
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(superposition,[],[f287,f293]) ).

fof(f287,plain,
    ( ! [X0,X1] :
        ( app(app(X0,sK0),X1) != sK0
        | ~ ssList(X0)
        | ~ ssList(X1)
        | memberP(X0,sK4(sK5,X0,X1)) )
    | ~ spl12_1
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f286,f267]) ).

fof(f286,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | app(app(X0,sK0),X1) != sK0
        | ~ ssItem(sK5)
        | ~ ssList(X1)
        | memberP(X0,sK4(sK5,X0,X1)) )
    | ~ spl12_1 ),
    inference(superposition,[],[f196,f249]) ).

fof(f196,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK0
      | ~ ssList(X6)
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | memberP(X5,sK4(X4,X5,X6)) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f277,plain,
    ( spl12_1
    | spl12_4 ),
    inference(avatar_split_clause,[],[f233,f261,f247]) ).

fof(f261,plain,
    ( spl12_4
  <=> nil = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).

fof(f233,plain,
    ( nil = sK0
    | sK0 = cons(sK5,nil) ),
    inference(definition_unfolding,[],[f185,f190,f190]) ).

fof(f190,plain,
    sK2 = sK0,
    inference(cnf_transformation,[],[f149]) ).

fof(f185,plain,
    ( sK2 = cons(sK5,nil)
    | nil = sK2 ),
    inference(cnf_transformation,[],[f149]) ).

fof(f275,plain,
    ~ spl12_4,
    inference(avatar_split_clause,[],[f181,f261]) ).

fof(f181,plain,
    nil != sK0,
    inference(cnf_transformation,[],[f149]) ).

fof(f268,plain,
    ( spl12_4
    | spl12_5 ),
    inference(avatar_split_clause,[],[f235,f265,f261]) ).

fof(f235,plain,
    ( ssItem(sK5)
    | nil = sK0 ),
    inference(definition_unfolding,[],[f183,f190]) ).

fof(f183,plain,
    ( ssItem(sK5)
    | nil = sK2 ),
    inference(cnf_transformation,[],[f149]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC239+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % 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 : n014.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 18:38:18 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (17251)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  % (17267)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)
% 0.20/0.50  % (17241)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)
% 0.20/0.51  % (17257)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)
% 0.20/0.51  % (17245)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  % (17259)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)
% 0.20/0.51  % (17249)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)
% 0.20/0.52  % (17260)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  % (17252)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)
% 0.20/0.52  % (17239)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)
% 0.20/0.52  % (17249)Instruction limit reached!
% 0.20/0.52  % (17249)------------------------------
% 0.20/0.52  % (17249)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (17262)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)
% 0.20/0.53  % (17249)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (17249)Termination reason: Unknown
% 0.20/0.53  % (17249)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (17249)Memory used [KB]: 6140
% 0.20/0.53  % (17249)Time elapsed: 0.121 s
% 0.20/0.53  % (17249)Instructions burned: 8 (million)
% 0.20/0.53  % (17263)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  % (17249)------------------------------
% 0.20/0.53  % (17249)------------------------------
% 0.20/0.53  % (17242)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  % (17243)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  % (17256)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)
% 0.20/0.53  % (17256)Instruction limit reached!
% 0.20/0.53  % (17256)------------------------------
% 0.20/0.53  % (17256)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (17256)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (17256)Termination reason: Unknown
% 0.20/0.53  % (17256)Termination phase: SInE selection
% 0.20/0.53  
% 0.20/0.53  % (17256)Memory used [KB]: 1407
% 0.20/0.53  % (17256)Time elapsed: 0.002 s
% 0.20/0.53  % (17256)Instructions burned: 2 (million)
% 0.20/0.53  % (17256)------------------------------
% 0.20/0.53  % (17256)------------------------------
% 0.20/0.53  % (17238)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.53  % (17240)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)
% 0.20/0.53  % (17257)Instruction limit reached!
% 0.20/0.53  % (17257)------------------------------
% 0.20/0.53  % (17257)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (17257)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (17257)Termination reason: Unknown
% 0.20/0.53  % (17257)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (17257)Memory used [KB]: 6268
% 0.20/0.53  % (17257)Time elapsed: 0.128 s
% 0.20/0.53  % (17257)Instructions burned: 11 (million)
% 0.20/0.53  % (17257)------------------------------
% 0.20/0.53  % (17257)------------------------------
% 0.20/0.53  % (17242)First to succeed.
% 0.20/0.53  % (17252)Instruction limit reached!
% 0.20/0.53  % (17252)------------------------------
% 0.20/0.53  % (17252)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (17252)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (17252)Termination reason: Unknown
% 0.20/0.53  % (17252)Termination phase: Preprocessing 3
% 0.20/0.53  
% 0.20/0.53  % (17252)Memory used [KB]: 1663
% 0.20/0.53  % (17252)Time elapsed: 0.005 s
% 0.20/0.53  % (17252)Instructions burned: 4 (million)
% 0.20/0.53  % (17252)------------------------------
% 0.20/0.53  % (17252)------------------------------
% 0.20/0.53  % (17244)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)
% 1.33/0.53  % (17264)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)
% 1.33/0.53  % (17240)Instruction limit reached!
% 1.33/0.53  % (17240)------------------------------
% 1.33/0.53  % (17240)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.53  % (17240)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.53  % (17240)Termination reason: Unknown
% 1.33/0.53  % (17240)Termination phase: Preprocessing 3
% 1.33/0.53  
% 1.33/0.53  % (17240)Memory used [KB]: 1663
% 1.33/0.53  % (17240)Time elapsed: 0.005 s
% 1.33/0.53  % (17240)Instructions burned: 5 (million)
% 1.33/0.53  % (17240)------------------------------
% 1.33/0.53  % (17240)------------------------------
% 1.33/0.54  % (17258)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)
% 1.33/0.54  % (17265)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)
% 1.33/0.54  % (17255)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.33/0.54  % (17254)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)
% 1.33/0.54  % (17247)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)
% 1.33/0.54  % (17266)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)
% 1.33/0.54  % (17261)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)
% 1.33/0.54  % (17255)Instruction limit reached!
% 1.33/0.54  % (17255)------------------------------
% 1.33/0.54  % (17255)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.54  % (17255)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.54  % (17255)Termination reason: Unknown
% 1.33/0.54  % (17255)Termination phase: Naming
% 1.33/0.54  
% 1.33/0.54  % (17255)Memory used [KB]: 1663
% 1.33/0.54  % (17255)Time elapsed: 0.005 s
% 1.33/0.54  % (17255)Instructions burned: 4 (million)
% 1.33/0.54  % (17255)------------------------------
% 1.33/0.54  % (17255)------------------------------
% 1.33/0.54  % (17248)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)
% 1.33/0.54  % (17250)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)
% 1.33/0.55  % (17246)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)
% 1.33/0.55  % (17239)Instruction limit reached!
% 1.33/0.55  % (17239)------------------------------
% 1.33/0.55  % (17239)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.55  % (17239)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.55  % (17239)Termination reason: Unknown
% 1.33/0.55  % (17239)Termination phase: Saturation
% 1.33/0.55  
% 1.33/0.55  % (17239)Memory used [KB]: 6396
% 1.33/0.55  % (17239)Time elapsed: 0.008 s
% 1.33/0.55  % (17239)Instructions burned: 13 (million)
% 1.33/0.55  % (17239)------------------------------
% 1.33/0.55  % (17239)------------------------------
% 1.33/0.55  % (17253)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)
% 1.33/0.55  % (17253)Instruction limit reached!
% 1.33/0.55  % (17253)------------------------------
% 1.33/0.55  % (17253)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.55  % (17253)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.55  % (17253)Termination reason: Unknown
% 1.33/0.55  % (17253)Termination phase: Property scanning
% 1.33/0.55  
% 1.33/0.55  % (17253)Memory used [KB]: 1791
% 1.33/0.55  % (17253)Time elapsed: 0.005 s
% 1.33/0.55  % (17253)Instructions burned: 7 (million)
% 1.33/0.55  % (17253)------------------------------
% 1.33/0.55  % (17253)------------------------------
% 1.56/0.55  % (17267)Instruction limit reached!
% 1.56/0.55  % (17267)------------------------------
% 1.56/0.55  % (17267)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.56/0.55  % (17244)Also succeeded, but the first one will report.
% 1.56/0.55  % (17243)Instruction limit reached!
% 1.56/0.55  % (17243)------------------------------
% 1.56/0.55  % (17243)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.56/0.55  % (17242)Refutation found. Thanks to Tanya!
% 1.56/0.55  % SZS status Theorem for theBenchmark
% 1.56/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 1.56/0.56  % (17242)------------------------------
% 1.56/0.56  % (17242)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.56/0.56  % (17242)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.56/0.56  % (17242)Termination reason: Refutation
% 1.56/0.56  
% 1.56/0.56  % (17242)Memory used [KB]: 6140
% 1.56/0.56  % (17242)Time elapsed: 0.125 s
% 1.56/0.56  % (17242)Instructions burned: 7 (million)
% 1.56/0.56  % (17242)------------------------------
% 1.56/0.56  % (17242)------------------------------
% 1.56/0.56  % (17237)Success in time 0.201 s
%------------------------------------------------------------------------------