TSTP Solution File: SWC252+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC252+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 : n023.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 18:39:54 EDT 2022

% Result   : Theorem 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   62 (  10 unt;   0 def)
%            Number of atoms       :  457 ( 138 equ)
%            Maximal formula atoms :   42 (   7 avg)
%            Number of connectives :  582 ( 187   ~; 170   |; 195   &)
%                                         (   3 <=>;  27  =>;   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   :  145 (  84   !;  61   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f314,plain,
    $false,
    inference(avatar_sat_refutation,[],[f266,f267,f270,f313]) ).

fof(f313,plain,
    ( ~ spl12_4
    | ~ spl12_5 ),
    inference(avatar_contradiction_clause,[],[f312]) ).

fof(f312,plain,
    ( $false
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f311,f309]) ).

fof(f309,plain,
    ( ssItem(sK6(sK7,nil,nil))
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f304,f213]) ).

fof(f213,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f304,plain,
    ( ssItem(sK6(sK7,nil,nil))
    | ~ ssList(nil)
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(trivial_inequality_removal,[],[f301]) ).

fof(f301,plain,
    ( sK2 != sK2
    | ssItem(sK6(sK7,nil,nil))
    | ~ ssList(nil)
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(superposition,[],[f292,f294]) ).

fof(f294,plain,
    sK2 = app(sK2,nil),
    inference(resolution,[],[f206,f228]) ).

fof(f228,plain,
    ssList(sK2),
    inference(definition_unfolding,[],[f192,f190]) ).

fof(f190,plain,
    sK4 = sK2,
    inference(cnf_transformation,[],[f150]) ).

fof(f150,plain,
    ( ssList(sK3)
    & ssList(sK4)
    & sK5 = sK3
    & sK4 = sK2
    & ! [X4] :
        ( ! [X5] :
            ( ~ ssList(X5)
            | ! [X6] :
                ( ~ ssList(X6)
                | app(app(X5,cons(X4,nil)),X6) != sK2
                | ( memberP(X5,sK6(X4,X5,X6))
                  & memberP(X6,sK6(X4,X5,X6))
                  & lt(X4,sK6(X4,X5,X6))
                  & ~ leq(X4,sK6(X4,X5,X6))
                  & ssItem(sK6(X4,X5,X6)) ) ) )
        | ~ ssItem(X4) )
    & ssList(sK5)
    & nil != sK2
    & ( ( nil = sK5
        & nil = sK4 )
      | ( cons(sK7,nil) = sK4
        & ssItem(sK7)
        & memberP(sK5,sK7) ) )
    & ssList(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7])],[f143,f149,f148,f147,f146,f145,f144]) ).

fof(f144,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X1 = X3
                    & X0 = X2
                    & ! [X4] :
                        ( ! [X5] :
                            ( ~ ssList(X5)
                            | ! [X6] :
                                ( ~ ssList(X6)
                                | app(app(X5,cons(X4,nil)),X6) != X0
                                | ? [X7] :
                                    ( memberP(X5,X7)
                                    & memberP(X6,X7)
                                    & lt(X4,X7)
                                    & ~ leq(X4,X7)
                                    & ssItem(X7) ) ) )
                        | ~ ssItem(X4) )
                    & ssList(X3)
                    & nil != X0
                    & ( ( nil = X3
                        & nil = X2 )
                      | ? [X8] :
                          ( cons(X8,nil) = X2
                          & ssItem(X8)
                          & memberP(X3,X8) ) ) ) ) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & sK2 = X2
                  & ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | app(app(X5,cons(X4,nil)),X6) != sK2
                              | ? [X7] :
                                  ( memberP(X5,X7)
                                  & memberP(X6,X7)
                                  & lt(X4,X7)
                                  & ~ leq(X4,X7)
                                  & ssItem(X7) ) ) )
                      | ~ ssItem(X4) )
                  & ssList(X3)
                  & nil != sK2
                  & ( ( nil = X3
                      & nil = X2 )
                    | ? [X8] :
                        ( cons(X8,nil) = X2
                        & ssItem(X8)
                        & memberP(X3,X8) ) ) ) ) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f145,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( X1 = X3
                & sK2 = X2
                & ! [X4] :
                    ( ! [X5] :
                        ( ~ ssList(X5)
                        | ! [X6] :
                            ( ~ ssList(X6)
                            | app(app(X5,cons(X4,nil)),X6) != sK2
                            | ? [X7] :
                                ( memberP(X5,X7)
                                & memberP(X6,X7)
                                & lt(X4,X7)
                                & ~ leq(X4,X7)
                                & ssItem(X7) ) ) )
                    | ~ ssItem(X4) )
                & ssList(X3)
                & nil != sK2
                & ( ( nil = X3
                    & nil = X2 )
                  | ? [X8] :
                      ( cons(X8,nil) = X2
                      & ssItem(X8)
                      & memberP(X3,X8) ) ) ) ) )
   => ( ssList(sK3)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK3 = X3
              & sK2 = X2
              & ! [X4] :
                  ( ! [X5] :
                      ( ~ ssList(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | app(app(X5,cons(X4,nil)),X6) != sK2
                          | ? [X7] :
                              ( memberP(X5,X7)
                              & memberP(X6,X7)
                              & lt(X4,X7)
                              & ~ leq(X4,X7)
                              & ssItem(X7) ) ) )
                  | ~ ssItem(X4) )
              & ssList(X3)
              & nil != sK2
              & ( ( nil = X3
                  & nil = X2 )
                | ? [X8] :
                    ( cons(X8,nil) = X2
                    & ssItem(X8)
                    & memberP(X3,X8) ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK3 = X3
            & sK2 = X2
            & ! [X4] :
                ( ! [X5] :
                    ( ~ ssList(X5)
                    | ! [X6] :
                        ( ~ ssList(X6)
                        | app(app(X5,cons(X4,nil)),X6) != sK2
                        | ? [X7] :
                            ( memberP(X5,X7)
                            & memberP(X6,X7)
                            & lt(X4,X7)
                            & ~ leq(X4,X7)
                            & ssItem(X7) ) ) )
                | ~ ssItem(X4) )
            & ssList(X3)
            & nil != sK2
            & ( ( nil = X3
                & nil = X2 )
              | ? [X8] :
                  ( cons(X8,nil) = X2
                  & ssItem(X8)
                  & memberP(X3,X8) ) ) ) )
   => ( ssList(sK4)
      & ? [X3] :
          ( sK3 = X3
          & sK4 = sK2
          & ! [X4] :
              ( ! [X5] :
                  ( ~ ssList(X5)
                  | ! [X6] :
                      ( ~ ssList(X6)
                      | app(app(X5,cons(X4,nil)),X6) != sK2
                      | ? [X7] :
                          ( memberP(X5,X7)
                          & memberP(X6,X7)
                          & lt(X4,X7)
                          & ~ leq(X4,X7)
                          & ssItem(X7) ) ) )
              | ~ ssItem(X4) )
          & ssList(X3)
          & nil != sK2
          & ( ( nil = X3
              & nil = sK4 )
            | ? [X8] :
                ( cons(X8,nil) = sK4
                & ssItem(X8)
                & memberP(X3,X8) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ( ? [X3] :
        ( sK3 = X3
        & sK4 = sK2
        & ! [X4] :
            ( ! [X5] :
                ( ~ ssList(X5)
                | ! [X6] :
                    ( ~ ssList(X6)
                    | app(app(X5,cons(X4,nil)),X6) != sK2
                    | ? [X7] :
                        ( memberP(X5,X7)
                        & memberP(X6,X7)
                        & lt(X4,X7)
                        & ~ leq(X4,X7)
                        & ssItem(X7) ) ) )
            | ~ ssItem(X4) )
        & ssList(X3)
        & nil != sK2
        & ( ( nil = X3
            & nil = sK4 )
          | ? [X8] :
              ( cons(X8,nil) = sK4
              & ssItem(X8)
              & memberP(X3,X8) ) ) )
   => ( sK5 = sK3
      & sK4 = sK2
      & ! [X4] :
          ( ! [X5] :
              ( ~ ssList(X5)
              | ! [X6] :
                  ( ~ ssList(X6)
                  | app(app(X5,cons(X4,nil)),X6) != sK2
                  | ? [X7] :
                      ( memberP(X5,X7)
                      & memberP(X6,X7)
                      & lt(X4,X7)
                      & ~ leq(X4,X7)
                      & ssItem(X7) ) ) )
          | ~ ssItem(X4) )
      & ssList(sK5)
      & nil != sK2
      & ( ( nil = sK5
          & nil = sK4 )
        | ? [X8] :
            ( cons(X8,nil) = sK4
            & ssItem(X8)
            & memberP(sK5,X8) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f148,plain,
    ! [X4,X5,X6] :
      ( ? [X7] :
          ( memberP(X5,X7)
          & memberP(X6,X7)
          & lt(X4,X7)
          & ~ leq(X4,X7)
          & ssItem(X7) )
     => ( memberP(X5,sK6(X4,X5,X6))
        & memberP(X6,sK6(X4,X5,X6))
        & lt(X4,sK6(X4,X5,X6))
        & ~ leq(X4,sK6(X4,X5,X6))
        & ssItem(sK6(X4,X5,X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f149,plain,
    ( ? [X8] :
        ( cons(X8,nil) = sK4
        & ssItem(X8)
        & memberP(sK5,X8) )
   => ( cons(sK7,nil) = sK4
      & ssItem(sK7)
      & memberP(sK5,sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & X0 = X2
                  & ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | app(app(X5,cons(X4,nil)),X6) != X0
                              | ? [X7] :
                                  ( memberP(X5,X7)
                                  & memberP(X6,X7)
                                  & lt(X4,X7)
                                  & ~ leq(X4,X7)
                                  & ssItem(X7) ) ) )
                      | ~ ssItem(X4) )
                  & ssList(X3)
                  & nil != X0
                  & ( ( nil = X3
                      & nil = X2 )
                    | ? [X8] :
                        ( cons(X8,nil) = X2
                        & ssItem(X8)
                        & memberP(X3,X8) ) ) ) ) )
      & ssList(X0) ),
    inference(rectify,[],[f106]) ).

fof(f106,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & X0 = X2
                  & ! [X5] :
                      ( ! [X6] :
                          ( ~ ssList(X6)
                          | ! [X7] :
                              ( ~ ssList(X7)
                              | app(app(X6,cons(X5,nil)),X7) != X0
                              | ? [X8] :
                                  ( memberP(X6,X8)
                                  & memberP(X7,X8)
                                  & lt(X5,X8)
                                  & ~ leq(X5,X8)
                                  & ssItem(X8) ) ) )
                      | ~ ssItem(X5) )
                  & ssList(X3)
                  & nil != X0
                  & ( ( nil = X3
                      & nil = X2 )
                    | ? [X4] :
                        ( cons(X4,nil) = X2
                        & ssItem(X4)
                        & memberP(X3,X4) ) ) ) ) )
      & ssList(X0) ),
    inference(flattening,[],[f105]) ).

fof(f105,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & nil != X0
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | ! [X7] :
                              ( ~ ssList(X7)
                              | app(app(X6,cons(X5,nil)),X7) != X0
                              | ? [X8] :
                                  ( ~ leq(X5,X8)
                                  & memberP(X7,X8)
                                  & lt(X5,X8)
                                  & memberP(X6,X8)
                                  & ssItem(X8) ) ) ) )
                  & X0 = X2
                  & ( ( nil = X3
                      & nil = X2 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

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

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

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

fof(f192,plain,
    ssList(sK4),
    inference(cnf_transformation,[],[f150]) ).

fof(f206,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,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/sandbox/benchmark/theBenchmark.p',ax84) ).

fof(f292,plain,
    ( ! [X4] :
        ( sK2 != app(sK2,X4)
        | ~ ssList(X4)
        | ssItem(sK6(sK7,nil,X4)) )
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f288,f213]) ).

fof(f288,plain,
    ( ! [X4] :
        ( ~ ssList(nil)
        | ssItem(sK6(sK7,nil,X4))
        | sK2 != app(sK2,X4)
        | ~ ssList(X4) )
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(superposition,[],[f272,f281]) ).

fof(f281,plain,
    sK2 = app(nil,sK2),
    inference(resolution,[],[f165,f228]) ).

fof(f165,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,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/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f272,plain,
    ( ! [X0,X1] :
        ( app(app(X0,sK2),X1) != sK2
        | ~ ssList(X0)
        | ~ ssList(X1)
        | ssItem(sK6(sK7,X0,X1)) )
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f271,f265]) ).

fof(f265,plain,
    ( ssItem(sK7)
    | ~ spl12_5 ),
    inference(avatar_component_clause,[],[f263]) ).

fof(f263,plain,
    ( spl12_5
  <=> ssItem(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).

fof(f271,plain,
    ( ! [X0,X1] :
        ( ssItem(sK6(sK7,X0,X1))
        | ~ ssList(X1)
        | ~ ssItem(sK7)
        | ~ ssList(X0)
        | app(app(X0,sK2),X1) != sK2 )
    | ~ spl12_4 ),
    inference(superposition,[],[f185,f260]) ).

fof(f260,plain,
    ( cons(sK7,nil) = sK2
    | ~ spl12_4 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f258,plain,
    ( spl12_4
  <=> cons(sK7,nil) = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).

fof(f185,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK2
      | ~ ssItem(X4)
      | ssItem(sK6(X4,X5,X6))
      | ~ ssList(X6)
      | ~ ssList(X5) ),
    inference(cnf_transformation,[],[f150]) ).

fof(f311,plain,
    ( ~ ssItem(sK6(sK7,nil,nil))
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(resolution,[],[f307,f224]) ).

fof(f224,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(nil,X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

fof(f307,plain,
    ( memberP(nil,sK6(sK7,nil,nil))
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f306,f213]) ).

fof(f306,plain,
    ( memberP(nil,sK6(sK7,nil,nil))
    | ~ ssList(nil)
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(trivial_inequality_removal,[],[f299]) ).

fof(f299,plain,
    ( memberP(nil,sK6(sK7,nil,nil))
    | sK2 != sK2
    | ~ ssList(nil)
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(superposition,[],[f290,f294]) ).

fof(f290,plain,
    ( ! [X1] :
        ( app(sK2,X1) != sK2
        | ~ ssList(X1)
        | memberP(X1,sK6(sK7,nil,X1)) )
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f285,f213]) ).

fof(f285,plain,
    ( ! [X1] :
        ( memberP(X1,sK6(sK7,nil,X1))
        | app(sK2,X1) != sK2
        | ~ ssList(nil)
        | ~ ssList(X1) )
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(superposition,[],[f278,f281]) ).

fof(f278,plain,
    ( ! [X0,X1] :
        ( app(app(X0,sK2),X1) != sK2
        | ~ ssList(X1)
        | memberP(X1,sK6(sK7,X0,X1))
        | ~ ssList(X0) )
    | ~ spl12_4
    | ~ spl12_5 ),
    inference(subsumption_resolution,[],[f277,f265]) ).

fof(f277,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssList(X1)
        | ~ ssItem(sK7)
        | app(app(X0,sK2),X1) != sK2
        | memberP(X1,sK6(sK7,X0,X1)) )
    | ~ spl12_4 ),
    inference(superposition,[],[f188,f260]) ).

fof(f188,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK2
      | ~ ssList(X6)
      | ~ ssItem(X4)
      | ~ ssList(X5)
      | memberP(X6,sK6(X4,X5,X6)) ),
    inference(cnf_transformation,[],[f150]) ).

fof(f270,plain,
    ( spl12_4
    | spl12_1 ),
    inference(avatar_split_clause,[],[f233,f245,f258]) ).

fof(f245,plain,
    ( spl12_1
  <=> nil = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f233,plain,
    ( nil = sK2
    | cons(sK7,nil) = sK2 ),
    inference(definition_unfolding,[],[f179,f190,f190]) ).

fof(f179,plain,
    ( nil = sK4
    | cons(sK7,nil) = sK4 ),
    inference(cnf_transformation,[],[f150]) ).

fof(f267,plain,
    ~ spl12_1,
    inference(avatar_split_clause,[],[f183,f245]) ).

fof(f183,plain,
    nil != sK2,
    inference(cnf_transformation,[],[f150]) ).

fof(f266,plain,
    ( spl12_5
    | spl12_1 ),
    inference(avatar_split_clause,[],[f234,f245,f263]) ).

fof(f234,plain,
    ( nil = sK2
    | ssItem(sK7) ),
    inference(definition_unfolding,[],[f178,f190]) ).

fof(f178,plain,
    ( nil = sK4
    | ssItem(sK7) ),
    inference(cnf_transformation,[],[f150]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC252+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % 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 : n023.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 19:00:20 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (27959)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)
% 0.20/0.51  % (27962)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)
% 0.20/0.52  % (27981)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)
% 0.20/0.52  % (27973)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  % (27963)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  % (27965)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)
% 0.20/0.53  % (27959)Instruction limit reached!
% 0.20/0.53  % (27959)------------------------------
% 0.20/0.53  % (27959)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (27986)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  % (27959)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (27959)Termination reason: Unknown
% 0.20/0.53  % (27959)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (27959)Memory used [KB]: 6396
% 0.20/0.53  % (27959)Time elapsed: 0.108 s
% 0.20/0.53  % (27959)Instructions burned: 14 (million)
% 0.20/0.53  % (27959)------------------------------
% 0.20/0.53  % (27959)------------------------------
% 0.20/0.53  % (27980)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)
% 0.20/0.53  % (27979)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)
% 0.20/0.53  % (27958)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  % (27960)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  % (27961)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  % (27982)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  % (27967)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  % (27968)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  % (27964)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  % (27962)First to succeed.
% 0.20/0.54  % (27972)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  % (27978)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  % (27969)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)
% 0.20/0.54  % (27975)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.54  % (27987)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)
% 0.20/0.54  % (27968)Refutation not found, incomplete strategy% (27968)------------------------------
% 0.20/0.54  % (27968)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (27972)Instruction limit reached!
% 0.20/0.54  % (27972)------------------------------
% 0.20/0.54  % (27972)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (27962)Refutation found. Thanks to Tanya!
% 0.20/0.54  % SZS status Theorem for theBenchmark
% 0.20/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (27962)------------------------------
% 0.20/0.54  % (27962)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (27962)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (27962)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (27962)Memory used [KB]: 6140
% 0.20/0.54  % (27962)Time elapsed: 0.126 s
% 0.20/0.54  % (27962)Instructions burned: 7 (million)
% 0.20/0.54  % (27962)------------------------------
% 0.20/0.54  % (27962)------------------------------
% 0.20/0.54  % (27954)Success in time 0.186 s
%------------------------------------------------------------------------------