TSTP Solution File: SWC219+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC219+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n006.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 : Thu Aug 31 20:57:34 EDT 2023

% Result   : Theorem 1.34s 0.67s
% Output   : Refutation 1.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   65 (   8 unt;   0 def)
%            Number of atoms       :  528 ( 147 equ)
%            Maximal formula atoms :   50 (   8 avg)
%            Number of connectives :  712 ( 249   ~; 231   |; 202   &)
%                                         (   3 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   4 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :  154 (;  96   !;  58   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8917,plain,
    $false,
    inference(avatar_sat_refutation,[],[f600,f605,f621,f8916]) ).

fof(f8916,plain,
    ( ~ spl53_4
    | ~ spl53_5 ),
    inference(avatar_contradiction_clause,[],[f8915]) ).

fof(f8915,plain,
    ( $false
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f8914,f6016]) ).

fof(f6016,plain,
    ( ssItem(sK5(sK4,nil,nil))
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f6015,f615]) ).

fof(f615,plain,
    ssList(sK0),
    inference(forward_demodulation,[],[f341,f344]) ).

fof(f344,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f230]) ).

fof(f230,plain,
    ( ( ( nil = sK2
        & nil = sK3 )
      | ( ! [X5] :
            ( ~ leq(X5,sK4)
            | ~ memberP(sK3,X5)
            | sK4 = X5
            | ~ ssItem(X5) )
        & memberP(sK3,sK4)
        & sK2 = cons(sK4,nil)
        & ssItem(sK4) ) )
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ( ~ leq(sK5(X6,X7,X8),X6)
                  & leq(X6,sK5(X6,X7,X8))
                  & memberP(X8,sK5(X6,X7,X8))
                  & memberP(X7,sK5(X6,X7,X8))
                  & ssItem(sK5(X6,X7,X8)) )
                | app(app(X7,cons(X6,nil)),X8) != sK0
                | ~ ssList(X8) )
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & nil != sK0
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f100,f229,f228,f227,f226,f225,f224]) ).

fof(f224,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | ? [X4] :
                          ( ! [X5] :
                              ( ~ leq(X5,X4)
                              | ~ memberP(X3,X5)
                              | X4 = X5
                              | ~ ssItem(X5) )
                          & memberP(X3,X4)
                          & cons(X4,nil) = X2
                          & ssItem(X4) ) )
                    & ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ? [X9] :
                                    ( ~ leq(X9,X6)
                                    & leq(X6,X9)
                                    & memberP(X8,X9)
                                    & memberP(X7,X9)
                                    & ssItem(X9) )
                                | app(app(X7,cons(X6,nil)),X8) != X0
                                | ~ ssList(X8) )
                            | ~ ssList(X7) )
                        | ~ ssItem(X6) )
                    & nil != X0
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ~ leq(X5,X4)
                            | ~ memberP(X3,X5)
                            | X4 = X5
                            | ~ ssItem(X5) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ? [X9] :
                                  ( ~ leq(X9,X6)
                                  & leq(X6,X9)
                                  & memberP(X8,X9)
                                  & memberP(X7,X9)
                                  & ssItem(X9) )
                              | app(app(X7,cons(X6,nil)),X8) != sK0
                              | ~ ssList(X8) )
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & nil != sK0
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | ? [X4] :
                      ( ! [X5] :
                          ( ~ leq(X5,X4)
                          | ~ memberP(X3,X5)
                          | X4 = X5
                          | ~ ssItem(X5) )
                      & memberP(X3,X4)
                      & cons(X4,nil) = X2
                      & ssItem(X4) ) )
                & ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ? [X9] :
                                ( ~ leq(X9,X6)
                                & leq(X6,X9)
                                & memberP(X8,X9)
                                & memberP(X7,X9)
                                & ssItem(X9) )
                            | app(app(X7,cons(X6,nil)),X8) != sK0
                            | ~ ssList(X8) )
                        | ~ ssList(X7) )
                    | ~ ssItem(X6) )
                & nil != sK0
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = X2
                  & nil = X3 )
                | ? [X4] :
                    ( ! [X5] :
                        ( ~ leq(X5,X4)
                        | ~ memberP(X3,X5)
                        | X4 = X5
                        | ~ ssItem(X5) )
                    & memberP(X3,X4)
                    & cons(X4,nil) = X2
                    & ssItem(X4) ) )
              & ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ? [X9] :
                              ( ~ leq(X9,X6)
                              & leq(X6,X9)
                              & memberP(X8,X9)
                              & memberP(X7,X9)
                              & ssItem(X9) )
                          | app(app(X7,cons(X6,nil)),X8) != sK0
                          | ~ ssList(X8) )
                      | ~ ssList(X7) )
                  | ~ ssItem(X6) )
              & nil != sK0
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f226,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | ? [X4] :
                  ( ! [X5] :
                      ( ~ leq(X5,X4)
                      | ~ memberP(X3,X5)
                      | X4 = X5
                      | ~ ssItem(X5) )
                  & memberP(X3,X4)
                  & cons(X4,nil) = X2
                  & ssItem(X4) ) )
            & ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ? [X9] :
                            ( ~ leq(X9,X6)
                            & leq(X6,X9)
                            & memberP(X8,X9)
                            & memberP(X7,X9)
                            & ssItem(X9) )
                        | app(app(X7,cons(X6,nil)),X8) != sK0
                        | ~ ssList(X8) )
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            & nil != sK0
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK2
              & nil = X3 )
            | ? [X4] :
                ( ! [X5] :
                    ( ~ leq(X5,X4)
                    | ~ memberP(X3,X5)
                    | X4 = X5
                    | ~ ssItem(X5) )
                & memberP(X3,X4)
                & cons(X4,nil) = sK2
                & ssItem(X4) ) )
          & ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ? [X9] :
                          ( ~ leq(X9,X6)
                          & leq(X6,X9)
                          & memberP(X8,X9)
                          & memberP(X7,X9)
                          & ssItem(X9) )
                      | app(app(X7,cons(X6,nil)),X8) != sK0
                      | ~ ssList(X8) )
                  | ~ ssList(X7) )
              | ~ ssItem(X6) )
          & nil != sK0
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f227,plain,
    ( ? [X3] :
        ( ( ( nil = sK2
            & nil = X3 )
          | ? [X4] :
              ( ! [X5] :
                  ( ~ leq(X5,X4)
                  | ~ memberP(X3,X5)
                  | X4 = X5
                  | ~ ssItem(X5) )
              & memberP(X3,X4)
              & cons(X4,nil) = sK2
              & ssItem(X4) ) )
        & ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ? [X9] :
                        ( ~ leq(X9,X6)
                        & leq(X6,X9)
                        & memberP(X8,X9)
                        & memberP(X7,X9)
                        & ssItem(X9) )
                    | app(app(X7,cons(X6,nil)),X8) != sK0
                    | ~ ssList(X8) )
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & nil != sK0
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( ( nil = sK2
          & nil = sK3 )
        | ? [X4] :
            ( ! [X5] :
                ( ~ leq(X5,X4)
                | ~ memberP(sK3,X5)
                | X4 = X5
                | ~ ssItem(X5) )
            & memberP(sK3,X4)
            & cons(X4,nil) = sK2
            & ssItem(X4) ) )
      & ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ? [X9] :
                      ( ~ leq(X9,X6)
                      & leq(X6,X9)
                      & memberP(X8,X9)
                      & memberP(X7,X9)
                      & ssItem(X9) )
                  | app(app(X7,cons(X6,nil)),X8) != sK0
                  | ~ ssList(X8) )
              | ~ ssList(X7) )
          | ~ ssItem(X6) )
      & nil != sK0
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f228,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ~ leq(X5,X4)
            | ~ memberP(sK3,X5)
            | X4 = X5
            | ~ ssItem(X5) )
        & memberP(sK3,X4)
        & cons(X4,nil) = sK2
        & ssItem(X4) )
   => ( ! [X5] :
          ( ~ leq(X5,sK4)
          | ~ memberP(sK3,X5)
          | sK4 = X5
          | ~ ssItem(X5) )
      & memberP(sK3,sK4)
      & sK2 = cons(sK4,nil)
      & ssItem(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f229,plain,
    ! [X6,X7,X8] :
      ( ? [X9] :
          ( ~ leq(X9,X6)
          & leq(X6,X9)
          & memberP(X8,X9)
          & memberP(X7,X9)
          & ssItem(X9) )
     => ( ~ leq(sK5(X6,X7,X8),X6)
        & leq(X6,sK5(X6,X7,X8))
        & memberP(X8,sK5(X6,X7,X8))
        & memberP(X7,sK5(X6,X7,X8))
        & ssItem(sK5(X6,X7,X8)) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ~ leq(X5,X4)
                            | ~ memberP(X3,X5)
                            | X4 = X5
                            | ~ ssItem(X5) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ? [X9] :
                                  ( ~ leq(X9,X6)
                                  & leq(X6,X9)
                                  & memberP(X8,X9)
                                  & memberP(X7,X9)
                                  & ssItem(X9) )
                              | app(app(X7,cons(X6,nil)),X8) != X0
                              | ~ ssList(X8) )
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ~ leq(X5,X4)
                            | ~ memberP(X3,X5)
                            | X4 = X5
                            | ~ ssItem(X5) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ? [X9] :
                                  ( ~ leq(X9,X6)
                                  & leq(X6,X9)
                                  & memberP(X8,X9)
                                  & memberP(X7,X9)
                                  & ssItem(X9) )
                              | app(app(X7,cons(X6,nil)),X8) != X0
                              | ~ ssList(X8) )
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & 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)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssItem(X4)
                           => ( ? [X5] :
                                  ( leq(X5,X4)
                                  & memberP(X3,X5)
                                  & X4 != X5
                                  & ssItem(X5) )
                              | ~ memberP(X3,X4)
                              | cons(X4,nil) != X2 ) ) )
                      | ? [X6] :
                          ( ? [X7] :
                              ( ? [X8] :
                                  ( ! [X9] :
                                      ( ssItem(X9)
                                     => ( leq(X9,X6)
                                        | ~ leq(X6,X9)
                                        | ~ memberP(X8,X9)
                                        | ~ memberP(X7,X9) ) )
                                  & app(app(X7,cons(X6,nil)),X8) = X0
                                  & ssList(X8) )
                              & ssList(X7) )
                          & ssItem(X6) )
                      | nil = X0
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil != X2
                        | nil != X3 )
                      & ! [X8] :
                          ( ssItem(X8)
                         => ( ? [X9] :
                                ( leq(X9,X8)
                                & memberP(X3,X9)
                                & X8 != X9
                                & ssItem(X9) )
                            | ~ memberP(X3,X8)
                            | cons(X8,nil) != X2 ) ) )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( ssItem(X7)
                                   => ( leq(X7,X4)
                                      | ~ leq(X4,X7)
                                      | ~ memberP(X6,X7)
                                      | ~ memberP(X5,X7) ) )
                                & app(app(X5,cons(X4,nil)),X6) = X0
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) )
                    | nil = X0
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.5zFGMw5wia/Vampire---4.8_6182',co1) ).

fof(f341,plain,
    ssList(sK2),
    inference(cnf_transformation,[],[f230]) ).

fof(f6015,plain,
    ( ssItem(sK5(sK4,nil,nil))
    | ~ ssList(sK0)
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f6007,f367]) ).

fof(f367,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/tmp/tmp.5zFGMw5wia/Vampire---4.8_6182',ax17) ).

fof(f6007,plain,
    ( ssItem(sK5(sK4,nil,nil))
    | ~ ssList(nil)
    | ~ ssList(sK0)
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(trivial_inequality_removal,[],[f6005]) ).

fof(f6005,plain,
    ( sK0 != sK0
    | ssItem(sK5(sK4,nil,nil))
    | ~ ssList(nil)
    | ~ ssList(sK0)
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(superposition,[],[f1618,f423]) ).

fof(f423,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,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/tmp/tmp.5zFGMw5wia/Vampire---4.8_6182',ax84) ).

fof(f1618,plain,
    ( ! [X9] :
        ( sK0 != app(sK0,X9)
        | ssItem(sK5(sK4,nil,X9))
        | ~ ssList(X9) )
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f1617,f615]) ).

fof(f1617,plain,
    ( ! [X9] :
        ( sK0 != app(sK0,X9)
        | ssItem(sK5(sK4,nil,X9))
        | ~ ssList(X9)
        | ~ ssList(sK0) )
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f1602,f367]) ).

fof(f1602,plain,
    ( ! [X9] :
        ( sK0 != app(sK0,X9)
        | ssItem(sK5(sK4,nil,X9))
        | ~ ssList(X9)
        | ~ ssList(nil)
        | ~ ssList(sK0) )
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(superposition,[],[f757,f424]) ).

fof(f424,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,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/tmp/tmp.5zFGMw5wia/Vampire---4.8_6182',ax28) ).

fof(f757,plain,
    ( ! [X0,X1] :
        ( sK0 != app(app(X0,sK0),X1)
        | ssItem(sK5(sK4,X0,X1))
        | ~ ssList(X1)
        | ~ ssList(X0) )
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f744,f604]) ).

fof(f604,plain,
    ( ssItem(sK4)
    | ~ spl53_5 ),
    inference(avatar_component_clause,[],[f602]) ).

fof(f602,plain,
    ( spl53_5
  <=> ssItem(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_5])]) ).

fof(f744,plain,
    ( ! [X0,X1] :
        ( sK0 != app(app(X0,sK0),X1)
        | ssItem(sK5(sK4,X0,X1))
        | ~ ssList(X1)
        | ~ ssList(X0)
        | ~ ssItem(sK4) )
    | ~ spl53_4 ),
    inference(superposition,[],[f346,f622]) ).

fof(f622,plain,
    ( sK0 = cons(sK4,nil)
    | ~ spl53_4 ),
    inference(forward_demodulation,[],[f599,f344]) ).

fof(f599,plain,
    ( sK2 = cons(sK4,nil)
    | ~ spl53_4 ),
    inference(avatar_component_clause,[],[f597]) ).

fof(f597,plain,
    ( spl53_4
  <=> sK2 = cons(sK4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_4])]) ).

fof(f346,plain,
    ! [X8,X6,X7] :
      ( app(app(X7,cons(X6,nil)),X8) != sK0
      | ssItem(sK5(X6,X7,X8))
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f230]) ).

fof(f8914,plain,
    ( ~ ssItem(sK5(sK4,nil,nil))
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(resolution,[],[f8912,f368]) ).

fof(f368,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.5zFGMw5wia/Vampire---4.8_6182',ax38) ).

fof(f8912,plain,
    ( memberP(nil,sK5(sK4,nil,nil))
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f8911,f615]) ).

fof(f8911,plain,
    ( memberP(nil,sK5(sK4,nil,nil))
    | ~ ssList(sK0)
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f8903,f367]) ).

fof(f8903,plain,
    ( memberP(nil,sK5(sK4,nil,nil))
    | ~ ssList(nil)
    | ~ ssList(sK0)
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(trivial_inequality_removal,[],[f8901]) ).

fof(f8901,plain,
    ( sK0 != sK0
    | memberP(nil,sK5(sK4,nil,nil))
    | ~ ssList(nil)
    | ~ ssList(sK0)
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(superposition,[],[f1669,f423]) ).

fof(f1669,plain,
    ( ! [X9] :
        ( sK0 != app(sK0,X9)
        | memberP(nil,sK5(sK4,nil,X9))
        | ~ ssList(X9) )
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f1668,f615]) ).

fof(f1668,plain,
    ( ! [X9] :
        ( sK0 != app(sK0,X9)
        | memberP(nil,sK5(sK4,nil,X9))
        | ~ ssList(X9)
        | ~ ssList(sK0) )
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f1653,f367]) ).

fof(f1653,plain,
    ( ! [X9] :
        ( sK0 != app(sK0,X9)
        | memberP(nil,sK5(sK4,nil,X9))
        | ~ ssList(X9)
        | ~ ssList(nil)
        | ~ ssList(sK0) )
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(superposition,[],[f781,f424]) ).

fof(f781,plain,
    ( ! [X0,X1] :
        ( sK0 != app(app(X0,sK0),X1)
        | memberP(X0,sK5(sK4,X0,X1))
        | ~ ssList(X1)
        | ~ ssList(X0) )
    | ~ spl53_4
    | ~ spl53_5 ),
    inference(subsumption_resolution,[],[f768,f604]) ).

fof(f768,plain,
    ( ! [X0,X1] :
        ( sK0 != app(app(X0,sK0),X1)
        | memberP(X0,sK5(sK4,X0,X1))
        | ~ ssList(X1)
        | ~ ssList(X0)
        | ~ ssItem(sK4) )
    | ~ spl53_4 ),
    inference(superposition,[],[f347,f622]) ).

fof(f347,plain,
    ! [X8,X6,X7] :
      ( app(app(X7,cons(X6,nil)),X8) != sK0
      | memberP(X7,sK5(X6,X7,X8))
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f230]) ).

fof(f621,plain,
    ~ spl53_2,
    inference(avatar_contradiction_clause,[],[f620]) ).

fof(f620,plain,
    ( $false
    | ~ spl53_2 ),
    inference(subsumption_resolution,[],[f617,f345]) ).

fof(f345,plain,
    nil != sK0,
    inference(cnf_transformation,[],[f230]) ).

fof(f617,plain,
    ( nil = sK0
    | ~ spl53_2 ),
    inference(superposition,[],[f344,f589]) ).

fof(f589,plain,
    ( nil = sK2
    | ~ spl53_2 ),
    inference(avatar_component_clause,[],[f587]) ).

fof(f587,plain,
    ( spl53_2
  <=> nil = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_2])]) ).

fof(f605,plain,
    ( spl53_5
    | spl53_2 ),
    inference(avatar_split_clause,[],[f355,f587,f602]) ).

fof(f355,plain,
    ( nil = sK2
    | ssItem(sK4) ),
    inference(cnf_transformation,[],[f230]) ).

fof(f600,plain,
    ( spl53_4
    | spl53_2 ),
    inference(avatar_split_clause,[],[f356,f587,f597]) ).

fof(f356,plain,
    ( nil = sK2
    | sK2 = cons(sK4,nil) ),
    inference(cnf_transformation,[],[f230]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWC219+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36  % Computer : n006.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon Aug 28 14:42:21 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.5zFGMw5wia/Vampire---4.8_6182
% 0.15/0.37  % (6292)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43  % (6299)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.21/0.43  % (6295)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.21/0.43  % (6297)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.43  % (6293)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.21/0.43  % (6294)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.21/0.45  % (6298)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.21/0.46  % (6296)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 1.34/0.67  % (6299)First to succeed.
% 1.34/0.67  % (6299)Refutation found. Thanks to Tanya!
% 1.34/0.67  % SZS status Theorem for Vampire---4
% 1.34/0.67  % SZS output start Proof for Vampire---4
% See solution above
% 1.34/0.67  % (6299)------------------------------
% 1.34/0.67  % (6299)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 1.34/0.67  % (6299)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 1.34/0.67  % (6299)Termination reason: Refutation
% 1.34/0.67  
% 1.34/0.67  % (6299)Memory used [KB]: 10362
% 1.34/0.67  % (6299)Time elapsed: 0.238 s
% 1.34/0.67  % (6299)------------------------------
% 1.34/0.67  % (6299)------------------------------
% 1.34/0.67  % (6292)Success in time 0.302 s
% 1.34/0.67  % Vampire---4.8 exiting
%------------------------------------------------------------------------------