TSTP Solution File: SWC224+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC224+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 : n002.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 20:57:36 EDT 2023

% Result   : Theorem 7.28s 1.44s
% Output   : Refutation 7.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  169 (  16 unt;   0 def)
%            Number of atoms       :  920 ( 270 equ)
%            Maximal formula atoms :   52 (   5 avg)
%            Number of connectives : 1213 ( 462   ~; 474   |; 217   &)
%                                         (  14 <=>;  46  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   18 (  16 usr;  11 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :  268 (; 204   !;  64   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f25659,plain,
    $false,
    inference(avatar_sat_refutation,[],[f588,f918,f1070,f1181,f1193,f1291,f9256,f9372,f25278,f25620,f25658]) ).

fof(f25658,plain,
    ( ~ spl53_43
    | ~ spl53_111
    | ~ spl53_115
    | ~ spl53_254 ),
    inference(avatar_contradiction_clause,[],[f25657]) ).

fof(f25657,plain,
    ( $false
    | ~ spl53_43
    | ~ spl53_111
    | ~ spl53_115
    | ~ spl53_254 ),
    inference(subsumption_resolution,[],[f25652,f25554]) ).

fof(f25554,plain,
    ( ssItem(sK5(hd(sK0),nil,tl(sK0)))
    | ~ spl53_43
    | ~ spl53_111
    | ~ spl53_115
    | ~ spl53_254 ),
    inference(subsumption_resolution,[],[f25553,f9163]) ).

fof(f9163,plain,
    ( ssList(cons(hd(sK0),nil))
    | ~ spl53_111 ),
    inference(avatar_component_clause,[],[f9162]) ).

fof(f9162,plain,
    ( spl53_111
  <=> ssList(cons(hd(sK0),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_111])]) ).

fof(f25553,plain,
    ( ssItem(sK5(hd(sK0),nil,tl(sK0)))
    | ~ ssList(cons(hd(sK0),nil))
    | ~ spl53_43
    | ~ spl53_115
    | ~ spl53_254 ),
    inference(subsumption_resolution,[],[f25552,f1163]) ).

fof(f1163,plain,
    ( ssItem(hd(sK0))
    | ~ spl53_43 ),
    inference(avatar_component_clause,[],[f1162]) ).

fof(f1162,plain,
    ( spl53_43
  <=> ssItem(hd(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_43])]) ).

fof(f25552,plain,
    ( ssItem(sK5(hd(sK0),nil,tl(sK0)))
    | ~ ssItem(hd(sK0))
    | ~ ssList(cons(hd(sK0),nil))
    | ~ spl53_115
    | ~ spl53_254 ),
    inference(subsumption_resolution,[],[f25484,f9203]) ).

fof(f9203,plain,
    ( ssList(tl(sK0))
    | ~ spl53_115 ),
    inference(avatar_component_clause,[],[f9202]) ).

fof(f9202,plain,
    ( spl53_115
  <=> ssList(tl(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_115])]) ).

fof(f25484,plain,
    ( ssItem(sK5(hd(sK0),nil,tl(sK0)))
    | ~ ssList(tl(sK0))
    | ~ ssItem(hd(sK0))
    | ~ ssList(cons(hd(sK0),nil))
    | ~ spl53_254 ),
    inference(trivial_inequality_removal,[],[f25452]) ).

fof(f25452,plain,
    ( sK0 != sK0
    | ssItem(sK5(hd(sK0),nil,tl(sK0)))
    | ~ ssList(tl(sK0))
    | ~ ssItem(hd(sK0))
    | ~ ssList(cons(hd(sK0),nil))
    | ~ spl53_254 ),
    inference(superposition,[],[f1511,f20283]) ).

fof(f20283,plain,
    ( sK0 = cons(hd(sK0),tl(sK0))
    | ~ spl53_254 ),
    inference(avatar_component_clause,[],[f20281]) ).

fof(f20281,plain,
    ( spl53_254
  <=> sK0 = cons(hd(sK0),tl(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_254])]) ).

fof(f1511,plain,
    ! [X0,X1] :
      ( cons(X0,X1) != sK0
      | ssItem(sK5(X0,nil,X1))
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil)) ),
    inference(duplicate_literal_removal,[],[f1504]) ).

fof(f1504,plain,
    ! [X0,X1] :
      ( cons(X0,X1) != sK0
      | ssItem(sK5(X0,nil,X1))
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil))
      | ~ ssItem(X0)
      | ~ ssList(X1) ),
    inference(superposition,[],[f721,f504]) ).

fof(f504,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f184]) ).

fof(f184,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax81) ).

fof(f721,plain,
    ! [X11,X12] :
      ( sK0 != app(cons(X11,nil),X12)
      | ssItem(sK5(X11,nil,X12))
      | ~ ssList(X12)
      | ~ ssItem(X11)
      | ~ ssList(cons(X11,nil)) ),
    inference(subsumption_resolution,[],[f710,f364]) ).

fof(f364,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax17) ).

fof(f710,plain,
    ! [X11,X12] :
      ( sK0 != app(cons(X11,nil),X12)
      | ssItem(sK5(X11,nil,X12))
      | ~ ssList(X12)
      | ~ ssList(nil)
      | ~ ssItem(X11)
      | ~ ssList(cons(X11,nil)) ),
    inference(superposition,[],[f346,f421]) ).

fof(f421,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/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax28) ).

fof(f346,plain,
    ! [X10,X8,X9] :
      ( app(app(X9,cons(X8,nil)),X10) != sK0
      | ssItem(sK5(X8,X9,X10))
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssItem(X8) ),
    inference(cnf_transformation,[],[f230]) ).

fof(f230,plain,
    ( ( nil != sK2
      | nil = sK3 )
    & ! [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( app(X7,cons(X5,nil)) != sK2
                | ~ ssList(X7) )
            | app(cons(X5,nil),X6) != sK4
            | ~ ssList(X6) )
        | ~ ssItem(X5) )
    & equalelemsP(sK2)
    & sK3 = app(sK2,sK4)
    & ssList(sK4)
    & ! [X8] :
        ( ! [X9] :
            ( ! [X10] :
                ( ( ~ leq(sK5(X8,X9,X10),X8)
                  & leq(X8,sK5(X8,X9,X10))
                  & memberP(X10,sK5(X8,X9,X10))
                  & memberP(X9,sK5(X8,X9,X10))
                  & ssItem(sK5(X8,X9,X10)) )
                | app(app(X9,cons(X8,nil)),X10) != sK0
                | ~ ssList(X10) )
            | ~ ssList(X9) )
        | ~ ssItem(X8) )
    & 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] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( app(X7,cons(X5,nil)) != X2
                                    | ~ ssList(X7) )
                                | app(cons(X5,nil),X6) != X4
                                | ~ ssList(X6) )
                            | ~ ssItem(X5) )
                        & equalelemsP(X2)
                        & app(X2,X4) = X3
                        & ssList(X4) )
                    & ! [X8] :
                        ( ! [X9] :
                            ( ! [X10] :
                                ( ? [X11] :
                                    ( ~ leq(X11,X8)
                                    & leq(X8,X11)
                                    & memberP(X10,X11)
                                    & memberP(X9,X11)
                                    & ssItem(X11) )
                                | app(app(X9,cons(X8,nil)),X10) != X0
                                | ~ ssList(X10) )
                            | ~ ssList(X9) )
                        | ~ ssItem(X8) )
                    & nil != X0
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( app(X7,cons(X5,nil)) != X2
                                  | ~ ssList(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & equalelemsP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ? [X11] :
                                  ( ~ leq(X11,X8)
                                  & leq(X8,X11)
                                  & memberP(X10,X11)
                                  & memberP(X9,X11)
                                  & ssItem(X11) )
                              | app(app(X9,cons(X8,nil)),X10) != sK0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  & 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] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( app(X7,cons(X5,nil)) != X2
                                | ~ ssList(X7) )
                            | app(cons(X5,nil),X6) != X4
                            | ~ ssList(X6) )
                        | ~ ssItem(X5) )
                    & equalelemsP(X2)
                    & app(X2,X4) = X3
                    & ssList(X4) )
                & ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( ? [X11] :
                                ( ~ leq(X11,X8)
                                & leq(X8,X11)
                                & memberP(X10,X11)
                                & memberP(X9,X11)
                                & ssItem(X11) )
                            | app(app(X9,cons(X8,nil)),X10) != sK0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssItem(X8) )
                & nil != sK0
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( app(X7,cons(X5,nil)) != X2
                              | ~ ssList(X7) )
                          | app(cons(X5,nil),X6) != X4
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) )
                  & equalelemsP(X2)
                  & app(X2,X4) = X3
                  & ssList(X4) )
              & ! [X8] :
                  ( ! [X9] :
                      ( ! [X10] :
                          ( ? [X11] :
                              ( ~ leq(X11,X8)
                              & leq(X8,X11)
                              & memberP(X10,X11)
                              & memberP(X9,X11)
                              & ssItem(X11) )
                          | app(app(X9,cons(X8,nil)),X10) != sK0
                          | ~ ssList(X10) )
                      | ~ ssList(X9) )
                  | ~ ssItem(X8) )
              & 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] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( app(X7,cons(X5,nil)) != X2
                            | ~ ssList(X7) )
                        | app(cons(X5,nil),X6) != X4
                        | ~ ssList(X6) )
                    | ~ ssItem(X5) )
                & equalelemsP(X2)
                & app(X2,X4) = X3
                & ssList(X4) )
            & ! [X8] :
                ( ! [X9] :
                    ( ! [X10] :
                        ( ? [X11] :
                            ( ~ leq(X11,X8)
                            & leq(X8,X11)
                            & memberP(X10,X11)
                            & memberP(X9,X11)
                            & ssItem(X11) )
                        | app(app(X9,cons(X8,nil)),X10) != sK0
                        | ~ ssList(X10) )
                    | ~ ssList(X9) )
                | ~ ssItem(X8) )
            & nil != sK0
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil != sK2
            | nil = X3 )
          & ? [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( app(X7,cons(X5,nil)) != sK2
                          | ~ ssList(X7) )
                      | app(cons(X5,nil),X6) != X4
                      | ~ ssList(X6) )
                  | ~ ssItem(X5) )
              & equalelemsP(sK2)
              & app(sK2,X4) = X3
              & ssList(X4) )
          & ! [X8] :
              ( ! [X9] :
                  ( ! [X10] :
                      ( ? [X11] :
                          ( ~ leq(X11,X8)
                          & leq(X8,X11)
                          & memberP(X10,X11)
                          & memberP(X9,X11)
                          & ssItem(X11) )
                      | app(app(X9,cons(X8,nil)),X10) != sK0
                      | ~ ssList(X10) )
                  | ~ ssList(X9) )
              | ~ ssItem(X8) )
          & nil != sK0
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f227,plain,
    ( ? [X3] :
        ( ( nil != sK2
          | nil = X3 )
        & ? [X4] :
            ( ! [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( app(X7,cons(X5,nil)) != sK2
                        | ~ ssList(X7) )
                    | app(cons(X5,nil),X6) != X4
                    | ~ ssList(X6) )
                | ~ ssItem(X5) )
            & equalelemsP(sK2)
            & app(sK2,X4) = X3
            & ssList(X4) )
        & ! [X8] :
            ( ! [X9] :
                ( ! [X10] :
                    ( ? [X11] :
                        ( ~ leq(X11,X8)
                        & leq(X8,X11)
                        & memberP(X10,X11)
                        & memberP(X9,X11)
                        & ssItem(X11) )
                    | app(app(X9,cons(X8,nil)),X10) != sK0
                    | ~ ssList(X10) )
                | ~ ssList(X9) )
            | ~ ssItem(X8) )
        & nil != sK0
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( nil != sK2
        | nil = sK3 )
      & ? [X4] :
          ( ! [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( app(X7,cons(X5,nil)) != sK2
                      | ~ ssList(X7) )
                  | app(cons(X5,nil),X6) != X4
                  | ~ ssList(X6) )
              | ~ ssItem(X5) )
          & equalelemsP(sK2)
          & app(sK2,X4) = sK3
          & ssList(X4) )
      & ! [X8] :
          ( ! [X9] :
              ( ! [X10] :
                  ( ? [X11] :
                      ( ~ leq(X11,X8)
                      & leq(X8,X11)
                      & memberP(X10,X11)
                      & memberP(X9,X11)
                      & ssItem(X11) )
                  | app(app(X9,cons(X8,nil)),X10) != sK0
                  | ~ ssList(X10) )
              | ~ ssList(X9) )
          | ~ ssItem(X8) )
      & nil != sK0
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f228,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( app(X7,cons(X5,nil)) != sK2
                    | ~ ssList(X7) )
                | app(cons(X5,nil),X6) != X4
                | ~ ssList(X6) )
            | ~ ssItem(X5) )
        & equalelemsP(sK2)
        & app(sK2,X4) = sK3
        & ssList(X4) )
   => ( ! [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( app(X7,cons(X5,nil)) != sK2
                  | ~ ssList(X7) )
              | app(cons(X5,nil),X6) != sK4
              | ~ ssList(X6) )
          | ~ ssItem(X5) )
      & equalelemsP(sK2)
      & sK3 = app(sK2,sK4)
      & ssList(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f229,plain,
    ! [X8,X9,X10] :
      ( ? [X11] :
          ( ~ leq(X11,X8)
          & leq(X8,X11)
          & memberP(X10,X11)
          & memberP(X9,X11)
          & ssItem(X11) )
     => ( ~ leq(sK5(X8,X9,X10),X8)
        & leq(X8,sK5(X8,X9,X10))
        & memberP(X10,sK5(X8,X9,X10))
        & memberP(X9,sK5(X8,X9,X10))
        & ssItem(sK5(X8,X9,X10)) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( app(X7,cons(X5,nil)) != X2
                                  | ~ ssList(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & equalelemsP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ? [X11] :
                                  ( ~ leq(X11,X8)
                                  & leq(X8,X11)
                                  & memberP(X10,X11)
                                  & memberP(X9,X11)
                                  & ssItem(X11) )
                              | app(app(X9,cons(X8,nil)),X10) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  & 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] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( app(X7,cons(X5,nil)) != X2
                                  | ~ ssList(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & equalelemsP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ? [X11] :
                                  ( ~ leq(X11,X8)
                                  & leq(X8,X11)
                                  & memberP(X10,X11)
                                  & memberP(X9,X11)
                                  & ssItem(X11) )
                              | app(app(X9,cons(X8,nil)),X10) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  & 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] :
                          ( ssList(X4)
                         => ( ? [X5] :
                                ( ? [X6] :
                                    ( ? [X7] :
                                        ( app(X7,cons(X5,nil)) = X2
                                        & ssList(X7) )
                                    & app(cons(X5,nil),X6) = X4
                                    & ssList(X6) )
                                & ssItem(X5) )
                            | ~ equalelemsP(X2)
                            | app(X2,X4) != X3 ) )
                      | ? [X8] :
                          ( ? [X9] :
                              ( ? [X10] :
                                  ( ! [X11] :
                                      ( ssItem(X11)
                                     => ( leq(X11,X8)
                                        | ~ leq(X8,X11)
                                        | ~ memberP(X10,X11)
                                        | ~ memberP(X9,X11) ) )
                                  & app(app(X9,cons(X8,nil)),X10) = X0
                                  & ssList(X10) )
                              & ssList(X9) )
                          & ssItem(X8) )
                      | 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] :
                          ( ssList(X8)
                         => ( ? [X9] :
                                ( ? [X10] :
                                    ( ? [X11] :
                                        ( app(X11,cons(X9,nil)) = X2
                                        & ssList(X11) )
                                    & app(cons(X9,nil),X10) = X8
                                    & ssList(X10) )
                                & ssItem(X9) )
                            | ~ equalelemsP(X2)
                            | app(X2,X8) != X3 ) )
                      | ? [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] :
                        ( ssList(X8)
                       => ( ? [X9] :
                              ( ? [X10] :
                                  ( ? [X11] :
                                      ( app(X11,cons(X9,nil)) = X2
                                      & ssList(X11) )
                                  & app(cons(X9,nil),X10) = X8
                                  & ssList(X10) )
                              & ssItem(X9) )
                          | ~ equalelemsP(X2)
                          | app(X2,X8) != X3 ) )
                    | ? [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/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',co1) ).

fof(f25652,plain,
    ( ~ ssItem(sK5(hd(sK0),nil,tl(sK0)))
    | ~ spl53_43
    | ~ spl53_111
    | ~ spl53_115
    | ~ spl53_254 ),
    inference(resolution,[],[f25557,f365]) ).

fof(f365,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/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax38) ).

fof(f25557,plain,
    ( memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
    | ~ spl53_43
    | ~ spl53_111
    | ~ spl53_115
    | ~ spl53_254 ),
    inference(subsumption_resolution,[],[f25556,f9163]) ).

fof(f25556,plain,
    ( memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
    | ~ ssList(cons(hd(sK0),nil))
    | ~ spl53_43
    | ~ spl53_115
    | ~ spl53_254 ),
    inference(subsumption_resolution,[],[f25555,f1163]) ).

fof(f25555,plain,
    ( memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
    | ~ ssItem(hd(sK0))
    | ~ ssList(cons(hd(sK0),nil))
    | ~ spl53_115
    | ~ spl53_254 ),
    inference(subsumption_resolution,[],[f25483,f9203]) ).

fof(f25483,plain,
    ( memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
    | ~ ssList(tl(sK0))
    | ~ ssItem(hd(sK0))
    | ~ ssList(cons(hd(sK0),nil))
    | ~ spl53_254 ),
    inference(trivial_inequality_removal,[],[f25454]) ).

fof(f25454,plain,
    ( sK0 != sK0
    | memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
    | ~ ssList(tl(sK0))
    | ~ ssItem(hd(sK0))
    | ~ ssList(cons(hd(sK0),nil))
    | ~ spl53_254 ),
    inference(superposition,[],[f1849,f20283]) ).

fof(f1849,plain,
    ! [X0,X1] :
      ( cons(X0,X1) != sK0
      | memberP(nil,sK5(X0,nil,X1))
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil)) ),
    inference(duplicate_literal_removal,[],[f1842]) ).

fof(f1842,plain,
    ! [X0,X1] :
      ( cons(X0,X1) != sK0
      | memberP(nil,sK5(X0,nil,X1))
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil))
      | ~ ssItem(X0)
      | ~ ssList(X1) ),
    inference(superposition,[],[f807,f504]) ).

fof(f807,plain,
    ! [X11,X12] :
      ( sK0 != app(cons(X11,nil),X12)
      | memberP(nil,sK5(X11,nil,X12))
      | ~ ssList(X12)
      | ~ ssItem(X11)
      | ~ ssList(cons(X11,nil)) ),
    inference(subsumption_resolution,[],[f796,f364]) ).

fof(f796,plain,
    ! [X11,X12] :
      ( sK0 != app(cons(X11,nil),X12)
      | memberP(nil,sK5(X11,nil,X12))
      | ~ ssList(X12)
      | ~ ssList(nil)
      | ~ ssItem(X11)
      | ~ ssList(cons(X11,nil)) ),
    inference(superposition,[],[f347,f421]) ).

fof(f347,plain,
    ! [X10,X8,X9] :
      ( app(app(X9,cons(X8,nil)),X10) != sK0
      | memberP(X9,sK5(X8,X9,X10))
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssItem(X8) ),
    inference(cnf_transformation,[],[f230]) ).

fof(f25620,plain,
    ( spl53_4
    | ~ spl53_327 ),
    inference(avatar_contradiction_clause,[],[f25619]) ).

fof(f25619,plain,
    ( $false
    | spl53_4
    | ~ spl53_327 ),
    inference(subsumption_resolution,[],[f25618,f646]) ).

fof(f646,plain,
    ( nil != sK1
    | spl53_4 ),
    inference(avatar_component_clause,[],[f644]) ).

fof(f644,plain,
    ( spl53_4
  <=> nil = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_4])]) ).

fof(f25618,plain,
    ( nil = sK1
    | ~ spl53_327 ),
    inference(subsumption_resolution,[],[f25617,f589]) ).

fof(f589,plain,
    ssList(sK1),
    inference(forward_demodulation,[],[f342,f343]) ).

fof(f343,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f230]) ).

fof(f342,plain,
    ssList(sK3),
    inference(cnf_transformation,[],[f230]) ).

fof(f25617,plain,
    ( ~ ssList(sK1)
    | nil = sK1
    | ~ spl53_327 ),
    inference(duplicate_literal_removal,[],[f25608]) ).

fof(f25608,plain,
    ( ~ ssList(sK1)
    | nil = sK1
    | ~ ssList(sK1)
    | ~ spl53_327 ),
    inference(resolution,[],[f25277,f416]) ).

fof(f416,plain,
    ! [X0] :
      ( frontsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0] :
      ( frontsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax42) ).

fof(f25277,plain,
    ( ! [X2] :
        ( ~ frontsegP(X2,sK1)
        | ~ ssList(X2)
        | nil = X2 )
    | ~ spl53_327 ),
    inference(avatar_component_clause,[],[f25276]) ).

fof(f25276,plain,
    ( spl53_327
  <=> ! [X2] :
        ( ~ frontsegP(X2,sK1)
        | ~ ssList(X2)
        | nil = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_327])]) ).

fof(f25278,plain,
    ( spl53_327
    | spl53_254
    | ~ spl53_16 ),
    inference(avatar_split_clause,[],[f25268,f916,f20281,f25276]) ).

fof(f916,plain,
    ( spl53_16
  <=> ! [X2,X3] :
        ( ~ frontsegP(cons(X2,X3),sK1)
        | ~ ssItem(X2)
        | ~ ssList(X3)
        | hd(sK0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_16])]) ).

fof(f25268,plain,
    ( ! [X2] :
        ( sK0 = cons(hd(sK0),tl(sK0))
        | ~ frontsegP(X2,sK1)
        | nil = X2
        | ~ ssList(X2) )
    | ~ spl53_16 ),
    inference(duplicate_literal_removal,[],[f25175]) ).

fof(f25175,plain,
    ( ! [X2] :
        ( sK0 = cons(hd(sK0),tl(sK0))
        | ~ frontsegP(X2,sK1)
        | nil = X2
        | ~ ssList(X2)
        | ~ frontsegP(X2,sK1)
        | nil = X2
        | ~ ssList(X2) )
    | ~ spl53_16 ),
    inference(superposition,[],[f12791,f3699]) ).

fof(f3699,plain,
    ( ! [X1] :
        ( hd(X1) = hd(sK0)
        | ~ frontsegP(X1,sK1)
        | nil = X1
        | ~ ssList(X1) )
    | ~ spl53_16 ),
    inference(subsumption_resolution,[],[f3698,f426]) ).

fof(f426,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f154,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f153]) ).

fof(f153,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax24) ).

fof(f3698,plain,
    ( ! [X1] :
        ( ~ frontsegP(X1,sK1)
        | ~ ssList(tl(X1))
        | hd(X1) = hd(sK0)
        | nil = X1
        | ~ ssList(X1) )
    | ~ spl53_16 ),
    inference(subsumption_resolution,[],[f3689,f425]) ).

fof(f425,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f151]) ).

fof(f151,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax22) ).

fof(f3689,plain,
    ( ! [X1] :
        ( ~ frontsegP(X1,sK1)
        | ~ ssItem(hd(X1))
        | ~ ssList(tl(X1))
        | hd(X1) = hd(sK0)
        | nil = X1
        | ~ ssList(X1) )
    | ~ spl53_16 ),
    inference(superposition,[],[f917,f427]) ).

fof(f427,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f156]) ).

fof(f156,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f155]) ).

fof(f155,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax78) ).

fof(f917,plain,
    ( ! [X2,X3] :
        ( ~ frontsegP(cons(X2,X3),sK1)
        | ~ ssItem(X2)
        | ~ ssList(X3)
        | hd(sK0) = X2 )
    | ~ spl53_16 ),
    inference(avatar_component_clause,[],[f916]) ).

fof(f12791,plain,
    ( ! [X19] :
        ( sK0 = cons(hd(X19),tl(sK0))
        | ~ frontsegP(X19,sK1)
        | nil = X19
        | ~ ssList(X19) )
    | ~ spl53_16 ),
    inference(subsumption_resolution,[],[f12790,f590]) ).

fof(f590,plain,
    ssList(sK0),
    inference(forward_demodulation,[],[f341,f344]) ).

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

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

fof(f12790,plain,
    ( ! [X19] :
        ( sK0 = cons(hd(X19),tl(sK0))
        | ~ ssList(sK0)
        | ~ frontsegP(X19,sK1)
        | nil = X19
        | ~ ssList(X19) )
    | ~ spl53_16 ),
    inference(subsumption_resolution,[],[f12780,f345]) ).

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

fof(f12780,plain,
    ( ! [X19] :
        ( sK0 = cons(hd(X19),tl(sK0))
        | nil = sK0
        | ~ ssList(sK0)
        | ~ frontsegP(X19,sK1)
        | nil = X19
        | ~ ssList(X19) )
    | ~ spl53_16 ),
    inference(superposition,[],[f427,f3699]) ).

fof(f9372,plain,
    ( ~ spl53_43
    | spl53_111 ),
    inference(avatar_contradiction_clause,[],[f9371]) ).

fof(f9371,plain,
    ( $false
    | ~ spl53_43
    | spl53_111 ),
    inference(subsumption_resolution,[],[f9370,f364]) ).

fof(f9370,plain,
    ( ~ ssList(nil)
    | ~ spl53_43
    | spl53_111 ),
    inference(subsumption_resolution,[],[f9369,f1163]) ).

fof(f9369,plain,
    ( ~ ssItem(hd(sK0))
    | ~ ssList(nil)
    | spl53_111 ),
    inference(resolution,[],[f9164,f499]) ).

fof(f499,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax16) ).

fof(f9164,plain,
    ( ~ ssList(cons(hd(sK0),nil))
    | spl53_111 ),
    inference(avatar_component_clause,[],[f9162]) ).

fof(f9256,plain,
    spl53_115,
    inference(avatar_contradiction_clause,[],[f9255]) ).

fof(f9255,plain,
    ( $false
    | spl53_115 ),
    inference(subsumption_resolution,[],[f9254,f590]) ).

fof(f9254,plain,
    ( ~ ssList(sK0)
    | spl53_115 ),
    inference(subsumption_resolution,[],[f9253,f345]) ).

fof(f9253,plain,
    ( nil = sK0
    | ~ ssList(sK0)
    | spl53_115 ),
    inference(resolution,[],[f9204,f426]) ).

fof(f9204,plain,
    ( ~ ssList(tl(sK0))
    | spl53_115 ),
    inference(avatar_component_clause,[],[f9202]) ).

fof(f1291,plain,
    spl53_43,
    inference(avatar_contradiction_clause,[],[f1290]) ).

fof(f1290,plain,
    ( $false
    | spl53_43 ),
    inference(subsumption_resolution,[],[f1289,f590]) ).

fof(f1289,plain,
    ( ~ ssList(sK0)
    | spl53_43 ),
    inference(subsumption_resolution,[],[f1288,f345]) ).

fof(f1288,plain,
    ( nil = sK0
    | ~ ssList(sK0)
    | spl53_43 ),
    inference(resolution,[],[f1164,f425]) ).

fof(f1164,plain,
    ( ~ ssItem(hd(sK0))
    | spl53_43 ),
    inference(avatar_component_clause,[],[f1162]) ).

fof(f1193,plain,
    ~ spl53_4,
    inference(avatar_split_clause,[],[f1192,f644]) ).

fof(f1192,plain,
    nil != sK1,
    inference(subsumption_resolution,[],[f1191,f590]) ).

fof(f1191,plain,
    ( ~ ssList(sK0)
    | nil != sK1 ),
    inference(forward_demodulation,[],[f1190,f344]) ).

fof(f1190,plain,
    ( nil != sK1
    | ~ ssList(sK2) ),
    inference(subsumption_resolution,[],[f1189,f345]) ).

fof(f1189,plain,
    ( nil = sK0
    | nil != sK1
    | ~ ssList(sK2) ),
    inference(forward_demodulation,[],[f1170,f344]) ).

fof(f1170,plain,
    ( nil != sK1
    | nil = sK2
    | ~ ssList(sK2) ),
    inference(forward_demodulation,[],[f1169,f343]) ).

fof(f1169,plain,
    ( nil != sK3
    | nil = sK2
    | ~ ssList(sK2) ),
    inference(subsumption_resolution,[],[f600,f351]) ).

fof(f351,plain,
    ssList(sK4),
    inference(cnf_transformation,[],[f230]) ).

fof(f600,plain,
    ( nil != sK3
    | nil = sK2
    | ~ ssList(sK4)
    | ~ ssList(sK2) ),
    inference(superposition,[],[f529,f352]) ).

fof(f352,plain,
    sK3 = app(sK2,sK4),
    inference(cnf_transformation,[],[f230]) ).

fof(f529,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f335]) ).

fof(f335,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f334]) ).

fof(f334,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f203]) ).

fof(f203,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax83) ).

fof(f1181,plain,
    ( spl53_4
    | ~ spl53_1 ),
    inference(avatar_split_clause,[],[f1174,f581,f644]) ).

fof(f581,plain,
    ( spl53_1
  <=> nil = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_1])]) ).

fof(f1174,plain,
    ( nil = sK1
    | ~ spl53_1 ),
    inference(superposition,[],[f583,f343]) ).

fof(f583,plain,
    ( nil = sK3
    | ~ spl53_1 ),
    inference(avatar_component_clause,[],[f581]) ).

fof(f1070,plain,
    ( spl53_4
    | spl53_13 ),
    inference(avatar_contradiction_clause,[],[f1069]) ).

fof(f1069,plain,
    ( $false
    | spl53_4
    | spl53_13 ),
    inference(subsumption_resolution,[],[f1068,f589]) ).

fof(f1068,plain,
    ( ~ ssList(sK1)
    | spl53_4
    | spl53_13 ),
    inference(subsumption_resolution,[],[f1067,f646]) ).

fof(f1067,plain,
    ( nil = sK1
    | ~ ssList(sK1)
    | spl53_13 ),
    inference(resolution,[],[f904,f426]) ).

fof(f904,plain,
    ( ~ ssList(tl(sK1))
    | spl53_13 ),
    inference(avatar_component_clause,[],[f902]) ).

fof(f902,plain,
    ( spl53_13
  <=> ssList(tl(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_13])]) ).

fof(f918,plain,
    ( ~ spl53_13
    | spl53_16
    | spl53_2
    | spl53_4 ),
    inference(avatar_split_clause,[],[f914,f644,f585,f916,f902]) ).

fof(f585,plain,
    ( spl53_2
  <=> nil = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl53_2])]) ).

fof(f914,plain,
    ( ! [X2,X3] :
        ( ~ frontsegP(cons(X2,X3),sK1)
        | hd(sK0) = X2
        | ~ ssList(tl(sK1))
        | ~ ssList(X3)
        | ~ ssItem(X2) )
    | spl53_2
    | spl53_4 ),
    inference(subsumption_resolution,[],[f866,f821]) ).

fof(f821,plain,
    ( ssItem(hd(sK0))
    | spl53_2
    | spl53_4 ),
    inference(subsumption_resolution,[],[f820,f589]) ).

fof(f820,plain,
    ( ssItem(hd(sK0))
    | ~ ssList(sK1)
    | spl53_2
    | spl53_4 ),
    inference(subsumption_resolution,[],[f815,f646]) ).

fof(f815,plain,
    ( ssItem(hd(sK0))
    | nil = sK1
    | ~ ssList(sK1)
    | spl53_2 ),
    inference(superposition,[],[f425,f634]) ).

fof(f634,plain,
    ( hd(sK1) = hd(sK0)
    | spl53_2 ),
    inference(subsumption_resolution,[],[f633,f590]) ).

fof(f633,plain,
    ( ~ ssList(sK0)
    | hd(sK1) = hd(sK0)
    | spl53_2 ),
    inference(forward_demodulation,[],[f632,f344]) ).

fof(f632,plain,
    ( hd(sK1) = hd(sK0)
    | ~ ssList(sK2)
    | spl53_2 ),
    inference(forward_demodulation,[],[f631,f344]) ).

fof(f631,plain,
    ( hd(sK2) = hd(sK1)
    | ~ ssList(sK2)
    | spl53_2 ),
    inference(forward_demodulation,[],[f630,f343]) ).

fof(f630,plain,
    ( hd(sK2) = hd(sK3)
    | ~ ssList(sK2)
    | spl53_2 ),
    inference(subsumption_resolution,[],[f629,f351]) ).

fof(f629,plain,
    ( hd(sK2) = hd(sK3)
    | ~ ssList(sK4)
    | ~ ssList(sK2)
    | spl53_2 ),
    inference(subsumption_resolution,[],[f598,f587]) ).

fof(f587,plain,
    ( nil != sK2
    | spl53_2 ),
    inference(avatar_component_clause,[],[f585]) ).

fof(f598,plain,
    ( hd(sK2) = hd(sK3)
    | nil = sK2
    | ~ ssList(sK4)
    | ~ ssList(sK2) ),
    inference(superposition,[],[f510,f352]) ).

fof(f510,plain,
    ! [X0,X1] :
      ( hd(X0) = hd(app(X0,X1))
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f188]) ).

fof(f188,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(X0) = hd(app(X0,X1))
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f187]) ).

fof(f187,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(X0) = hd(app(X0,X1))
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f85]) ).

fof(f85,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil != X0
           => hd(X0) = hd(app(X0,X1)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax85) ).

fof(f866,plain,
    ( ! [X2,X3] :
        ( ~ frontsegP(cons(X2,X3),sK1)
        | hd(sK0) = X2
        | ~ ssList(tl(sK1))
        | ~ ssList(X3)
        | ~ ssItem(hd(sK0))
        | ~ ssItem(X2) )
    | spl53_2
    | spl53_4 ),
    inference(superposition,[],[f398,f819]) ).

fof(f819,plain,
    ( sK1 = cons(hd(sK0),tl(sK1))
    | spl53_2
    | spl53_4 ),
    inference(subsumption_resolution,[],[f818,f589]) ).

fof(f818,plain,
    ( sK1 = cons(hd(sK0),tl(sK1))
    | ~ ssList(sK1)
    | spl53_2
    | spl53_4 ),
    inference(subsumption_resolution,[],[f814,f646]) ).

fof(f814,plain,
    ( sK1 = cons(hd(sK0),tl(sK1))
    | nil = sK1
    | ~ ssList(sK1)
    | spl53_2 ),
    inference(superposition,[],[f427,f634]) ).

fof(f398,plain,
    ! [X2,X3,X0,X1] :
      ( ~ frontsegP(cons(X0,X2),cons(X1,X3))
      | X0 = X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f239]) ).

fof(f239,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
                      | ~ frontsegP(X2,X3)
                      | X0 != X1 )
                    & ( ( frontsegP(X2,X3)
                        & X0 = X1 )
                      | ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f238]) ).

fof(f238,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
                      | ~ frontsegP(X2,X3)
                      | X0 != X1 )
                    & ( ( frontsegP(X2,X3)
                        & X0 = X1 )
                      | ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f137]) ).

fof(f137,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( frontsegP(cons(X0,X2),cons(X1,X3))
                  <=> ( frontsegP(X2,X3)
                      & X0 = X1 ) )
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( frontsegP(cons(X0,X2),cons(X1,X3))
                  <=> ( frontsegP(X2,X3)
                      & X0 = X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax44) ).

fof(f588,plain,
    ( spl53_1
    | ~ spl53_2 ),
    inference(avatar_split_clause,[],[f355,f585,f581]) ).

fof(f355,plain,
    ( nil != sK2
    | nil = sK3 ),
    inference(cnf_transformation,[],[f230]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : SWC224+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36  % Computer : n002.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 16:10:50 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/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355
% 0.15/0.37  % (14612)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43  % (14614)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.21/0.43  % (14617)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  % (14615)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  % (14613)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  % (14618)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)
% 0.21/0.43  % (14616)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.21/0.43  % (14619)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 7.28/1.43  % (14619)First to succeed.
% 7.28/1.44  % (14619)Refutation found. Thanks to Tanya!
% 7.28/1.44  % SZS status Theorem for Vampire---4
% 7.28/1.44  % SZS output start Proof for Vampire---4
% See solution above
% 7.28/1.44  % (14619)------------------------------
% 7.28/1.44  % (14619)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 7.28/1.44  % (14619)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 7.28/1.44  % (14619)Termination reason: Refutation
% 7.28/1.44  
% 7.28/1.44  % (14619)Memory used [KB]: 19701
% 7.28/1.44  % (14619)Time elapsed: 1.007 s
% 7.28/1.44  % (14619)------------------------------
% 7.28/1.44  % (14619)------------------------------
% 7.28/1.44  % (14612)Success in time 1.073 s
% 7.28/1.44  % Vampire---4.8 exiting
%------------------------------------------------------------------------------