TSTP Solution File: SWC180+1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC180+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 : n011.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 20:57:14 EDT 2023

% Result   : Theorem 10.19s 1.94s
% Output   : Refutation 10.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  139 (  11 unt;   0 def)
%            Number of atoms       :  811 ( 108 equ)
%            Maximal formula atoms :   32 (   5 avg)
%            Number of connectives : 1122 ( 450   ~; 450   |; 170   &)
%                                         (  12 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   7 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   8 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   5 con; 0-2 aty)
%            Number of variables   :  276 (; 197   !;  79   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f27782,plain,
    $false,
    inference(avatar_sat_refutation,[],[f6532,f6536,f6564,f9351,f9367,f14094,f14487,f27781]) ).

fof(f27781,plain,
    ( ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_76
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(avatar_contradiction_clause,[],[f27780]) ).

fof(f27780,plain,
    ( $false
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_76
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27779,f570]) ).

fof(f570,plain,
    ssList(sK0),
    inference(forward_demodulation,[],[f338,f341]) ).

fof(f341,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f227]) ).

fof(f227,plain,
    ( ~ duplicatefreeP(sK0)
    & ! [X4] :
        ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ( ( ~ memberP(X5,X7)
                        | lt(X7,X4) )
                      & ( ~ memberP(X6,X7)
                        | lt(X4,X7) ) )
                    | ~ ssItem(X7) )
                | app(app(X5,cons(X4,nil)),X6) != sK2
                | ~ ssList(X6) )
            | ~ ssList(X5) )
        | ~ ssItem(X4) )
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f99,f226,f225,f224,f223]) ).

fof(f223,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ~ duplicatefreeP(X0)
                    & ! [X4] :
                        ( ! [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( ( ( ~ memberP(X5,X7)
                                        | lt(X7,X4) )
                                      & ( ~ memberP(X6,X7)
                                        | lt(X4,X7) ) )
                                    | ~ ssItem(X7) )
                                | app(app(X5,cons(X4,nil)),X6) != X2
                                | ~ ssList(X6) )
                            | ~ ssList(X5) )
                        | ~ ssItem(X4) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ duplicatefreeP(sK0)
                  & ! [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ( ( ~ memberP(X5,X7)
                                      | lt(X7,X4) )
                                    & ( ~ memberP(X6,X7)
                                      | lt(X4,X7) ) )
                                  | ~ ssItem(X7) )
                              | app(app(X5,cons(X4,nil)),X6) != X2
                              | ~ ssList(X6) )
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f224,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ~ duplicatefreeP(sK0)
                & ! [X4] :
                    ( ! [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ( ( ~ memberP(X5,X7)
                                    | lt(X7,X4) )
                                  & ( ~ memberP(X6,X7)
                                    | lt(X4,X7) ) )
                                | ~ ssItem(X7) )
                            | app(app(X5,cons(X4,nil)),X6) != X2
                            | ~ ssList(X6) )
                        | ~ ssList(X5) )
                    | ~ ssItem(X4) )
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ~ duplicatefreeP(sK0)
              & ! [X4] :
                  ( ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ( ( ~ memberP(X5,X7)
                                  | lt(X7,X4) )
                                & ( ~ memberP(X6,X7)
                                  | lt(X4,X7) ) )
                              | ~ ssItem(X7) )
                          | app(app(X5,cons(X4,nil)),X6) != X2
                          | ~ ssList(X6) )
                      | ~ ssList(X5) )
                  | ~ ssItem(X4) )
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ~ duplicatefreeP(sK0)
            & ! [X4] :
                ( ! [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ( ( ~ memberP(X5,X7)
                                | lt(X7,X4) )
                              & ( ~ memberP(X6,X7)
                                | lt(X4,X7) ) )
                            | ~ ssItem(X7) )
                        | app(app(X5,cons(X4,nil)),X6) != X2
                        | ~ ssList(X6) )
                    | ~ ssList(X5) )
                | ~ ssItem(X4) )
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ~ duplicatefreeP(sK0)
          & ! [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ( ( ~ memberP(X5,X7)
                              | lt(X7,X4) )
                            & ( ~ memberP(X6,X7)
                              | lt(X4,X7) ) )
                          | ~ ssItem(X7) )
                      | app(app(X5,cons(X4,nil)),X6) != sK2
                      | ~ ssList(X6) )
                  | ~ ssList(X5) )
              | ~ ssItem(X4) )
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f226,plain,
    ( ? [X3] :
        ( ~ duplicatefreeP(sK0)
        & ! [X4] :
            ( ! [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ( ( ~ memberP(X5,X7)
                            | lt(X7,X4) )
                          & ( ~ memberP(X6,X7)
                            | lt(X4,X7) ) )
                        | ~ ssItem(X7) )
                    | app(app(X5,cons(X4,nil)),X6) != sK2
                    | ~ ssList(X6) )
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ~ duplicatefreeP(sK0)
      & ! [X4] :
          ( ! [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ( ( ~ memberP(X5,X7)
                          | lt(X7,X4) )
                        & ( ~ memberP(X6,X7)
                          | lt(X4,X7) ) )
                      | ~ ssItem(X7) )
                  | app(app(X5,cons(X4,nil)),X6) != sK2
                  | ~ ssList(X6) )
              | ~ ssList(X5) )
          | ~ ssItem(X4) )
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ duplicatefreeP(X0)
                  & ! [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ( ( ~ memberP(X5,X7)
                                      | lt(X7,X4) )
                                    & ( ~ memberP(X6,X7)
                                      | lt(X4,X7) ) )
                                  | ~ ssItem(X7) )
                              | app(app(X5,cons(X4,nil)),X6) != X2
                              | ~ ssList(X6) )
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

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

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

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( duplicatefreeP(X0)
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ? [X7] :
                                    ( ( ( memberP(X5,X7)
                                        & ~ lt(X7,X4) )
                                      | ( memberP(X6,X7)
                                        & ~ lt(X4,X7) ) )
                                    & ssItem(X7) )
                                & app(app(X5,cons(X4,nil)),X6) = X2
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.82bo7Lp6Mx/Vampire---4.8_8822',co1) ).

fof(f338,plain,
    ssList(sK2),
    inference(cnf_transformation,[],[f227]) ).

fof(f27779,plain,
    ( ~ ssList(sK0)
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_76
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27778,f344]) ).

fof(f344,plain,
    ~ duplicatefreeP(sK0),
    inference(cnf_transformation,[],[f227]) ).

fof(f27778,plain,
    ( duplicatefreeP(sK0)
    | ~ ssList(sK0)
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_76
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27777,f27706]) ).

fof(f27706,plain,
    ( lt(sK38(sK0),sK38(sK0))
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27705,f570]) ).

fof(f27705,plain,
    ( lt(sK38(sK0),sK38(sK0))
    | ~ ssList(sK0)
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27694,f344]) ).

fof(f27694,plain,
    ( lt(sK38(sK0),sK38(sK0))
    | duplicatefreeP(sK0)
    | ~ ssList(sK0)
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(superposition,[],[f27669,f481]) ).

fof(f481,plain,
    ! [X0] :
      ( sK38(X0) = sK39(X0)
      | duplicatefreeP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f308,plain,
    ! [X0] :
      ( ( ( duplicatefreeP(X0)
          | ( sK38(X0) = sK39(X0)
            & app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
            & ssList(sK42(X0))
            & ssList(sK41(X0))
            & ssList(sK40(X0))
            & ssItem(sK39(X0))
            & ssItem(sK38(X0)) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( X6 != X7
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ duplicatefreeP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40,sK41,sK42])],[f302,f307,f306,f305,f304,f303]) ).

fof(f303,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( X1 = X2
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( sK38(X0) = X2
                        & app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK38(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f304,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( sK38(X0) = X2
                      & app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( sK38(X0) = sK39(X0)
                    & app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK39(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f305,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( sK38(X0) = sK39(X0)
                  & app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( sK38(X0) = sK39(X0)
                & app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK40(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f306,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( sK38(X0) = sK39(X0)
              & app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( sK38(X0) = sK39(X0)
            & app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK41(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f307,plain,
    ! [X0] :
      ( ? [X5] :
          ( sK38(X0) = sK39(X0)
          & app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
          & ssList(X5) )
     => ( sK38(X0) = sK39(X0)
        & app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
        & ssList(sK42(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f302,plain,
    ! [X0] :
      ( ( ( duplicatefreeP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( X1 = X2
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( X6 != X7
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ duplicatefreeP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f301]) ).

fof(f301,plain,
    ! [X0] :
      ( ( ( duplicatefreeP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( X1 = X2
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X1] :
              ( ! [X2] :
                  ( ! [X3] :
                      ( ! [X4] :
                          ( ! [X5] :
                              ( X1 != X2
                              | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                              | ~ ssList(X5) )
                          | ~ ssList(X4) )
                      | ~ ssList(X3) )
                  | ~ ssItem(X2) )
              | ~ ssItem(X1) )
          | ~ duplicatefreeP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f174]) ).

fof(f174,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f173]) ).

fof(f173,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => X1 != X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.82bo7Lp6Mx/Vampire---4.8_8822',ax13) ).

fof(f27669,plain,
    ( lt(sK38(sK0),sK39(sK0))
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27668,f9323]) ).

fof(f9323,plain,
    ( ssList(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))))
    | ~ spl51_73 ),
    inference(avatar_component_clause,[],[f9322]) ).

fof(f9322,plain,
    ( spl51_73
  <=> ssList(app(sK40(sK0),cons(sK38(sK0),sK41(sK0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_73])]) ).

fof(f27668,plain,
    ( lt(sK38(sK0),sK39(sK0))
    | ~ ssList(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))))
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27667,f14084]) ).

fof(f14084,plain,
    ( ssList(sK40(sK0))
    | ~ spl51_80 ),
    inference(avatar_component_clause,[],[f14083]) ).

fof(f14083,plain,
    ( spl51_80
  <=> ssList(sK40(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_80])]) ).

fof(f27667,plain,
    ( lt(sK38(sK0),sK39(sK0))
    | ~ ssList(sK40(sK0))
    | ~ ssList(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))))
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27666,f6526]) ).

fof(f6526,plain,
    ( ssList(sK41(sK0))
    | ~ spl51_62 ),
    inference(avatar_component_clause,[],[f6525]) ).

fof(f6525,plain,
    ( spl51_62
  <=> ssList(sK41(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_62])]) ).

fof(f27666,plain,
    ( lt(sK38(sK0),sK39(sK0))
    | ~ ssList(sK41(sK0))
    | ~ ssList(sK40(sK0))
    | ~ ssList(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))))
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27659,f6530]) ).

fof(f6530,plain,
    ( ssItem(sK38(sK0))
    | ~ spl51_63 ),
    inference(avatar_component_clause,[],[f6529]) ).

fof(f6529,plain,
    ( spl51_63
  <=> ssItem(sK38(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_63])]) ).

fof(f27659,plain,
    ( ~ ssItem(sK38(sK0))
    | lt(sK38(sK0),sK39(sK0))
    | ~ ssList(sK41(sK0))
    | ~ ssList(sK40(sK0))
    | ~ ssList(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))))
    | ~ spl51_73
    | ~ spl51_82 ),
    inference(duplicate_literal_removal,[],[f27658]) ).

fof(f27658,plain,
    ( ~ ssItem(sK38(sK0))
    | lt(sK38(sK0),sK39(sK0))
    | ~ ssList(sK41(sK0))
    | ~ ssList(sK40(sK0))
    | ~ ssItem(sK38(sK0))
    | ~ ssList(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))))
    | ~ spl51_73
    | ~ spl51_82 ),
    inference(resolution,[],[f27637,f555]) ).

fof(f555,plain,
    ! [X2,X3,X1] :
      ( memberP(app(X2,cons(X1,X3)),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(app(X2,cons(X1,X3))) ),
    inference(equality_resolution,[],[f497]) ).

fof(f497,plain,
    ! [X2,X3,X0,X1] :
      ( memberP(X0,X1)
      | app(X2,cons(X1,X3)) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f316]) ).

fof(f316,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(sK43(X0,X1),cons(X1,sK44(X0,X1))) = X0
                & ssList(sK44(X0,X1))
                & ssList(sK43(X0,X1)) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44])],[f313,f315,f314]) ).

fof(f314,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X4,cons(X1,X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(sK43(X0,X1),cons(X1,X5)) = X0
            & ssList(X5) )
        & ssList(sK43(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f315,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(sK43(X0,X1),cons(X1,X5)) = X0
          & ssList(X5) )
     => ( app(sK43(X0,X1),cons(X1,sK44(X0,X1))) = X0
        & ssList(sK44(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f313,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(X4,cons(X1,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f312]) ).

fof(f312,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(X2,cons(X1,X3)) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f184]) ).

fof(f184,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.82bo7Lp6Mx/Vampire---4.8_8822',ax3) ).

fof(f27637,plain,
    ( ! [X0] :
        ( ~ memberP(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))),X0)
        | ~ ssItem(X0)
        | lt(X0,sK39(sK0)) )
    | ~ spl51_73
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27636,f570]) ).

fof(f27636,plain,
    ( ! [X0] :
        ( lt(X0,sK39(sK0))
        | ~ ssItem(X0)
        | ~ memberP(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))),X0)
        | ~ ssList(sK0) )
    | ~ spl51_73
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27635,f344]) ).

fof(f27635,plain,
    ( ! [X0] :
        ( lt(X0,sK39(sK0))
        | ~ ssItem(X0)
        | ~ memberP(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))),X0)
        | duplicatefreeP(sK0)
        | ~ ssList(sK0) )
    | ~ spl51_73
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27634,f14477]) ).

fof(f14477,plain,
    ( ssList(cons(sK39(sK0),nil))
    | ~ spl51_82 ),
    inference(avatar_component_clause,[],[f14476]) ).

fof(f14476,plain,
    ( spl51_82
  <=> ssList(cons(sK39(sK0),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_82])]) ).

fof(f27634,plain,
    ( ! [X0] :
        ( lt(X0,sK39(sK0))
        | ~ ssItem(X0)
        | ~ memberP(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))),X0)
        | ~ ssList(cons(sK39(sK0),nil))
        | duplicatefreeP(sK0)
        | ~ ssList(sK0) )
    | ~ spl51_73 ),
    inference(subsumption_resolution,[],[f27633,f9323]) ).

fof(f27633,plain,
    ! [X0] :
      ( lt(X0,sK39(sK0))
      | ~ ssItem(X0)
      | ~ memberP(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))),X0)
      | ~ ssList(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))))
      | ~ ssList(cons(sK39(sK0),nil))
      | duplicatefreeP(sK0)
      | ~ ssList(sK0) ),
    inference(equality_resolution,[],[f1701]) ).

fof(f1701,plain,
    ! [X19,X20] :
      ( sK0 != X19
      | lt(X20,sK39(X19))
      | ~ ssItem(X20)
      | ~ memberP(app(sK40(X19),cons(sK38(X19),sK41(X19))),X20)
      | ~ ssList(app(sK40(X19),cons(sK38(X19),sK41(X19))))
      | ~ ssList(cons(sK39(X19),nil))
      | duplicatefreeP(X19)
      | ~ ssList(X19) ),
    inference(subsumption_resolution,[],[f1700,f476]) ).

fof(f476,plain,
    ! [X0] :
      ( ssItem(sK39(X0))
      | duplicatefreeP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f1700,plain,
    ! [X19,X20] :
      ( sK0 != X19
      | lt(X20,sK39(X19))
      | ~ ssItem(X20)
      | ~ memberP(app(sK40(X19),cons(sK38(X19),sK41(X19))),X20)
      | ~ ssList(app(sK40(X19),cons(sK38(X19),sK41(X19))))
      | ~ ssItem(sK39(X19))
      | ~ ssList(cons(sK39(X19),nil))
      | duplicatefreeP(X19)
      | ~ ssList(X19) ),
    inference(subsumption_resolution,[],[f1674,f479]) ).

fof(f479,plain,
    ! [X0] :
      ( ssList(sK42(X0))
      | duplicatefreeP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f1674,plain,
    ! [X19,X20] :
      ( sK0 != X19
      | lt(X20,sK39(X19))
      | ~ ssItem(X20)
      | ~ memberP(app(sK40(X19),cons(sK38(X19),sK41(X19))),X20)
      | ~ ssList(sK42(X19))
      | ~ ssList(app(sK40(X19),cons(sK38(X19),sK41(X19))))
      | ~ ssItem(sK39(X19))
      | ~ ssList(cons(sK39(X19),nil))
      | duplicatefreeP(X19)
      | ~ ssList(X19) ),
    inference(superposition,[],[f911,f480]) ).

fof(f480,plain,
    ! [X0] :
      ( app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
      | duplicatefreeP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f911,plain,
    ! [X2,X3,X0,X1] :
      ( sK0 != app(X2,cons(X0,X1))
      | lt(X3,X0)
      | ~ ssItem(X3)
      | ~ memberP(X2,X3)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil)) ),
    inference(duplicate_literal_removal,[],[f898]) ).

fof(f898,plain,
    ! [X2,X3,X0,X1] :
      ( sK0 != app(X2,cons(X0,X1))
      | lt(X3,X0)
      | ~ ssItem(X3)
      | ~ memberP(X2,X3)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil))
      | ~ ssItem(X0)
      | ~ ssList(X1) ),
    inference(superposition,[],[f628,f493]) ).

fof(f493,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f183,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.82bo7Lp6Mx/Vampire---4.8_8822',ax81) ).

fof(f628,plain,
    ! [X3,X6,X4,X5] :
      ( sK0 != app(X3,app(cons(X4,nil),X5))
      | lt(X6,X4)
      | ~ ssItem(X6)
      | ~ memberP(X3,X6)
      | ~ ssList(X5)
      | ~ ssList(X3)
      | ~ ssItem(X4)
      | ~ ssList(cons(X4,nil)) ),
    inference(forward_demodulation,[],[f613,f341]) ).

fof(f613,plain,
    ! [X3,X6,X4,X5] :
      ( sK2 != app(X3,app(cons(X4,nil),X5))
      | lt(X6,X4)
      | ~ ssItem(X6)
      | ~ memberP(X3,X6)
      | ~ ssList(X5)
      | ~ ssList(X3)
      | ~ ssItem(X4)
      | ~ ssList(cons(X4,nil)) ),
    inference(duplicate_literal_removal,[],[f610]) ).

fof(f610,plain,
    ! [X3,X6,X4,X5] :
      ( sK2 != app(X3,app(cons(X4,nil),X5))
      | lt(X6,X4)
      | ~ ssItem(X6)
      | ~ memberP(X3,X6)
      | ~ ssList(X5)
      | ~ ssList(X3)
      | ~ ssItem(X4)
      | ~ ssList(X5)
      | ~ ssList(cons(X4,nil))
      | ~ ssList(X3) ),
    inference(superposition,[],[f343,f523]) ).

fof(f523,plain,
    ! [X2,X0,X1] :
      ( app(app(X0,X1),X2) = app(X0,app(X1,X2))
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f206]) ).

fof(f206,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( app(app(X0,X1),X2) = app(X0,app(X1,X2))
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f82]) ).

fof(f82,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.82bo7Lp6Mx/Vampire---4.8_8822',ax82) ).

fof(f343,plain,
    ! [X6,X7,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK2
      | lt(X7,X4)
      | ~ ssItem(X7)
      | ~ memberP(X5,X7)
      | ~ ssList(X6)
      | ~ ssList(X5)
      | ~ ssItem(X4) ),
    inference(cnf_transformation,[],[f227]) ).

fof(f27777,plain,
    ( ~ lt(sK38(sK0),sK38(sK0))
    | duplicatefreeP(sK0)
    | ~ ssList(sK0)
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_76
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(superposition,[],[f27704,f481]) ).

fof(f27704,plain,
    ( ~ lt(sK39(sK0),sK38(sK0))
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_76
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27703,f9337]) ).

fof(f9337,plain,
    ( ssItem(sK39(sK0))
    | ~ spl51_76 ),
    inference(avatar_component_clause,[],[f9336]) ).

fof(f9336,plain,
    ( spl51_76
  <=> ssItem(sK39(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_76])]) ).

fof(f27703,plain,
    ( ~ lt(sK39(sK0),sK38(sK0))
    | ~ ssItem(sK39(sK0))
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(subsumption_resolution,[],[f27693,f6530]) ).

fof(f27693,plain,
    ( ~ lt(sK39(sK0),sK38(sK0))
    | ~ ssItem(sK38(sK0))
    | ~ ssItem(sK39(sK0))
    | ~ spl51_62
    | ~ spl51_63
    | ~ spl51_73
    | ~ spl51_80
    | ~ spl51_82 ),
    inference(resolution,[],[f27669,f367]) ).

fof(f367,plain,
    ! [X0,X1] :
      ( ~ lt(X1,X0)
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ lt(X1,X0)
          | ~ lt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f115]) ).

fof(f115,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ lt(X1,X0)
          | ~ lt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( lt(X0,X1)
           => ~ lt(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.82bo7Lp6Mx/Vampire---4.8_8822',ax33) ).

fof(f14487,plain,
    ( ~ spl51_76
    | spl51_82 ),
    inference(avatar_contradiction_clause,[],[f14486]) ).

fof(f14486,plain,
    ( $false
    | ~ spl51_76
    | spl51_82 ),
    inference(subsumption_resolution,[],[f14485,f353]) ).

fof(f353,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/tmp/tmp.82bo7Lp6Mx/Vampire---4.8_8822',ax17) ).

fof(f14485,plain,
    ( ~ ssList(nil)
    | ~ spl51_76
    | spl51_82 ),
    inference(subsumption_resolution,[],[f14483,f9337]) ).

fof(f14483,plain,
    ( ~ ssItem(sK39(sK0))
    | ~ ssList(nil)
    | spl51_82 ),
    inference(resolution,[],[f14478,f488]) ).

fof(f488,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f178,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.82bo7Lp6Mx/Vampire---4.8_8822',ax16) ).

fof(f14478,plain,
    ( ~ ssList(cons(sK39(sK0),nil))
    | spl51_82 ),
    inference(avatar_component_clause,[],[f14476]) ).

fof(f14094,plain,
    spl51_80,
    inference(avatar_contradiction_clause,[],[f14093]) ).

fof(f14093,plain,
    ( $false
    | spl51_80 ),
    inference(subsumption_resolution,[],[f14092,f570]) ).

fof(f14092,plain,
    ( ~ ssList(sK0)
    | spl51_80 ),
    inference(subsumption_resolution,[],[f14091,f344]) ).

fof(f14091,plain,
    ( duplicatefreeP(sK0)
    | ~ ssList(sK0)
    | spl51_80 ),
    inference(resolution,[],[f14085,f477]) ).

fof(f477,plain,
    ! [X0] :
      ( ssList(sK40(X0))
      | duplicatefreeP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f14085,plain,
    ( ~ ssList(sK40(sK0))
    | spl51_80 ),
    inference(avatar_component_clause,[],[f14083]) ).

fof(f9367,plain,
    ( ~ spl51_58
    | spl51_73 ),
    inference(avatar_contradiction_clause,[],[f9366]) ).

fof(f9366,plain,
    ( $false
    | ~ spl51_58
    | spl51_73 ),
    inference(subsumption_resolution,[],[f9365,f570]) ).

fof(f9365,plain,
    ( ~ ssList(sK0)
    | ~ spl51_58
    | spl51_73 ),
    inference(subsumption_resolution,[],[f9364,f344]) ).

fof(f9364,plain,
    ( duplicatefreeP(sK0)
    | ~ ssList(sK0)
    | ~ spl51_58
    | spl51_73 ),
    inference(resolution,[],[f9362,f477]) ).

fof(f9362,plain,
    ( ~ ssList(sK40(sK0))
    | ~ spl51_58
    | spl51_73 ),
    inference(subsumption_resolution,[],[f9361,f6499]) ).

fof(f6499,plain,
    ( ssList(cons(sK38(sK0),sK41(sK0)))
    | ~ spl51_58 ),
    inference(avatar_component_clause,[],[f6498]) ).

fof(f6498,plain,
    ( spl51_58
  <=> ssList(cons(sK38(sK0),sK41(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_58])]) ).

fof(f9361,plain,
    ( ~ ssList(cons(sK38(sK0),sK41(sK0)))
    | ~ ssList(sK40(sK0))
    | spl51_73 ),
    inference(resolution,[],[f9324,f498]) ).

fof(f498,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f185]) ).

fof(f185,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.82bo7Lp6Mx/Vampire---4.8_8822',ax26) ).

fof(f9324,plain,
    ( ~ ssList(app(sK40(sK0),cons(sK38(sK0),sK41(sK0))))
    | spl51_73 ),
    inference(avatar_component_clause,[],[f9322]) ).

fof(f9351,plain,
    spl51_76,
    inference(avatar_contradiction_clause,[],[f9350]) ).

fof(f9350,plain,
    ( $false
    | spl51_76 ),
    inference(subsumption_resolution,[],[f9349,f570]) ).

fof(f9349,plain,
    ( ~ ssList(sK0)
    | spl51_76 ),
    inference(subsumption_resolution,[],[f9347,f344]) ).

fof(f9347,plain,
    ( duplicatefreeP(sK0)
    | ~ ssList(sK0)
    | spl51_76 ),
    inference(resolution,[],[f9338,f476]) ).

fof(f9338,plain,
    ( ~ ssItem(sK39(sK0))
    | spl51_76 ),
    inference(avatar_component_clause,[],[f9336]) ).

fof(f6564,plain,
    spl51_63,
    inference(avatar_contradiction_clause,[],[f6563]) ).

fof(f6563,plain,
    ( $false
    | spl51_63 ),
    inference(subsumption_resolution,[],[f6562,f570]) ).

fof(f6562,plain,
    ( ~ ssList(sK0)
    | spl51_63 ),
    inference(subsumption_resolution,[],[f6561,f344]) ).

fof(f6561,plain,
    ( duplicatefreeP(sK0)
    | ~ ssList(sK0)
    | spl51_63 ),
    inference(resolution,[],[f6531,f475]) ).

fof(f475,plain,
    ! [X0] :
      ( ssItem(sK38(X0))
      | duplicatefreeP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f6531,plain,
    ( ~ ssItem(sK38(sK0))
    | spl51_63 ),
    inference(avatar_component_clause,[],[f6529]) ).

fof(f6536,plain,
    spl51_62,
    inference(avatar_contradiction_clause,[],[f6535]) ).

fof(f6535,plain,
    ( $false
    | spl51_62 ),
    inference(subsumption_resolution,[],[f6534,f570]) ).

fof(f6534,plain,
    ( ~ ssList(sK0)
    | spl51_62 ),
    inference(subsumption_resolution,[],[f6533,f344]) ).

fof(f6533,plain,
    ( duplicatefreeP(sK0)
    | ~ ssList(sK0)
    | spl51_62 ),
    inference(resolution,[],[f6527,f478]) ).

fof(f478,plain,
    ! [X0] :
      ( ssList(sK41(X0))
      | duplicatefreeP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f6527,plain,
    ( ~ ssList(sK41(sK0))
    | spl51_62 ),
    inference(avatar_component_clause,[],[f6525]) ).

fof(f6532,plain,
    ( ~ spl51_62
    | ~ spl51_63
    | spl51_58 ),
    inference(avatar_split_clause,[],[f6523,f6498,f6529,f6525]) ).

fof(f6523,plain,
    ( ~ ssItem(sK38(sK0))
    | ~ ssList(sK41(sK0))
    | spl51_58 ),
    inference(resolution,[],[f6500,f488]) ).

fof(f6500,plain,
    ( ~ ssList(cons(sK38(sK0),sK41(sK0)))
    | spl51_58 ),
    inference(avatar_component_clause,[],[f6498]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14  % Problem    : SWC180+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Mon Aug 28 16:14:11 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.82bo7Lp6Mx/Vampire---4.8_8822
% 0.16/0.38  % (8933)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43  % (8941)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.23/0.44  % (8938)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.23/0.44  % (8937)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)
% 0.23/0.44  % (8939)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)
% 0.23/0.44  % (8936)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.23/0.44  % (8940)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)
% 0.23/0.46  % (8935)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)
% 10.19/1.94  % (8941)First to succeed.
% 10.19/1.94  % (8941)Refutation found. Thanks to Tanya!
% 10.19/1.94  % SZS status Theorem for Vampire---4
% 10.19/1.94  % SZS output start Proof for Vampire---4
% See solution above
% 10.19/1.95  % (8941)------------------------------
% 10.19/1.95  % (8941)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 10.19/1.95  % (8941)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 10.19/1.95  % (8941)Termination reason: Refutation
% 10.19/1.95  
% 10.19/1.95  % (8941)Memory used [KB]: 26225
% 10.19/1.95  % (8941)Time elapsed: 1.522 s
% 10.19/1.95  % (8941)------------------------------
% 10.19/1.95  % (8941)------------------------------
% 10.19/1.95  % (8933)Success in time 1.566 s
% 10.19/1.95  % Vampire---4.8 exiting
%------------------------------------------------------------------------------