TSTP Solution File: SWC298+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC298+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n024.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 : Sun May  5 09:50:06 EDT 2024

% Result   : Theorem 0.60s 0.82s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  167 (  38 unt;   0 def)
%            Number of atoms       :  796 ( 190 equ)
%            Maximal formula atoms :   44 (   4 avg)
%            Number of connectives :  952 ( 323   ~; 314   |; 247   &)
%                                         (  10 <=>;  58  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   5 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  18 con; 0-2 aty)
%            Number of variables   :  258 ( 145   !; 113   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1166,plain,
    $false,
    inference(avatar_sat_refutation,[],[f272,f277,f393,f397,f1159]) ).

fof(f1159,plain,
    ( ~ spl23_4
    | ~ spl23_5 ),
    inference(avatar_contradiction_clause,[],[f1158]) ).

fof(f1158,plain,
    ( $false
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(subsumption_resolution,[],[f1157,f1152]) ).

fof(f1152,plain,
    ( lt(sK4,sK4)
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(forward_demodulation,[],[f1139,f1136]) ).

fof(f1136,plain,
    ( sK4 = sK5
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(subsumption_resolution,[],[f1134,f174]) ).

fof(f174,plain,
    ssItem(sK5),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,plain,
    ( ( ( nil = sK2
        & nil = sK3 )
      | ( ! [X5] :
            ( ~ leq(X5,sK4)
            | ~ memberP(sK3,X5)
            | sK4 = X5
            | ~ ssItem(X5) )
        & memberP(sK3,sK4)
        & sK2 = cons(sK4,nil)
        & ssItem(sK4) ) )
    & lt(sK6,sK5)
    & sK0 = app(app(app(app(sK7,cons(sK5,nil)),sK8),cons(sK6,nil)),sK9)
    & ssList(sK9)
    & ssList(sK8)
    & ssList(sK7)
    & ssItem(sK6)
    & ssItem(sK5)
    & 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,sK6,sK7,sK8,sK9])],[f100,f147,f146,f145,f144,f143,f142,f141,f140,f139,f138]) ).

fof(f138,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | ? [X4] :
                          ( ! [X5] :
                              ( ~ leq(X5,X4)
                              | ~ memberP(X3,X5)
                              | X4 = X5
                              | ~ ssItem(X5) )
                          & memberP(X3,X4)
                          & cons(X4,nil) = X2
                          & ssItem(X4) ) )
                    & ? [X6] :
                        ( ? [X7] :
                            ( ? [X8] :
                                ( ? [X9] :
                                    ( ? [X10] :
                                        ( lt(X7,X6)
                                        & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = X0
                                        & ssList(X10) )
                                    & ssList(X9) )
                                & ssList(X8) )
                            & ssItem(X7) )
                        & ssItem(X6) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ~ leq(X5,X4)
                            | ~ memberP(X3,X5)
                            | X4 = X5
                            | ~ ssItem(X5) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ? [X6] :
                      ( ? [X7] :
                          ( ? [X8] :
                              ( ? [X9] :
                                  ( ? [X10] :
                                      ( lt(X7,X6)
                                      & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = sK0
                                      & ssList(X10) )
                                  & ssList(X9) )
                              & ssList(X8) )
                          & ssItem(X7) )
                      & ssItem(X6) )
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f139,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | ? [X4] :
                      ( ! [X5] :
                          ( ~ leq(X5,X4)
                          | ~ memberP(X3,X5)
                          | X4 = X5
                          | ~ ssItem(X5) )
                      & memberP(X3,X4)
                      & cons(X4,nil) = X2
                      & ssItem(X4) ) )
                & ? [X6] :
                    ( ? [X7] :
                        ( ? [X8] :
                            ( ? [X9] :
                                ( ? [X10] :
                                    ( lt(X7,X6)
                                    & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = sK0
                                    & ssList(X10) )
                                & ssList(X9) )
                            & ssList(X8) )
                        & ssItem(X7) )
                    & ssItem(X6) )
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = X2
                  & nil = X3 )
                | ? [X4] :
                    ( ! [X5] :
                        ( ~ leq(X5,X4)
                        | ~ memberP(X3,X5)
                        | X4 = X5
                        | ~ ssItem(X5) )
                    & memberP(X3,X4)
                    & cons(X4,nil) = X2
                    & ssItem(X4) ) )
              & ? [X6] :
                  ( ? [X7] :
                      ( ? [X8] :
                          ( ? [X9] :
                              ( ? [X10] :
                                  ( lt(X7,X6)
                                  & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = sK0
                                  & ssList(X10) )
                              & ssList(X9) )
                          & ssList(X8) )
                      & ssItem(X7) )
                  & ssItem(X6) )
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f140,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | ? [X4] :
                  ( ! [X5] :
                      ( ~ leq(X5,X4)
                      | ~ memberP(X3,X5)
                      | X4 = X5
                      | ~ ssItem(X5) )
                  & memberP(X3,X4)
                  & cons(X4,nil) = X2
                  & ssItem(X4) ) )
            & ? [X6] :
                ( ? [X7] :
                    ( ? [X8] :
                        ( ? [X9] :
                            ( ? [X10] :
                                ( lt(X7,X6)
                                & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = sK0
                                & ssList(X10) )
                            & ssList(X9) )
                        & ssList(X8) )
                    & ssItem(X7) )
                & ssItem(X6) )
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK2
              & nil = X3 )
            | ? [X4] :
                ( ! [X5] :
                    ( ~ leq(X5,X4)
                    | ~ memberP(X3,X5)
                    | X4 = X5
                    | ~ ssItem(X5) )
                & memberP(X3,X4)
                & cons(X4,nil) = sK2
                & ssItem(X4) ) )
          & ? [X6] :
              ( ? [X7] :
                  ( ? [X8] :
                      ( ? [X9] :
                          ( ? [X10] :
                              ( lt(X7,X6)
                              & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = sK0
                              & ssList(X10) )
                          & ssList(X9) )
                      & ssList(X8) )
                  & ssItem(X7) )
              & ssItem(X6) )
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f141,plain,
    ( ? [X3] :
        ( ( ( nil = sK2
            & nil = X3 )
          | ? [X4] :
              ( ! [X5] :
                  ( ~ leq(X5,X4)
                  | ~ memberP(X3,X5)
                  | X4 = X5
                  | ~ ssItem(X5) )
              & memberP(X3,X4)
              & cons(X4,nil) = sK2
              & ssItem(X4) ) )
        & ? [X6] :
            ( ? [X7] :
                ( ? [X8] :
                    ( ? [X9] :
                        ( ? [X10] :
                            ( lt(X7,X6)
                            & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = sK0
                            & ssList(X10) )
                        & ssList(X9) )
                    & ssList(X8) )
                & ssItem(X7) )
            & ssItem(X6) )
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( ( nil = sK2
          & nil = sK3 )
        | ? [X4] :
            ( ! [X5] :
                ( ~ leq(X5,X4)
                | ~ memberP(sK3,X5)
                | X4 = X5
                | ~ ssItem(X5) )
            & memberP(sK3,X4)
            & cons(X4,nil) = sK2
            & ssItem(X4) ) )
      & ? [X6] :
          ( ? [X7] :
              ( ? [X8] :
                  ( ? [X9] :
                      ( ? [X10] :
                          ( lt(X7,X6)
                          & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = sK0
                          & ssList(X10) )
                      & ssList(X9) )
                  & ssList(X8) )
              & ssItem(X7) )
          & ssItem(X6) )
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f142,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ~ leq(X5,X4)
            | ~ memberP(sK3,X5)
            | X4 = X5
            | ~ ssItem(X5) )
        & memberP(sK3,X4)
        & cons(X4,nil) = sK2
        & ssItem(X4) )
   => ( ! [X5] :
          ( ~ leq(X5,sK4)
          | ~ memberP(sK3,X5)
          | sK4 = X5
          | ~ ssItem(X5) )
      & memberP(sK3,sK4)
      & sK2 = cons(sK4,nil)
      & ssItem(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ( ? [X6] :
        ( ? [X7] :
            ( ? [X8] :
                ( ? [X9] :
                    ( ? [X10] :
                        ( lt(X7,X6)
                        & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = sK0
                        & ssList(X10) )
                    & ssList(X9) )
                & ssList(X8) )
            & ssItem(X7) )
        & ssItem(X6) )
   => ( ? [X7] :
          ( ? [X8] :
              ( ? [X9] :
                  ( ? [X10] :
                      ( lt(X7,sK5)
                      & sK0 = app(app(app(app(X8,cons(sK5,nil)),X9),cons(X7,nil)),X10)
                      & ssList(X10) )
                  & ssList(X9) )
              & ssList(X8) )
          & ssItem(X7) )
      & ssItem(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f144,plain,
    ( ? [X7] :
        ( ? [X8] :
            ( ? [X9] :
                ( ? [X10] :
                    ( lt(X7,sK5)
                    & sK0 = app(app(app(app(X8,cons(sK5,nil)),X9),cons(X7,nil)),X10)
                    & ssList(X10) )
                & ssList(X9) )
            & ssList(X8) )
        & ssItem(X7) )
   => ( ? [X8] :
          ( ? [X9] :
              ( ? [X10] :
                  ( lt(sK6,sK5)
                  & sK0 = app(app(app(app(X8,cons(sK5,nil)),X9),cons(sK6,nil)),X10)
                  & ssList(X10) )
              & ssList(X9) )
          & ssList(X8) )
      & ssItem(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f145,plain,
    ( ? [X8] :
        ( ? [X9] :
            ( ? [X10] :
                ( lt(sK6,sK5)
                & sK0 = app(app(app(app(X8,cons(sK5,nil)),X9),cons(sK6,nil)),X10)
                & ssList(X10) )
            & ssList(X9) )
        & ssList(X8) )
   => ( ? [X9] :
          ( ? [X10] :
              ( lt(sK6,sK5)
              & sK0 = app(app(app(app(sK7,cons(sK5,nil)),X9),cons(sK6,nil)),X10)
              & ssList(X10) )
          & ssList(X9) )
      & ssList(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ( ? [X9] :
        ( ? [X10] :
            ( lt(sK6,sK5)
            & sK0 = app(app(app(app(sK7,cons(sK5,nil)),X9),cons(sK6,nil)),X10)
            & ssList(X10) )
        & ssList(X9) )
   => ( ? [X10] :
          ( lt(sK6,sK5)
          & sK0 = app(app(app(app(sK7,cons(sK5,nil)),sK8),cons(sK6,nil)),X10)
          & ssList(X10) )
      & ssList(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ( ? [X10] :
        ( lt(sK6,sK5)
        & sK0 = app(app(app(app(sK7,cons(sK5,nil)),sK8),cons(sK6,nil)),X10)
        & ssList(X10) )
   => ( lt(sK6,sK5)
      & sK0 = app(app(app(app(sK7,cons(sK5,nil)),sK8),cons(sK6,nil)),sK9)
      & ssList(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ~ leq(X5,X4)
                            | ~ memberP(X3,X5)
                            | X4 = X5
                            | ~ ssItem(X5) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ? [X6] :
                      ( ? [X7] :
                          ( ? [X8] :
                              ( ? [X9] :
                                  ( ? [X10] :
                                      ( lt(X7,X6)
                                      & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = X0
                                      & ssList(X10) )
                                  & ssList(X9) )
                              & ssList(X8) )
                          & ssItem(X7) )
                      & ssItem(X6) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ! [X5] :
                            ( ~ leq(X5,X4)
                            | ~ memberP(X3,X5)
                            | X4 = X5
                            | ~ ssItem(X5) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ? [X6] :
                      ( ? [X7] :
                          ( ? [X8] :
                              ( ? [X9] :
                                  ( ? [X10] :
                                      ( lt(X7,X6)
                                      & app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) = X0
                                      & ssList(X10) )
                                  & ssList(X9) )
                              & ssList(X8) )
                          & ssItem(X7) )
                      & ssItem(X6) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssItem(X4)
                           => ( ? [X5] :
                                  ( leq(X5,X4)
                                  & memberP(X3,X5)
                                  & X4 != X5
                                  & ssItem(X5) )
                              | ~ memberP(X3,X4)
                              | cons(X4,nil) != X2 ) ) )
                      | ! [X6] :
                          ( ssItem(X6)
                         => ! [X7] :
                              ( ssItem(X7)
                             => ! [X8] :
                                  ( ssList(X8)
                                 => ! [X9] :
                                      ( ssList(X9)
                                     => ! [X10] :
                                          ( ssList(X10)
                                         => ( ~ lt(X7,X6)
                                            | app(app(app(app(X8,cons(X6,nil)),X9),cons(X7,nil)),X10) != 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 )
                        & ! [X9] :
                            ( ssItem(X9)
                           => ( ? [X10] :
                                  ( leq(X10,X9)
                                  & memberP(X3,X10)
                                  & X9 != X10
                                  & ssItem(X10) )
                              | ~ memberP(X3,X9)
                              | cons(X9,nil) != X2 ) ) )
                      | ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( ssItem(X5)
                             => ! [X6] :
                                  ( ssList(X6)
                                 => ! [X7] :
                                      ( ssList(X7)
                                     => ! [X8] :
                                          ( ssList(X8)
                                         => ( ~ lt(X5,X4)
                                            | app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != 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 )
                      & ! [X9] :
                          ( ssItem(X9)
                         => ( ? [X10] :
                                ( leq(X10,X9)
                                & memberP(X3,X10)
                                & X9 != X10
                                & ssItem(X10) )
                            | ~ memberP(X3,X9)
                            | cons(X9,nil) != X2 ) ) )
                    | ! [X4] :
                        ( ssItem(X4)
                       => ! [X5] :
                            ( ssItem(X5)
                           => ! [X6] :
                                ( ssList(X6)
                               => ! [X7] :
                                    ( ssList(X7)
                                   => ! [X8] :
                                        ( ssList(X8)
                                       => ( ~ lt(X5,X4)
                                          | app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0 ) ) ) ) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KIvKtjKhCy/Vampire---4.8_1965',co1) ).

fof(f1134,plain,
    ( sK4 = sK5
    | ~ ssItem(sK5)
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(resolution,[],[f895,f1081]) ).

fof(f1081,plain,
    memberP(sK2,sK5),
    inference(subsumption_resolution,[],[f1080,f174]) ).

fof(f1080,plain,
    ( memberP(sK2,sK5)
    | ~ ssItem(sK5) ),
    inference(resolution,[],[f525,f1060]) ).

fof(f1060,plain,
    memberP(sF21,sK5),
    inference(subsumption_resolution,[],[f1059,f174]) ).

fof(f1059,plain,
    ( memberP(sF21,sK5)
    | ~ ssItem(sK5) ),
    inference(resolution,[],[f521,f562]) ).

fof(f562,plain,
    memberP(sF19,sK5),
    inference(subsumption_resolution,[],[f561,f174]) ).

fof(f561,plain,
    ( memberP(sF19,sK5)
    | ~ ssItem(sK5) ),
    inference(resolution,[],[f557,f519]) ).

fof(f519,plain,
    ! [X0] :
      ( ~ memberP(sF18,X0)
      | memberP(sF19,X0)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f518,f310]) ).

fof(f310,plain,
    ssList(sF18),
    inference(subsumption_resolution,[],[f309,f176]) ).

fof(f176,plain,
    ssList(sK7),
    inference(cnf_transformation,[],[f148]) ).

fof(f309,plain,
    ( ssList(sF18)
    | ~ ssList(sK7) ),
    inference(subsumption_resolution,[],[f303,f298]) ).

fof(f298,plain,
    ssList(sF17),
    inference(subsumption_resolution,[],[f297,f211]) ).

fof(f211,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/tmp/tmp.KIvKtjKhCy/Vampire---4.8_1965',ax17) ).

fof(f297,plain,
    ( ssList(sF17)
    | ~ ssList(nil) ),
    inference(subsumption_resolution,[],[f289,f174]) ).

fof(f289,plain,
    ( ssList(sF17)
    | ~ ssItem(sK5)
    | ~ ssList(nil) ),
    inference(superposition,[],[f209,f245]) ).

fof(f245,plain,
    cons(sK5,nil) = sF17,
    introduced(function_definition,[new_symbols(definition,[sF17])]) ).

fof(f209,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,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.KIvKtjKhCy/Vampire---4.8_1965',ax16) ).

fof(f303,plain,
    ( ssList(sF18)
    | ~ ssList(sF17)
    | ~ ssList(sK7) ),
    inference(superposition,[],[f210,f246]) ).

fof(f246,plain,
    app(sK7,sF17) = sF18,
    introduced(function_definition,[new_symbols(definition,[sF18])]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,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.KIvKtjKhCy/Vampire---4.8_1965',ax26) ).

fof(f518,plain,
    ! [X0] :
      ( memberP(sF19,X0)
      | ~ memberP(sF18,X0)
      | ~ ssList(sF18)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f507,f177]) ).

fof(f177,plain,
    ssList(sK8),
    inference(cnf_transformation,[],[f148]) ).

fof(f507,plain,
    ! [X0] :
      ( memberP(sF19,X0)
      | ~ memberP(sF18,X0)
      | ~ ssList(sK8)
      | ~ ssList(sF18)
      | ~ ssItem(X0) ),
    inference(superposition,[],[f217,f247]) ).

fof(f247,plain,
    app(sF18,sK8) = sF19,
    introduced(function_definition,[new_symbols(definition,[sF19])]) ).

fof(f217,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f159]) ).

fof(f159,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( memberP(app(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | memberP(X1,X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(app(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | memberP(X1,X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KIvKtjKhCy/Vampire---4.8_1965',ax36) ).

fof(f557,plain,
    memberP(sF18,sK5),
    inference(subsumption_resolution,[],[f556,f174]) ).

fof(f556,plain,
    ( memberP(sF18,sK5)
    | ~ ssItem(sK5) ),
    inference(resolution,[],[f546,f332]) ).

fof(f332,plain,
    memberP(sF17,sK5),
    inference(subsumption_resolution,[],[f331,f174]) ).

fof(f331,plain,
    ( memberP(sF17,sK5)
    | ~ ssItem(sK5) ),
    inference(subsumption_resolution,[],[f329,f211]) ).

fof(f329,plain,
    ( memberP(sF17,sK5)
    | ~ ssList(nil)
    | ~ ssItem(sK5) ),
    inference(superposition,[],[f253,f245]) ).

fof(f253,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f239]) ).

fof(f239,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f214]) ).

fof(f214,plain,
    ! [X2,X0,X1] :
      ( memberP(cons(X1,X2),X0)
      | X0 != X1
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f158]) ).

fof(f158,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f157]) ).

fof(f157,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KIvKtjKhCy/Vampire---4.8_1965',ax37) ).

fof(f546,plain,
    ! [X0] :
      ( ~ memberP(sF17,X0)
      | memberP(sF18,X0)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f545,f176]) ).

fof(f545,plain,
    ! [X0] :
      ( memberP(sF18,X0)
      | ~ memberP(sF17,X0)
      | ~ ssList(sK7)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f535,f298]) ).

fof(f535,plain,
    ! [X0] :
      ( memberP(sF18,X0)
      | ~ memberP(sF17,X0)
      | ~ ssList(sF17)
      | ~ ssList(sK7)
      | ~ ssItem(X0) ),
    inference(superposition,[],[f218,f246]) ).

fof(f218,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f521,plain,
    ! [X0] :
      ( ~ memberP(sF19,X0)
      | memberP(sF21,X0)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f520,f312]) ).

fof(f312,plain,
    ssList(sF19),
    inference(subsumption_resolution,[],[f311,f310]) ).

fof(f311,plain,
    ( ssList(sF19)
    | ~ ssList(sF18) ),
    inference(subsumption_resolution,[],[f304,f177]) ).

fof(f304,plain,
    ( ssList(sF19)
    | ~ ssList(sK8)
    | ~ ssList(sF18) ),
    inference(superposition,[],[f210,f247]) ).

fof(f520,plain,
    ! [X0] :
      ( memberP(sF21,X0)
      | ~ memberP(sF19,X0)
      | ~ ssList(sF19)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f508,f300]) ).

fof(f300,plain,
    ssList(sF20),
    inference(subsumption_resolution,[],[f299,f211]) ).

fof(f299,plain,
    ( ssList(sF20)
    | ~ ssList(nil) ),
    inference(subsumption_resolution,[],[f290,f175]) ).

fof(f175,plain,
    ssItem(sK6),
    inference(cnf_transformation,[],[f148]) ).

fof(f290,plain,
    ( ssList(sF20)
    | ~ ssItem(sK6)
    | ~ ssList(nil) ),
    inference(superposition,[],[f209,f248]) ).

fof(f248,plain,
    cons(sK6,nil) = sF20,
    introduced(function_definition,[new_symbols(definition,[sF20])]) ).

fof(f508,plain,
    ! [X0] :
      ( memberP(sF21,X0)
      | ~ memberP(sF19,X0)
      | ~ ssList(sF20)
      | ~ ssList(sF19)
      | ~ ssItem(X0) ),
    inference(superposition,[],[f217,f249]) ).

fof(f249,plain,
    app(sF19,sF20) = sF21,
    introduced(function_definition,[new_symbols(definition,[sF21])]) ).

fof(f525,plain,
    ! [X0] :
      ( ~ memberP(sF21,X0)
      | memberP(sK2,X0)
      | ~ ssItem(X0) ),
    inference(forward_demodulation,[],[f524,f251]) ).

fof(f251,plain,
    sK2 = sF22,
    inference(definition_folding,[],[f234,f250,f249,f248,f247,f246,f245]) ).

fof(f250,plain,
    app(sF21,sK9) = sF22,
    introduced(function_definition,[new_symbols(definition,[sF22])]) ).

fof(f234,plain,
    sK2 = app(app(app(app(sK7,cons(sK5,nil)),sK8),cons(sK6,nil)),sK9),
    inference(definition_unfolding,[],[f179,f173]) ).

fof(f173,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f148]) ).

fof(f179,plain,
    sK0 = app(app(app(app(sK7,cons(sK5,nil)),sK8),cons(sK6,nil)),sK9),
    inference(cnf_transformation,[],[f148]) ).

fof(f524,plain,
    ! [X0] :
      ( memberP(sF22,X0)
      | ~ memberP(sF21,X0)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f523,f314]) ).

fof(f314,plain,
    ssList(sF21),
    inference(subsumption_resolution,[],[f313,f312]) ).

fof(f313,plain,
    ( ssList(sF21)
    | ~ ssList(sF19) ),
    inference(subsumption_resolution,[],[f305,f300]) ).

fof(f305,plain,
    ( ssList(sF21)
    | ~ ssList(sF20)
    | ~ ssList(sF19) ),
    inference(superposition,[],[f210,f249]) ).

fof(f523,plain,
    ! [X0] :
      ( memberP(sF22,X0)
      | ~ memberP(sF21,X0)
      | ~ ssList(sF21)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f509,f178]) ).

fof(f178,plain,
    ssList(sK9),
    inference(cnf_transformation,[],[f148]) ).

fof(f509,plain,
    ! [X0] :
      ( memberP(sF22,X0)
      | ~ memberP(sF21,X0)
      | ~ ssList(sK9)
      | ~ ssList(sF21)
      | ~ ssItem(X0) ),
    inference(superposition,[],[f217,f250]) ).

fof(f895,plain,
    ( ! [X0] :
        ( ~ memberP(sK2,X0)
        | sK4 = X0
        | ~ ssItem(X0) )
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(forward_demodulation,[],[f894,f271]) ).

fof(f271,plain,
    ( sK2 = sF16
    | ~ spl23_4 ),
    inference(avatar_component_clause,[],[f269]) ).

fof(f269,plain,
    ( spl23_4
  <=> sK2 = sF16 ),
    introduced(avatar_definition,[new_symbols(naming,[spl23_4])]) ).

fof(f894,plain,
    ( ! [X0] :
        ( ~ memberP(sF16,X0)
        | sK4 = X0
        | ~ ssItem(X0) )
    | ~ spl23_5 ),
    inference(subsumption_resolution,[],[f893,f212]) ).

fof(f212,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,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.KIvKtjKhCy/Vampire---4.8_1965',ax38) ).

fof(f893,plain,
    ( ! [X0] :
        ( ~ memberP(sF16,X0)
        | sK4 = X0
        | memberP(nil,X0)
        | ~ ssItem(X0) )
    | ~ spl23_5 ),
    inference(subsumption_resolution,[],[f892,f276]) ).

fof(f276,plain,
    ( ssItem(sK4)
    | ~ spl23_5 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f274,plain,
    ( spl23_5
  <=> ssItem(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl23_5])]) ).

fof(f892,plain,
    ! [X0] :
      ( ~ memberP(sF16,X0)
      | sK4 = X0
      | memberP(nil,X0)
      | ~ ssItem(sK4)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f883,f211]) ).

fof(f883,plain,
    ! [X0] :
      ( ~ memberP(sF16,X0)
      | sK4 = X0
      | memberP(nil,X0)
      | ~ ssList(nil)
      | ~ ssItem(sK4)
      | ~ ssItem(X0) ),
    inference(superposition,[],[f213,f242]) ).

fof(f242,plain,
    cons(sK4,nil) = sF16,
    introduced(function_definition,[new_symbols(definition,[sF16])]) ).

fof(f213,plain,
    ! [X2,X0,X1] :
      ( ~ memberP(cons(X1,X2),X0)
      | X0 = X1
      | memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f158]) ).

fof(f1139,plain,
    ( lt(sK4,sK5)
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(superposition,[],[f180,f1137]) ).

fof(f1137,plain,
    ( sK4 = sK6
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(subsumption_resolution,[],[f1135,f175]) ).

fof(f1135,plain,
    ( sK4 = sK6
    | ~ ssItem(sK6)
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(resolution,[],[f895,f1132]) ).

fof(f1132,plain,
    memberP(sK2,sK6),
    inference(subsumption_resolution,[],[f1131,f175]) ).

fof(f1131,plain,
    ( memberP(sK2,sK6)
    | ~ ssItem(sK6) ),
    inference(resolution,[],[f1130,f525]) ).

fof(f1130,plain,
    memberP(sF21,sK6),
    inference(subsumption_resolution,[],[f1129,f175]) ).

fof(f1129,plain,
    ( memberP(sF21,sK6)
    | ~ ssItem(sK6) ),
    inference(resolution,[],[f550,f334]) ).

fof(f334,plain,
    memberP(sF20,sK6),
    inference(subsumption_resolution,[],[f333,f175]) ).

fof(f333,plain,
    ( memberP(sF20,sK6)
    | ~ ssItem(sK6) ),
    inference(subsumption_resolution,[],[f330,f211]) ).

fof(f330,plain,
    ( memberP(sF20,sK6)
    | ~ ssList(nil)
    | ~ ssItem(sK6) ),
    inference(superposition,[],[f253,f248]) ).

fof(f550,plain,
    ! [X0] :
      ( ~ memberP(sF20,X0)
      | memberP(sF21,X0)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f549,f312]) ).

fof(f549,plain,
    ! [X0] :
      ( memberP(sF21,X0)
      | ~ memberP(sF20,X0)
      | ~ ssList(sF19)
      | ~ ssItem(X0) ),
    inference(subsumption_resolution,[],[f537,f300]) ).

fof(f537,plain,
    ! [X0] :
      ( memberP(sF21,X0)
      | ~ memberP(sF20,X0)
      | ~ ssList(sF20)
      | ~ ssList(sF19)
      | ~ ssItem(X0) ),
    inference(superposition,[],[f218,f249]) ).

fof(f180,plain,
    lt(sK6,sK5),
    inference(cnf_transformation,[],[f148]) ).

fof(f1157,plain,
    ( ~ lt(sK4,sK4)
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(forward_demodulation,[],[f1143,f1136]) ).

fof(f1143,plain,
    ( ~ lt(sK5,sK4)
    | ~ spl23_4
    | ~ spl23_5 ),
    inference(superposition,[],[f340,f1137]) ).

fof(f340,plain,
    ~ lt(sK5,sK6),
    inference(subsumption_resolution,[],[f339,f174]) ).

fof(f339,plain,
    ( ~ lt(sK5,sK6)
    | ~ ssItem(sK5) ),
    inference(subsumption_resolution,[],[f338,f175]) ).

fof(f338,plain,
    ( ~ lt(sK5,sK6)
    | ~ ssItem(sK6)
    | ~ ssItem(sK5) ),
    inference(resolution,[],[f233,f180]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( ~ lt(X1,X0)
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f137,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ lt(X1,X0)
          | ~ lt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f136]) ).

fof(f136,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.KIvKtjKhCy/Vampire---4.8_1965',ax33) ).

fof(f397,plain,
    ~ spl23_11,
    inference(avatar_split_clause,[],[f396,f372]) ).

fof(f372,plain,
    ( spl23_11
  <=> nil = sF22 ),
    introduced(avatar_definition,[new_symbols(naming,[spl23_11])]) ).

fof(f396,plain,
    nil != sF22,
    inference(subsumption_resolution,[],[f395,f314]) ).

fof(f395,plain,
    ( nil != sF22
    | ~ ssList(sF21) ),
    inference(subsumption_resolution,[],[f394,f178]) ).

fof(f394,plain,
    ( nil != sF22
    | ~ ssList(sK9)
    | ~ ssList(sF21) ),
    inference(subsumption_resolution,[],[f381,f364]) ).

fof(f364,plain,
    nil != sF21,
    inference(subsumption_resolution,[],[f363,f312]) ).

fof(f363,plain,
    ( nil != sF21
    | ~ ssList(sF19) ),
    inference(subsumption_resolution,[],[f362,f300]) ).

fof(f362,plain,
    ( nil != sF21
    | ~ ssList(sF20)
    | ~ ssList(sF19) ),
    inference(subsumption_resolution,[],[f345,f324]) ).

fof(f324,plain,
    nil != sF20,
    inference(subsumption_resolution,[],[f323,f211]) ).

fof(f323,plain,
    ( nil != sF20
    | ~ ssList(nil) ),
    inference(subsumption_resolution,[],[f320,f175]) ).

fof(f320,plain,
    ( nil != sF20
    | ~ ssItem(sK6)
    | ~ ssList(nil) ),
    inference(superposition,[],[f199,f248]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0] :
      ( ! [X1] :
          ( nil != cons(X1,X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KIvKtjKhCy/Vampire---4.8_1965',ax21) ).

fof(f345,plain,
    ( nil != sF21
    | nil = sF20
    | ~ ssList(sF20)
    | ~ ssList(sF19) ),
    inference(superposition,[],[f190,f249]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f150]) ).

fof(f150,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,[],[f149]) ).

fof(f149,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,[],[f102]) ).

fof(f102,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.KIvKtjKhCy/Vampire---4.8_1965',ax83) ).

fof(f381,plain,
    ( nil != sF22
    | nil = sF21
    | ~ ssList(sK9)
    | ~ ssList(sF21) ),
    inference(superposition,[],[f191,f250]) ).

fof(f191,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f150]) ).

fof(f393,plain,
    ( ~ spl23_2
    | spl23_11 ),
    inference(avatar_contradiction_clause,[],[f392]) ).

fof(f392,plain,
    ( $false
    | ~ spl23_2
    | spl23_11 ),
    inference(subsumption_resolution,[],[f391,f261]) ).

fof(f261,plain,
    ( nil = sK2
    | ~ spl23_2 ),
    inference(avatar_component_clause,[],[f259]) ).

fof(f259,plain,
    ( spl23_2
  <=> nil = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl23_2])]) ).

fof(f391,plain,
    ( nil != sK2
    | spl23_11 ),
    inference(superposition,[],[f374,f251]) ).

fof(f374,plain,
    ( nil != sF22
    | spl23_11 ),
    inference(avatar_component_clause,[],[f372]) ).

fof(f277,plain,
    ( spl23_5
    | spl23_2 ),
    inference(avatar_split_clause,[],[f185,f259,f274]) ).

fof(f185,plain,
    ( nil = sK2
    | ssItem(sK4) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f272,plain,
    ( spl23_4
    | spl23_2 ),
    inference(avatar_split_clause,[],[f243,f259,f269]) ).

fof(f243,plain,
    ( nil = sK2
    | sK2 = sF16 ),
    inference(definition_folding,[],[f186,f242]) ).

fof(f186,plain,
    ( nil = sK2
    | sK2 = cons(sK4,nil) ),
    inference(cnf_transformation,[],[f148]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWC298+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 20:30:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.KIvKtjKhCy/Vampire---4.8_1965
% 0.60/0.77  % (2161)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.60/0.77  % (2159)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.60/0.77  % (2154)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.77  % (2156)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.77  % (2157)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.60/0.77  % (2155)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.60/0.77  % (2158)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.77  % (2160)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.60/0.79  % (2161)Instruction limit reached!
% 0.60/0.79  % (2161)------------------------------
% 0.60/0.79  % (2161)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79  % (2161)Termination reason: Unknown
% 0.60/0.79  % (2161)Termination phase: Saturation
% 0.60/0.79  
% 0.60/0.79  % (2161)Memory used [KB]: 1553
% 0.60/0.79  % (2161)Time elapsed: 0.016 s
% 0.60/0.79  % (2161)Instructions burned: 56 (million)
% 0.60/0.79  % (2161)------------------------------
% 0.60/0.79  % (2161)------------------------------
% 0.60/0.79  % (2159)Instruction limit reached!
% 0.60/0.79  % (2159)------------------------------
% 0.60/0.79  % (2159)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79  % (2159)Termination reason: Unknown
% 0.60/0.79  % (2159)Termination phase: Saturation
% 0.60/0.79  
% 0.60/0.79  % (2159)Memory used [KB]: 1647
% 0.60/0.79  % (2159)Time elapsed: 0.017 s
% 0.60/0.79  % (2159)Instructions burned: 48 (million)
% 0.60/0.79  % (2159)------------------------------
% 0.60/0.79  % (2159)------------------------------
% 0.60/0.79  % (2170)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.60/0.79  % (2171)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.60/0.79  % (2158)Instruction limit reached!
% 0.60/0.79  % (2158)------------------------------
% 0.60/0.79  % (2158)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79  % (2158)Termination reason: Unknown
% 0.60/0.79  % (2158)Termination phase: Saturation
% 0.60/0.79  
% 0.60/0.79  % (2158)Memory used [KB]: 1785
% 0.60/0.79  % (2158)Time elapsed: 0.019 s
% 0.60/0.79  % (2158)Instructions burned: 34 (million)
% 0.60/0.79  % (2158)------------------------------
% 0.60/0.79  % (2158)------------------------------
% 0.60/0.79  % (2157)Instruction limit reached!
% 0.60/0.79  % (2157)------------------------------
% 0.60/0.79  % (2157)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79  % (2157)Termination reason: Unknown
% 0.60/0.79  % (2157)Termination phase: Saturation
% 0.60/0.79  
% 0.60/0.79  % (2157)Memory used [KB]: 1717
% 0.60/0.79  % (2157)Time elapsed: 0.020 s
% 0.60/0.79  % (2157)Instructions burned: 34 (million)
% 0.60/0.79  % (2157)------------------------------
% 0.60/0.79  % (2157)------------------------------
% 0.60/0.79  % (2154)Instruction limit reached!
% 0.60/0.79  % (2154)------------------------------
% 0.60/0.79  % (2154)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79  % (2154)Termination reason: Unknown
% 0.60/0.79  % (2154)Termination phase: Saturation
% 0.60/0.79  
% 0.60/0.79  % (2154)Memory used [KB]: 1538
% 0.60/0.79  % (2154)Time elapsed: 0.022 s
% 0.60/0.79  % (2154)Instructions burned: 34 (million)
% 0.60/0.79  % (2154)------------------------------
% 0.60/0.79  % (2154)------------------------------
% 0.60/0.79  % (2174)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.60/0.80  % (2175)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.60/0.80  % (2178)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.60/0.80  % (2171)Instruction limit reached!
% 0.60/0.80  % (2171)------------------------------
% 0.60/0.80  % (2171)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.80  % (2171)Termination reason: Unknown
% 0.60/0.80  % (2171)Termination phase: Saturation
% 0.60/0.80  
% 0.60/0.80  % (2171)Memory used [KB]: 1924
% 0.60/0.80  % (2171)Time elapsed: 0.038 s
% 0.60/0.80  % (2171)Instructions burned: 53 (million)
% 0.60/0.80  % (2171)------------------------------
% 0.60/0.80  % (2171)------------------------------
% 0.60/0.81  % (2155)Instruction limit reached!
% 0.60/0.81  % (2155)------------------------------
% 0.60/0.81  % (2155)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.81  % (2155)Termination reason: Unknown
% 0.60/0.81  % (2155)Termination phase: Saturation
% 0.60/0.81  
% 0.60/0.81  % (2155)Memory used [KB]: 1996
% 0.60/0.81  % (2155)Time elapsed: 0.034 s
% 0.60/0.81  % (2155)Instructions burned: 52 (million)
% 0.60/0.81  % (2155)------------------------------
% 0.60/0.81  % (2155)------------------------------
% 0.60/0.81  % (2170)Instruction limit reached!
% 0.60/0.81  % (2170)------------------------------
% 0.60/0.81  % (2170)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.81  % (2170)Termination reason: Unknown
% 0.60/0.81  % (2170)Termination phase: Saturation
% 0.60/0.81  
% 0.60/0.81  % (2170)Memory used [KB]: 2172
% 0.60/0.81  % (2170)Time elapsed: 0.040 s
% 0.60/0.81  % (2170)Instructions burned: 55 (million)
% 0.60/0.81  % (2170)------------------------------
% 0.60/0.81  % (2170)------------------------------
% 0.60/0.81  % (2186)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.60/0.81  % (2188)lrs+1011_2:9_sil=2000:lsd=10:newcnf=on:i=117:sd=2:awrs=decay:ss=included:amm=off:ep=R_0 on Vampire---4 for (2995ds/117Mi)
% 0.60/0.81  % (2187)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on Vampire---4 for (2995ds/243Mi)
% 0.60/0.81  % (2160)Instruction limit reached!
% 0.60/0.81  % (2160)------------------------------
% 0.60/0.81  % (2160)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.81  % (2160)Termination reason: Unknown
% 0.60/0.81  % (2160)Termination phase: Saturation
% 0.60/0.81  
% 0.60/0.81  % (2160)Memory used [KB]: 2129
% 0.60/0.81  % (2160)Time elapsed: 0.040 s
% 0.60/0.81  % (2160)Instructions burned: 83 (million)
% 0.60/0.81  % (2160)------------------------------
% 0.60/0.81  % (2160)------------------------------
% 0.60/0.82  % (2174)First to succeed.
% 0.60/0.82  % (2192)dis+1011_11:1_sil=2000:avsq=on:i=143:avsqr=1,16:ep=RS:rawr=on:aac=none:lsd=100:mep=off:fde=none:newcnf=on:bsr=unit_only_0 on Vampire---4 for (2995ds/143Mi)
% 0.60/0.82  % (2174)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2136"
% 0.60/0.82  % (2174)Refutation found. Thanks to Tanya!
% 0.60/0.82  % SZS status Theorem for Vampire---4
% 0.60/0.82  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.82  % (2174)------------------------------
% 0.60/0.82  % (2174)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.82  % (2174)Termination reason: Refutation
% 0.60/0.82  
% 0.60/0.82  % (2174)Memory used [KB]: 1467
% 0.60/0.82  % (2174)Time elapsed: 0.049 s
% 0.60/0.82  % (2174)Instructions burned: 44 (million)
% 0.60/0.82  % (2136)Success in time 0.463 s
% 0.60/0.82  % Vampire---4.8 exiting
%------------------------------------------------------------------------------