TSTP Solution File: SWC230+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC230+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:39:45 EDT 2022

% Result   : Theorem 0.19s 0.54s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   82 (   8 unt;   0 def)
%            Number of atoms       :  571 ( 139 equ)
%            Maximal formula atoms :   44 (   6 avg)
%            Number of connectives :  787 ( 298   ~; 288   |; 169   &)
%                                         (   3 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   8 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   4 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :  222 ( 156   !;  66   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f412,plain,
    $false,
    inference(avatar_sat_refutation,[],[f246,f398,f404,f411]) ).

fof(f411,plain,
    ( ~ spl11_2
    | ~ spl11_3
    | ~ spl11_4 ),
    inference(avatar_contradiction_clause,[],[f410]) ).

fof(f410,plain,
    ( $false
    | ~ spl11_2
    | ~ spl11_3
    | ~ spl11_4 ),
    inference(subsumption_resolution,[],[f409,f397]) ).

fof(f397,plain,
    ( ssItem(sK10(sK5(sK8),nil,sK4(sK8)))
    | ~ spl11_4 ),
    inference(avatar_component_clause,[],[f395]) ).

fof(f395,plain,
    ( spl11_4
  <=> ssItem(sK10(sK5(sK8),nil,sK4(sK8))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).

fof(f409,plain,
    ( ~ ssItem(sK10(sK5(sK8),nil,sK4(sK8)))
    | ~ spl11_2
    | ~ spl11_3 ),
    inference(resolution,[],[f408,f193]) ).

fof(f193,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f408,plain,
    ( memberP(nil,sK10(sK5(sK8),nil,sK4(sK8)))
    | ~ spl11_2
    | ~ spl11_3 ),
    inference(subsumption_resolution,[],[f407,f206]) ).

fof(f206,plain,
    ssList(sK8),
    inference(cnf_transformation,[],[f162]) ).

fof(f162,plain,
    ( ssList(sK6)
    & sK6 = sK8
    & ssList(sK9)
    & nil != sK6
    & sK9 = sK7
    & ! [X4] :
        ( ~ ssItem(X4)
        | ! [X5] :
            ( ! [X6] :
                ( ~ ssList(X6)
                | ! [X7] :
                    ( ~ ssList(X7)
                    | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != sK8
                    | X4 = X5 ) )
            | ~ ssItem(X5) ) )
    & ! [X8] :
        ( ~ ssItem(X8)
        | ! [X9] :
            ( ~ ssList(X9)
            | ! [X10] :
                ( ~ ssList(X10)
                | ( memberP(X10,sK10(X8,X9,X10))
                  & leq(X8,sK10(X8,X9,X10))
                  & ssItem(sK10(X8,X9,X10))
                  & memberP(X9,sK10(X8,X9,X10))
                  & ~ lt(X8,sK10(X8,X9,X10)) )
                | sK6 != app(app(X9,cons(X8,nil)),X10) ) ) )
    & ssList(sK8)
    & ssList(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f133,f161,f160,f159,f158,f157]) ).

fof(f157,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( X0 = X2
                    & ssList(X3)
                    & nil != X0
                    & X1 = X3
                    & ! [X4] :
                        ( ~ ssItem(X4)
                        | ! [X5] :
                            ( ! [X6] :
                                ( ~ ssList(X6)
                                | ! [X7] :
                                    ( ~ ssList(X7)
                                    | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X2
                                    | X4 = X5 ) )
                            | ~ ssItem(X5) ) )
                    & ! [X8] :
                        ( ~ ssItem(X8)
                        | ! [X9] :
                            ( ~ ssList(X9)
                            | ! [X10] :
                                ( ~ ssList(X10)
                                | ? [X11] :
                                    ( memberP(X10,X11)
                                    & leq(X8,X11)
                                    & ssItem(X11)
                                    & memberP(X9,X11)
                                    & ~ lt(X8,X11) )
                                | app(app(X9,cons(X8,nil)),X10) != X0 ) ) ) )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK6)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( sK6 = X2
                  & ssList(X3)
                  & nil != sK6
                  & X1 = X3
                  & ! [X4] :
                      ( ~ ssItem(X4)
                      | ! [X5] :
                          ( ! [X6] :
                              ( ~ ssList(X6)
                              | ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X2
                                  | X4 = X5 ) )
                          | ~ ssItem(X5) ) )
                  & ! [X8] :
                      ( ~ ssItem(X8)
                      | ! [X9] :
                          ( ~ ssList(X9)
                          | ! [X10] :
                              ( ~ ssList(X10)
                              | ? [X11] :
                                  ( memberP(X10,X11)
                                  & leq(X8,X11)
                                  & ssItem(X11)
                                  & memberP(X9,X11)
                                  & ~ lt(X8,X11) )
                              | sK6 != app(app(X9,cons(X8,nil)),X10) ) ) ) )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f158,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( sK6 = X2
                & ssList(X3)
                & nil != sK6
                & X1 = X3
                & ! [X4] :
                    ( ~ ssItem(X4)
                    | ! [X5] :
                        ( ! [X6] :
                            ( ~ ssList(X6)
                            | ! [X7] :
                                ( ~ ssList(X7)
                                | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X2
                                | X4 = X5 ) )
                        | ~ ssItem(X5) ) )
                & ! [X8] :
                    ( ~ ssItem(X8)
                    | ! [X9] :
                        ( ~ ssList(X9)
                        | ! [X10] :
                            ( ~ ssList(X10)
                            | ? [X11] :
                                ( memberP(X10,X11)
                                & leq(X8,X11)
                                & ssItem(X11)
                                & memberP(X9,X11)
                                & ~ lt(X8,X11) )
                            | sK6 != app(app(X9,cons(X8,nil)),X10) ) ) ) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( sK6 = X2
              & ssList(X3)
              & nil != sK6
              & sK7 = X3
              & ! [X4] :
                  ( ~ ssItem(X4)
                  | ! [X5] :
                      ( ! [X6] :
                          ( ~ ssList(X6)
                          | ! [X7] :
                              ( ~ ssList(X7)
                              | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X2
                              | X4 = X5 ) )
                      | ~ ssItem(X5) ) )
              & ! [X8] :
                  ( ~ ssItem(X8)
                  | ! [X9] :
                      ( ~ ssList(X9)
                      | ! [X10] :
                          ( ~ ssList(X10)
                          | ? [X11] :
                              ( memberP(X10,X11)
                              & leq(X8,X11)
                              & ssItem(X11)
                              & memberP(X9,X11)
                              & ~ lt(X8,X11) )
                          | sK6 != app(app(X9,cons(X8,nil)),X10) ) ) ) )
          & ssList(X2) )
      & ssList(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( sK6 = X2
            & ssList(X3)
            & nil != sK6
            & sK7 = X3
            & ! [X4] :
                ( ~ ssItem(X4)
                | ! [X5] :
                    ( ! [X6] :
                        ( ~ ssList(X6)
                        | ! [X7] :
                            ( ~ ssList(X7)
                            | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X2
                            | X4 = X5 ) )
                    | ~ ssItem(X5) ) )
            & ! [X8] :
                ( ~ ssItem(X8)
                | ! [X9] :
                    ( ~ ssList(X9)
                    | ! [X10] :
                        ( ~ ssList(X10)
                        | ? [X11] :
                            ( memberP(X10,X11)
                            & leq(X8,X11)
                            & ssItem(X11)
                            & memberP(X9,X11)
                            & ~ lt(X8,X11) )
                        | sK6 != app(app(X9,cons(X8,nil)),X10) ) ) ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( sK6 = sK8
          & ssList(X3)
          & nil != sK6
          & sK7 = X3
          & ! [X4] :
              ( ~ ssItem(X4)
              | ! [X5] :
                  ( ! [X6] :
                      ( ~ ssList(X6)
                      | ! [X7] :
                          ( ~ ssList(X7)
                          | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != sK8
                          | X4 = X5 ) )
                  | ~ ssItem(X5) ) )
          & ! [X8] :
              ( ~ ssItem(X8)
              | ! [X9] :
                  ( ~ ssList(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | ? [X11] :
                          ( memberP(X10,X11)
                          & leq(X8,X11)
                          & ssItem(X11)
                          & memberP(X9,X11)
                          & ~ lt(X8,X11) )
                      | sK6 != app(app(X9,cons(X8,nil)),X10) ) ) ) )
      & ssList(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f160,plain,
    ( ? [X3] :
        ( sK6 = sK8
        & ssList(X3)
        & nil != sK6
        & sK7 = X3
        & ! [X4] :
            ( ~ ssItem(X4)
            | ! [X5] :
                ( ! [X6] :
                    ( ~ ssList(X6)
                    | ! [X7] :
                        ( ~ ssList(X7)
                        | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != sK8
                        | X4 = X5 ) )
                | ~ ssItem(X5) ) )
        & ! [X8] :
            ( ~ ssItem(X8)
            | ! [X9] :
                ( ~ ssList(X9)
                | ! [X10] :
                    ( ~ ssList(X10)
                    | ? [X11] :
                        ( memberP(X10,X11)
                        & leq(X8,X11)
                        & ssItem(X11)
                        & memberP(X9,X11)
                        & ~ lt(X8,X11) )
                    | sK6 != app(app(X9,cons(X8,nil)),X10) ) ) ) )
   => ( sK6 = sK8
      & ssList(sK9)
      & nil != sK6
      & sK9 = sK7
      & ! [X4] :
          ( ~ ssItem(X4)
          | ! [X5] :
              ( ! [X6] :
                  ( ~ ssList(X6)
                  | ! [X7] :
                      ( ~ ssList(X7)
                      | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != sK8
                      | X4 = X5 ) )
              | ~ ssItem(X5) ) )
      & ! [X8] :
          ( ~ ssItem(X8)
          | ! [X9] :
              ( ~ ssList(X9)
              | ! [X10] :
                  ( ~ ssList(X10)
                  | ? [X11] :
                      ( memberP(X10,X11)
                      & leq(X8,X11)
                      & ssItem(X11)
                      & memberP(X9,X11)
                      & ~ lt(X8,X11) )
                  | sK6 != app(app(X9,cons(X8,nil)),X10) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f161,plain,
    ! [X8,X9,X10] :
      ( ? [X11] :
          ( memberP(X10,X11)
          & leq(X8,X11)
          & ssItem(X11)
          & memberP(X9,X11)
          & ~ lt(X8,X11) )
     => ( memberP(X10,sK10(X8,X9,X10))
        & leq(X8,sK10(X8,X9,X10))
        & ssItem(sK10(X8,X9,X10))
        & memberP(X9,sK10(X8,X9,X10))
        & ~ lt(X8,sK10(X8,X9,X10)) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & ssList(X3)
                  & nil != X0
                  & X1 = X3
                  & ! [X4] :
                      ( ~ ssItem(X4)
                      | ! [X5] :
                          ( ! [X6] :
                              ( ~ ssList(X6)
                              | ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X2
                                  | X4 = X5 ) )
                          | ~ ssItem(X5) ) )
                  & ! [X8] :
                      ( ~ ssItem(X8)
                      | ! [X9] :
                          ( ~ ssList(X9)
                          | ! [X10] :
                              ( ~ ssList(X10)
                              | ? [X11] :
                                  ( memberP(X10,X11)
                                  & leq(X8,X11)
                                  & ssItem(X11)
                                  & memberP(X9,X11)
                                  & ~ lt(X8,X11) )
                              | app(app(X9,cons(X8,nil)),X10) != X0 ) ) ) )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(flattening,[],[f132]) ).

fof(f132,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ! [X8] :
                      ( ~ ssItem(X8)
                      | ! [X9] :
                          ( ! [X10] :
                              ( ? [X11] :
                                  ( leq(X8,X11)
                                  & memberP(X10,X11)
                                  & ~ lt(X8,X11)
                                  & memberP(X9,X11)
                                  & ssItem(X11) )
                              | app(app(X9,cons(X8,nil)),X10) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) ) )
                  & X1 = X3
                  & X0 = X2
                  & nil != X0
                  & ! [X4] :
                      ( ~ ssItem(X4)
                      | ! [X5] :
                          ( ! [X6] :
                              ( ~ ssList(X6)
                              | ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X2
                                  | X4 = X5 ) )
                          | ~ ssItem(X5) ) )
                  & 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)
                   => ( ? [X8] :
                          ( ssItem(X8)
                          & ? [X9] :
                              ( ? [X10] :
                                  ( ! [X11] :
                                      ( ssItem(X11)
                                     => ( ~ leq(X8,X11)
                                        | ~ memberP(X10,X11)
                                        | lt(X8,X11)
                                        | ~ memberP(X9,X11) ) )
                                  & app(app(X9,cons(X8,nil)),X10) = X0
                                  & ssList(X10) )
                              & ssList(X9) ) )
                      | X1 != X3
                      | X0 != X2
                      | nil = X0
                      | ? [X4] :
                          ( ? [X5] :
                              ( ? [X6] :
                                  ( ? [X7] :
                                      ( X4 != X5
                                      & app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X2
                                      & ssList(X7) )
                                  & ssList(X6) )
                              & ssItem(X5) )
                          & ssItem(X4) ) ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ? [X8] :
                          ( ssItem(X8)
                          & ? [X9] :
                              ( ? [X10] :
                                  ( ? [X11] :
                                      ( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) = X2
                                      & X8 != X9
                                      & ssList(X11) )
                                  & ssList(X10) )
                              & ssItem(X9) ) )
                      | X0 != X2
                      | nil = X0
                      | ? [X4] :
                          ( ssItem(X4)
                          & ? [X5] :
                              ( ssList(X5)
                              & ? [X6] :
                                  ( app(app(X5,cons(X4,nil)),X6) = X0
                                  & ! [X7] :
                                      ( ssItem(X7)
                                     => ( ~ memberP(X6,X7)
                                        | ~ memberP(X5,X7)
                                        | lt(X4,X7)
                                        | ~ leq(X4,X7) ) )
                                  & ssList(X6) ) ) )
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ? [X8] :
                        ( ssItem(X8)
                        & ? [X9] :
                            ( ? [X10] :
                                ( ? [X11] :
                                    ( app(app(app(X10,cons(X8,nil)),cons(X9,nil)),X11) = X2
                                    & X8 != X9
                                    & ssList(X11) )
                                & ssList(X10) )
                            & ssItem(X9) ) )
                    | X0 != X2
                    | nil = X0
                    | ? [X4] :
                        ( ssItem(X4)
                        & ? [X5] :
                            ( ssList(X5)
                            & ? [X6] :
                                ( app(app(X5,cons(X4,nil)),X6) = X0
                                & ! [X7] :
                                    ( ssItem(X7)
                                   => ( ~ memberP(X6,X7)
                                      | ~ memberP(X5,X7)
                                      | lt(X4,X7)
                                      | ~ leq(X4,X7) ) )
                                & ssList(X6) ) ) )
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f407,plain,
    ( ~ ssList(sK8)
    | memberP(nil,sK10(sK5(sK8),nil,sK4(sK8)))
    | ~ spl11_2
    | ~ spl11_3 ),
    inference(subsumption_resolution,[],[f406,f223]) ).

fof(f223,plain,
    nil != sK8,
    inference(definition_unfolding,[],[f214,f216]) ).

fof(f216,plain,
    sK6 = sK8,
    inference(cnf_transformation,[],[f162]) ).

fof(f214,plain,
    nil != sK6,
    inference(cnf_transformation,[],[f162]) ).

fof(f406,plain,
    ( nil = sK8
    | ~ ssList(sK8)
    | memberP(nil,sK10(sK5(sK8),nil,sK4(sK8)))
    | ~ spl11_2
    | ~ spl11_3 ),
    inference(subsumption_resolution,[],[f405,f392]) ).

fof(f392,plain,
    ( ssList(cons(sK5(sK8),nil))
    | ~ spl11_3 ),
    inference(avatar_component_clause,[],[f391]) ).

fof(f391,plain,
    ( spl11_3
  <=> ssList(cons(sK5(sK8),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).

fof(f405,plain,
    ( ~ ssList(cons(sK5(sK8),nil))
    | memberP(nil,sK10(sK5(sK8),nil,sK4(sK8)))
    | nil = sK8
    | ~ ssList(sK8)
    | ~ spl11_2 ),
    inference(equality_resolution,[],[f375]) ).

fof(f375,plain,
    ( ! [X0] :
        ( sK8 != X0
        | ~ ssList(X0)
        | ~ ssList(cons(sK5(X0),nil))
        | nil = X0
        | memberP(nil,sK10(sK5(X0),nil,sK4(X0))) )
    | ~ spl11_2 ),
    inference(subsumption_resolution,[],[f374,f188]) ).

fof(f188,plain,
    ! [X0] :
      ( ssItem(sK5(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ssList(sK4(X0))
        & cons(sK5(X0),sK4(X0)) = X0
        & ssItem(sK5(X0)) )
      | nil = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f135,f151,f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) ) )
     => ( ssList(sK4(X0))
        & ? [X2] :
            ( cons(X2,sK4(X0)) = X0
            & ssItem(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f151,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,sK4(X0)) = X0
          & ssItem(X2) )
     => ( cons(sK5(X0),sK4(X0)) = X0
        & ssItem(sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) ) )
      | nil = X0 ),
    inference(flattening,[],[f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) ) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( cons(X2,X1) = X0
                & ssItem(X2) ) )
        | nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).

fof(f374,plain,
    ( ! [X0] :
        ( sK8 != X0
        | ~ ssList(cons(sK5(X0),nil))
        | nil = X0
        | ~ ssList(X0)
        | memberP(nil,sK10(sK5(X0),nil,sK4(X0)))
        | ~ ssItem(sK5(X0)) )
    | ~ spl11_2 ),
    inference(subsumption_resolution,[],[f373,f190]) ).

fof(f190,plain,
    ! [X0] :
      ( ssList(sK4(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f373,plain,
    ( ! [X0] :
        ( sK8 != X0
        | ~ ssList(sK4(X0))
        | ~ ssItem(sK5(X0))
        | ~ ssList(cons(sK5(X0),nil))
        | memberP(nil,sK10(sK5(X0),nil,sK4(X0)))
        | nil = X0
        | ~ ssList(X0) )
    | ~ spl11_2 ),
    inference(superposition,[],[f356,f189]) ).

fof(f189,plain,
    ! [X0] :
      ( cons(sK5(X0),sK4(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f356,plain,
    ( ! [X4,X5] :
        ( cons(X4,X5) != sK8
        | memberP(nil,sK10(X4,nil,X5))
        | ~ ssList(cons(X4,nil))
        | ~ ssItem(X4)
        | ~ ssList(X5) )
    | ~ spl11_2 ),
    inference(duplicate_literal_removal,[],[f328]) ).

fof(f328,plain,
    ( ! [X4,X5] :
        ( ~ ssList(X5)
        | memberP(nil,sK10(X4,nil,X5))
        | ~ ssItem(X4)
        | ~ ssItem(X4)
        | ~ ssList(cons(X4,nil))
        | cons(X4,X5) != sK8
        | ~ ssList(X5) )
    | ~ spl11_2 ),
    inference(superposition,[],[f255,f191]) ).

fof(f191,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) ) ),
    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/benchmark/theBenchmark.p',ax81) ).

fof(f255,plain,
    ( ! [X6,X5] :
        ( sK8 != app(cons(X5,nil),X6)
        | ~ ssList(X6)
        | ~ ssList(cons(X5,nil))
        | ~ ssItem(X5)
        | memberP(nil,sK10(X5,nil,X6)) )
    | ~ spl11_2 ),
    inference(subsumption_resolution,[],[f249,f243]) ).

fof(f243,plain,
    ( ssList(nil)
    | ~ spl11_2 ),
    inference(avatar_component_clause,[],[f242]) ).

fof(f242,plain,
    ( spl11_2
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).

fof(f249,plain,
    ! [X6,X5] :
      ( ~ ssList(cons(X5,nil))
      | ~ ssList(nil)
      | sK8 != app(cons(X5,nil),X6)
      | memberP(nil,sK10(X5,nil,X6))
      | ~ ssList(X6)
      | ~ ssItem(X5) ),
    inference(superposition,[],[f227,f170]) ).

fof(f170,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f227,plain,
    ! [X10,X8,X9] :
      ( sK8 != app(app(X9,cons(X8,nil)),X10)
      | ~ ssList(X9)
      | ~ ssList(X10)
      | ~ ssItem(X8)
      | memberP(X9,sK10(X8,X9,X10)) ),
    inference(definition_unfolding,[],[f208,f216]) ).

fof(f208,plain,
    ! [X10,X8,X9] :
      ( ~ ssItem(X8)
      | ~ ssList(X9)
      | ~ ssList(X10)
      | memberP(X9,sK10(X8,X9,X10))
      | sK6 != app(app(X9,cons(X8,nil)),X10) ),
    inference(cnf_transformation,[],[f162]) ).

fof(f404,plain,
    ( ~ spl11_2
    | spl11_3 ),
    inference(avatar_contradiction_clause,[],[f403]) ).

fof(f403,plain,
    ( $false
    | ~ spl11_2
    | spl11_3 ),
    inference(subsumption_resolution,[],[f402,f223]) ).

fof(f402,plain,
    ( nil = sK8
    | ~ spl11_2
    | spl11_3 ),
    inference(subsumption_resolution,[],[f401,f206]) ).

fof(f401,plain,
    ( ~ ssList(sK8)
    | nil = sK8
    | ~ spl11_2
    | spl11_3 ),
    inference(resolution,[],[f400,f188]) ).

fof(f400,plain,
    ( ~ ssItem(sK5(sK8))
    | ~ spl11_2
    | spl11_3 ),
    inference(subsumption_resolution,[],[f399,f243]) ).

fof(f399,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sK5(sK8))
    | spl11_3 ),
    inference(resolution,[],[f393,f165]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) ) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

fof(f393,plain,
    ( ~ ssList(cons(sK5(sK8),nil))
    | spl11_3 ),
    inference(avatar_component_clause,[],[f391]) ).

fof(f398,plain,
    ( ~ spl11_3
    | spl11_4
    | ~ spl11_2 ),
    inference(avatar_split_clause,[],[f389,f242,f395,f391]) ).

fof(f389,plain,
    ( ssItem(sK10(sK5(sK8),nil,sK4(sK8)))
    | ~ ssList(cons(sK5(sK8),nil))
    | ~ spl11_2 ),
    inference(subsumption_resolution,[],[f388,f223]) ).

fof(f388,plain,
    ( ssItem(sK10(sK5(sK8),nil,sK4(sK8)))
    | nil = sK8
    | ~ ssList(cons(sK5(sK8),nil))
    | ~ spl11_2 ),
    inference(subsumption_resolution,[],[f387,f206]) ).

fof(f387,plain,
    ( ssItem(sK10(sK5(sK8),nil,sK4(sK8)))
    | ~ ssList(cons(sK5(sK8),nil))
    | ~ ssList(sK8)
    | nil = sK8
    | ~ spl11_2 ),
    inference(equality_resolution,[],[f366]) ).

fof(f366,plain,
    ( ! [X0] :
        ( sK8 != X0
        | ~ ssList(cons(sK5(X0),nil))
        | ~ ssList(X0)
        | nil = X0
        | ssItem(sK10(sK5(X0),nil,sK4(X0))) )
    | ~ spl11_2 ),
    inference(subsumption_resolution,[],[f365,f188]) ).

fof(f365,plain,
    ( ! [X0] :
        ( ~ ssItem(sK5(X0))
        | ~ ssList(X0)
        | ssItem(sK10(sK5(X0),nil,sK4(X0)))
        | nil = X0
        | ~ ssList(cons(sK5(X0),nil))
        | sK8 != X0 )
    | ~ spl11_2 ),
    inference(subsumption_resolution,[],[f364,f190]) ).

fof(f364,plain,
    ( ! [X0] :
        ( nil = X0
        | ~ ssList(sK4(X0))
        | ~ ssList(X0)
        | sK8 != X0
        | ~ ssList(cons(sK5(X0),nil))
        | ssItem(sK10(sK5(X0),nil,sK4(X0)))
        | ~ ssItem(sK5(X0)) )
    | ~ spl11_2 ),
    inference(superposition,[],[f350,f189]) ).

fof(f350,plain,
    ( ! [X8,X9] :
        ( sK8 != cons(X8,X9)
        | ssItem(sK10(X8,nil,X9))
        | ~ ssItem(X8)
        | ~ ssList(X9)
        | ~ ssList(cons(X8,nil)) )
    | ~ spl11_2 ),
    inference(duplicate_literal_removal,[],[f330]) ).

fof(f330,plain,
    ( ! [X8,X9] :
        ( ~ ssList(cons(X8,nil))
        | ~ ssList(X9)
        | ~ ssList(X9)
        | sK8 != cons(X8,X9)
        | ~ ssItem(X8)
        | ssItem(sK10(X8,nil,X9))
        | ~ ssItem(X8) )
    | ~ spl11_2 ),
    inference(superposition,[],[f257,f191]) ).

fof(f257,plain,
    ( ! [X11,X12] :
        ( app(cons(X11,nil),X12) != sK8
        | ssItem(sK10(X11,nil,X12))
        | ~ ssList(X12)
        | ~ ssList(cons(X11,nil))
        | ~ ssItem(X11) )
    | ~ spl11_2 ),
    inference(subsumption_resolution,[],[f252,f243]) ).

fof(f252,plain,
    ! [X11,X12] :
      ( ~ ssList(nil)
      | ~ ssList(X12)
      | ~ ssItem(X11)
      | ssItem(sK10(X11,nil,X12))
      | ~ ssList(cons(X11,nil))
      | app(cons(X11,nil),X12) != sK8 ),
    inference(superposition,[],[f226,f170]) ).

fof(f226,plain,
    ! [X10,X8,X9] :
      ( sK8 != app(app(X9,cons(X8,nil)),X10)
      | ~ ssList(X9)
      | ssItem(sK10(X8,X9,X10))
      | ~ ssList(X10)
      | ~ ssItem(X8) ),
    inference(definition_unfolding,[],[f209,f216]) ).

fof(f209,plain,
    ! [X10,X8,X9] :
      ( ~ ssItem(X8)
      | ~ ssList(X9)
      | ~ ssList(X10)
      | ssItem(sK10(X8,X9,X10))
      | sK6 != app(app(X9,cons(X8,nil)),X10) ),
    inference(cnf_transformation,[],[f162]) ).

fof(f246,plain,
    spl11_2,
    inference(avatar_split_clause,[],[f197,f242]) ).

fof(f197,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWC230+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 18:40:55 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.50  % (23079)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (23087)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51  % (23088)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.51  % (23080)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51  % (23080)Instruction limit reached!
% 0.19/0.51  % (23080)------------------------------
% 0.19/0.51  % (23080)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (23080)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (23080)Termination reason: Unknown
% 0.19/0.51  % (23080)Termination phase: Preprocessing 3
% 0.19/0.51  
% 0.19/0.51  % (23080)Memory used [KB]: 1535
% 0.19/0.51  % (23080)Time elapsed: 0.004 s
% 0.19/0.51  % (23080)Instructions burned: 3 (million)
% 0.19/0.51  % (23080)------------------------------
% 0.19/0.51  % (23080)------------------------------
% 0.19/0.52  % (23072)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.53  % (23070)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.53  % (23068)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.53  % (23095)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.53  % (23082)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53  % (23072)First to succeed.
% 0.19/0.53  % (23073)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.53  % (23085)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.53  % (23075)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.54  % (23090)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.54  % (23071)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.54  % (23067)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.54  % (23074)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.54  % (23072)Refutation found. Thanks to Tanya!
% 0.19/0.54  % SZS status Theorem for theBenchmark
% 0.19/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.54  % (23072)------------------------------
% 0.19/0.54  % (23072)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54  % (23072)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54  % (23072)Termination reason: Refutation
% 0.19/0.54  
% 0.19/0.54  % (23072)Memory used [KB]: 6268
% 0.19/0.54  % (23072)Time elapsed: 0.088 s
% 0.19/0.54  % (23072)Instructions burned: 14 (million)
% 0.19/0.54  % (23072)------------------------------
% 0.19/0.54  % (23072)------------------------------
% 0.19/0.54  % (23065)Success in time 0.193 s
%------------------------------------------------------------------------------