TSTP Solution File: SWC224+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC224+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 : n028.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 18:39:43 EDT 2022

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   83 (   7 unt;   0 def)
%            Number of atoms       :  672 ( 193 equ)
%            Maximal formula atoms :   52 (   8 avg)
%            Number of connectives :  920 ( 331   ~; 317   |; 235   &)
%                                         (   4 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   8 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   5 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :  234 ( 154   !;  80   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f449,plain,
    $false,
    inference(avatar_sat_refutation,[],[f257,f258,f408,f414,f448]) ).

fof(f448,plain,
    ( spl16_2
    | ~ spl16_4
    | ~ spl16_5
    | ~ spl16_6 ),
    inference(avatar_contradiction_clause,[],[f447]) ).

fof(f447,plain,
    ( $false
    | spl16_2
    | ~ spl16_4
    | ~ spl16_5
    | ~ spl16_6 ),
    inference(subsumption_resolution,[],[f446,f403]) ).

fof(f403,plain,
    ( ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
    | ~ spl16_5 ),
    inference(avatar_component_clause,[],[f401]) ).

fof(f401,plain,
    ( spl16_5
  <=> ssItem(sK14(sK3(sK10),nil,sK2(sK10))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).

fof(f446,plain,
    ( ~ ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
    | spl16_2
    | ~ spl16_4
    | ~ spl16_6 ),
    inference(resolution,[],[f445,f197]) ).

fof(f197,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(nil,X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

fof(f445,plain,
    ( memberP(nil,sK14(sK3(sK10),nil,sK2(sK10)))
    | spl16_2
    | ~ spl16_4
    | ~ spl16_6 ),
    inference(subsumption_resolution,[],[f444,f246]) ).

fof(f246,plain,
    ( nil != sK10
    | spl16_2 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f244,plain,
    ( spl16_2
  <=> nil = sK10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).

fof(f444,plain,
    ( memberP(nil,sK14(sK3(sK10),nil,sK2(sK10)))
    | nil = sK10
    | ~ spl16_4
    | ~ spl16_6 ),
    inference(subsumption_resolution,[],[f443,f203]) ).

fof(f203,plain,
    ssList(sK10),
    inference(cnf_transformation,[],[f160]) ).

fof(f160,plain,
    ( ssList(sK11)
    & ssList(sK12)
    & ( nil = sK13
      | nil != sK12 )
    & ! [X4] :
        ( ! [X5] :
            ( ~ ssList(X5)
            | ! [X6] :
                ( app(app(X5,cons(X4,nil)),X6) != sK10
                | ~ ssList(X6)
                | ( memberP(X5,sK14(X4,X5,X6))
                  & ssItem(sK14(X4,X5,X6))
                  & memberP(X6,sK14(X4,X5,X6))
                  & ~ leq(sK14(X4,X5,X6),X4)
                  & leq(X4,sK14(X4,X5,X6)) ) ) )
        | ~ ssItem(X4) )
    & sK11 = sK13
    & sK12 = sK10
    & ssList(sK15)
    & ! [X9] :
        ( ~ ssItem(X9)
        | ! [X10] :
            ( ~ ssList(X10)
            | ! [X11] :
                ( ~ ssList(X11)
                | app(X11,cons(X9,nil)) != sK12 )
            | app(cons(X9,nil),X10) != sK15 ) )
    & equalelemsP(sK12)
    & app(sK12,sK15) = sK13
    & nil != sK10
    & ssList(sK13)
    & ssList(sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14,sK15])],[f153,f159,f158,f157,f156,f155,f154]) ).

fof(f154,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ( nil = X3
                      | nil != X2 )
                    & ! [X4] :
                        ( ! [X5] :
                            ( ~ ssList(X5)
                            | ! [X6] :
                                ( app(app(X5,cons(X4,nil)),X6) != X0
                                | ~ ssList(X6)
                                | ? [X7] :
                                    ( memberP(X5,X7)
                                    & ssItem(X7)
                                    & memberP(X6,X7)
                                    & ~ leq(X7,X4)
                                    & leq(X4,X7) ) ) )
                        | ~ ssItem(X4) )
                    & X1 = X3
                    & X0 = X2
                    & ? [X8] :
                        ( ssList(X8)
                        & ! [X9] :
                            ( ~ ssItem(X9)
                            | ! [X10] :
                                ( ~ ssList(X10)
                                | ! [X11] :
                                    ( ~ ssList(X11)
                                    | app(X11,cons(X9,nil)) != X2 )
                                | app(cons(X9,nil),X10) != X8 ) )
                        & equalelemsP(X2)
                        & app(X2,X8) = X3 )
                    & nil != X0
                    & ssList(X3) ) ) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ( nil = X3
                    | nil != X2 )
                  & ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( app(app(X5,cons(X4,nil)),X6) != sK10
                              | ~ ssList(X6)
                              | ? [X7] :
                                  ( memberP(X5,X7)
                                  & ssItem(X7)
                                  & memberP(X6,X7)
                                  & ~ leq(X7,X4)
                                  & leq(X4,X7) ) ) )
                      | ~ ssItem(X4) )
                  & X1 = X3
                  & sK10 = X2
                  & ? [X8] :
                      ( ssList(X8)
                      & ! [X9] :
                          ( ~ ssItem(X9)
                          | ! [X10] :
                              ( ~ ssList(X10)
                              | ! [X11] :
                                  ( ~ ssList(X11)
                                  | app(X11,cons(X9,nil)) != X2 )
                              | app(cons(X9,nil),X10) != X8 ) )
                      & equalelemsP(X2)
                      & app(X2,X8) = X3 )
                  & nil != sK10
                  & ssList(X3) ) ) )
      & ssList(sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f155,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ( nil = X3
                  | nil != X2 )
                & ! [X4] :
                    ( ! [X5] :
                        ( ~ ssList(X5)
                        | ! [X6] :
                            ( app(app(X5,cons(X4,nil)),X6) != sK10
                            | ~ ssList(X6)
                            | ? [X7] :
                                ( memberP(X5,X7)
                                & ssItem(X7)
                                & memberP(X6,X7)
                                & ~ leq(X7,X4)
                                & leq(X4,X7) ) ) )
                    | ~ ssItem(X4) )
                & X1 = X3
                & sK10 = X2
                & ? [X8] :
                    ( ssList(X8)
                    & ! [X9] :
                        ( ~ ssItem(X9)
                        | ! [X10] :
                            ( ~ ssList(X10)
                            | ! [X11] :
                                ( ~ ssList(X11)
                                | app(X11,cons(X9,nil)) != X2 )
                            | app(cons(X9,nil),X10) != X8 ) )
                    & equalelemsP(X2)
                    & app(X2,X8) = X3 )
                & nil != sK10
                & ssList(X3) ) ) )
   => ( ssList(sK11)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ( nil = X3
                | nil != X2 )
              & ! [X4] :
                  ( ! [X5] :
                      ( ~ ssList(X5)
                      | ! [X6] :
                          ( app(app(X5,cons(X4,nil)),X6) != sK10
                          | ~ ssList(X6)
                          | ? [X7] :
                              ( memberP(X5,X7)
                              & ssItem(X7)
                              & memberP(X6,X7)
                              & ~ leq(X7,X4)
                              & leq(X4,X7) ) ) )
                  | ~ ssItem(X4) )
              & sK11 = X3
              & sK10 = X2
              & ? [X8] :
                  ( ssList(X8)
                  & ! [X9] :
                      ( ~ ssItem(X9)
                      | ! [X10] :
                          ( ~ ssList(X10)
                          | ! [X11] :
                              ( ~ ssList(X11)
                              | app(X11,cons(X9,nil)) != X2 )
                          | app(cons(X9,nil),X10) != X8 ) )
                  & equalelemsP(X2)
                  & app(X2,X8) = X3 )
              & nil != sK10
              & ssList(X3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f156,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ( nil = X3
              | nil != X2 )
            & ! [X4] :
                ( ! [X5] :
                    ( ~ ssList(X5)
                    | ! [X6] :
                        ( app(app(X5,cons(X4,nil)),X6) != sK10
                        | ~ ssList(X6)
                        | ? [X7] :
                            ( memberP(X5,X7)
                            & ssItem(X7)
                            & memberP(X6,X7)
                            & ~ leq(X7,X4)
                            & leq(X4,X7) ) ) )
                | ~ ssItem(X4) )
            & sK11 = X3
            & sK10 = X2
            & ? [X8] :
                ( ssList(X8)
                & ! [X9] :
                    ( ~ ssItem(X9)
                    | ! [X10] :
                        ( ~ ssList(X10)
                        | ! [X11] :
                            ( ~ ssList(X11)
                            | app(X11,cons(X9,nil)) != X2 )
                        | app(cons(X9,nil),X10) != X8 ) )
                & equalelemsP(X2)
                & app(X2,X8) = X3 )
            & nil != sK10
            & ssList(X3) ) )
   => ( ssList(sK12)
      & ? [X3] :
          ( ( nil = X3
            | nil != sK12 )
          & ! [X4] :
              ( ! [X5] :
                  ( ~ ssList(X5)
                  | ! [X6] :
                      ( app(app(X5,cons(X4,nil)),X6) != sK10
                      | ~ ssList(X6)
                      | ? [X7] :
                          ( memberP(X5,X7)
                          & ssItem(X7)
                          & memberP(X6,X7)
                          & ~ leq(X7,X4)
                          & leq(X4,X7) ) ) )
              | ~ ssItem(X4) )
          & sK11 = X3
          & sK12 = sK10
          & ? [X8] :
              ( ssList(X8)
              & ! [X9] :
                  ( ~ ssItem(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | ! [X11] :
                          ( ~ ssList(X11)
                          | app(X11,cons(X9,nil)) != sK12 )
                      | app(cons(X9,nil),X10) != X8 ) )
              & equalelemsP(sK12)
              & app(sK12,X8) = X3 )
          & nil != sK10
          & ssList(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ( ? [X3] :
        ( ( nil = X3
          | nil != sK12 )
        & ! [X4] :
            ( ! [X5] :
                ( ~ ssList(X5)
                | ! [X6] :
                    ( app(app(X5,cons(X4,nil)),X6) != sK10
                    | ~ ssList(X6)
                    | ? [X7] :
                        ( memberP(X5,X7)
                        & ssItem(X7)
                        & memberP(X6,X7)
                        & ~ leq(X7,X4)
                        & leq(X4,X7) ) ) )
            | ~ ssItem(X4) )
        & sK11 = X3
        & sK12 = sK10
        & ? [X8] :
            ( ssList(X8)
            & ! [X9] :
                ( ~ ssItem(X9)
                | ! [X10] :
                    ( ~ ssList(X10)
                    | ! [X11] :
                        ( ~ ssList(X11)
                        | app(X11,cons(X9,nil)) != sK12 )
                    | app(cons(X9,nil),X10) != X8 ) )
            & equalelemsP(sK12)
            & app(sK12,X8) = X3 )
        & nil != sK10
        & ssList(X3) )
   => ( ( nil = sK13
        | nil != sK12 )
      & ! [X4] :
          ( ! [X5] :
              ( ~ ssList(X5)
              | ! [X6] :
                  ( app(app(X5,cons(X4,nil)),X6) != sK10
                  | ~ ssList(X6)
                  | ? [X7] :
                      ( memberP(X5,X7)
                      & ssItem(X7)
                      & memberP(X6,X7)
                      & ~ leq(X7,X4)
                      & leq(X4,X7) ) ) )
          | ~ ssItem(X4) )
      & sK11 = sK13
      & sK12 = sK10
      & ? [X8] :
          ( ssList(X8)
          & ! [X9] :
              ( ~ ssItem(X9)
              | ! [X10] :
                  ( ~ ssList(X10)
                  | ! [X11] :
                      ( ~ ssList(X11)
                      | app(X11,cons(X9,nil)) != sK12 )
                  | app(cons(X9,nil),X10) != X8 ) )
          & equalelemsP(sK12)
          & sK13 = app(sK12,X8) )
      & nil != sK10
      & ssList(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f158,plain,
    ! [X4,X5,X6] :
      ( ? [X7] :
          ( memberP(X5,X7)
          & ssItem(X7)
          & memberP(X6,X7)
          & ~ leq(X7,X4)
          & leq(X4,X7) )
     => ( memberP(X5,sK14(X4,X5,X6))
        & ssItem(sK14(X4,X5,X6))
        & memberP(X6,sK14(X4,X5,X6))
        & ~ leq(sK14(X4,X5,X6),X4)
        & leq(X4,sK14(X4,X5,X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ( ? [X8] :
        ( ssList(X8)
        & ! [X9] :
            ( ~ ssItem(X9)
            | ! [X10] :
                ( ~ ssList(X10)
                | ! [X11] :
                    ( ~ ssList(X11)
                    | app(X11,cons(X9,nil)) != sK12 )
                | app(cons(X9,nil),X10) != X8 ) )
        & equalelemsP(sK12)
        & sK13 = app(sK12,X8) )
   => ( ssList(sK15)
      & ! [X9] :
          ( ~ ssItem(X9)
          | ! [X10] :
              ( ~ ssList(X10)
              | ! [X11] :
                  ( ~ ssList(X11)
                  | app(X11,cons(X9,nil)) != sK12 )
              | app(cons(X9,nil),X10) != sK15 ) )
      & equalelemsP(sK12)
      & app(sK12,sK15) = sK13 ) ),
    introduced(choice_axiom,[]) ).

fof(f153,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ( nil = X3
                    | nil != X2 )
                  & ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( app(app(X5,cons(X4,nil)),X6) != X0
                              | ~ ssList(X6)
                              | ? [X7] :
                                  ( memberP(X5,X7)
                                  & ssItem(X7)
                                  & memberP(X6,X7)
                                  & ~ leq(X7,X4)
                                  & leq(X4,X7) ) ) )
                      | ~ ssItem(X4) )
                  & X1 = X3
                  & X0 = X2
                  & ? [X8] :
                      ( ssList(X8)
                      & ! [X9] :
                          ( ~ ssItem(X9)
                          | ! [X10] :
                              ( ~ ssList(X10)
                              | ! [X11] :
                                  ( ~ ssList(X11)
                                  | app(X11,cons(X9,nil)) != X2 )
                              | app(cons(X9,nil),X10) != X8 ) )
                      & equalelemsP(X2)
                      & app(X2,X8) = X3 )
                  & nil != X0
                  & ssList(X3) ) ) )
      & ssList(X0) ),
    inference(rectify,[],[f124]) ).

fof(f124,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ( nil = X3
                    | nil != X2 )
                  & ! [X8] :
                      ( ! [X9] :
                          ( ~ ssList(X9)
                          | ! [X10] :
                              ( app(app(X9,cons(X8,nil)),X10) != X0
                              | ~ ssList(X10)
                              | ? [X11] :
                                  ( memberP(X9,X11)
                                  & ssItem(X11)
                                  & memberP(X10,X11)
                                  & ~ leq(X11,X8)
                                  & leq(X8,X11) ) ) )
                      | ~ ssItem(X8) )
                  & X1 = X3
                  & X0 = X2
                  & ? [X4] :
                      ( ssList(X4)
                      & ! [X5] :
                          ( ~ ssItem(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(X7,cons(X5,nil)) != X2 )
                              | app(cons(X5,nil),X6) != X4 ) )
                      & equalelemsP(X2)
                      & app(X2,X4) = X3 )
                  & nil != X0
                  & ssList(X3) ) ) )
      & ssList(X0) ),
    inference(flattening,[],[f123]) ).

fof(f123,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & nil != X0
                  & ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( ? [X11] :
                                  ( memberP(X10,X11)
                                  & leq(X8,X11)
                                  & ~ leq(X11,X8)
                                  & memberP(X9,X11)
                                  & ssItem(X11) )
                              | app(app(X9,cons(X8,nil)),X10) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  & ? [X4] :
                      ( app(X2,X4) = X3
                      & equalelemsP(X2)
                      & ! [X5] :
                          ( ~ ssItem(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(X7,cons(X5,nil)) != X2 )
                              | app(cons(X5,nil),X6) != X4 ) )
                      & ssList(X4) )
                  & ( nil = X3
                    | nil != X2 )
                  & X0 = X2
                  & 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)
                   => ( X1 != X3
                      | nil = X0
                      | ? [X8] :
                          ( ? [X9] :
                              ( ? [X10] :
                                  ( ! [X11] :
                                      ( ssItem(X11)
                                     => ( ~ memberP(X10,X11)
                                        | ~ leq(X8,X11)
                                        | leq(X11,X8)
                                        | ~ memberP(X9,X11) ) )
                                  & app(app(X9,cons(X8,nil)),X10) = X0
                                  & ssList(X10) )
                              & ssList(X9) )
                          & ssItem(X8) )
                      | ! [X4] :
                          ( ssList(X4)
                         => ( app(X2,X4) != X3
                            | ~ equalelemsP(X2)
                            | ? [X5] :
                                ( ssItem(X5)
                                & ? [X6] :
                                    ( ssList(X6)
                                    & ? [X7] :
                                        ( app(X7,cons(X5,nil)) = X2
                                        & ssList(X7) )
                                    & app(cons(X5,nil),X6) = X4 ) ) ) )
                      | ( nil = X2
                        & nil != X3 )
                      | X0 != X2 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

fof(f443,plain,
    ( ~ ssList(sK10)
    | nil = sK10
    | memberP(nil,sK14(sK3(sK10),nil,sK2(sK10)))
    | ~ spl16_4
    | ~ spl16_6 ),
    inference(subsumption_resolution,[],[f442,f406]) ).

fof(f406,plain,
    ( ssList(cons(sK3(sK10),nil))
    | ~ spl16_6 ),
    inference(avatar_component_clause,[],[f405]) ).

fof(f405,plain,
    ( spl16_6
  <=> ssList(cons(sK3(sK10),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).

fof(f442,plain,
    ( ~ ssList(cons(sK3(sK10),nil))
    | nil = sK10
    | memberP(nil,sK14(sK3(sK10),nil,sK2(sK10)))
    | ~ ssList(sK10)
    | ~ spl16_4 ),
    inference(equality_resolution,[],[f396]) ).

fof(f396,plain,
    ( ! [X0] :
        ( sK10 != X0
        | ~ ssList(cons(sK3(X0),nil))
        | nil = X0
        | ~ ssList(X0)
        | memberP(nil,sK14(sK3(X0),nil,sK2(X0))) )
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f395,f173]) ).

fof(f173,plain,
    ! [X0] :
      ( ssList(sK2(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( nil = X0
      | ( ssList(sK2(X0))
        & cons(sK3(X0),sK2(X0)) = X0
        & ssItem(sK3(X0)) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f127,f135,f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) ) )
     => ( ssList(sK2(X0))
        & ? [X2] :
            ( cons(X2,sK2(X0)) = X0
            & ssItem(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,sK2(X0)) = X0
          & ssItem(X2) )
     => ( cons(sK3(X0),sK2(X0)) = X0
        & ssItem(sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ! [X0] :
      ( nil = X0
      | ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f126]) ).

fof(f126,plain,
    ! [X0] :
      ( nil = X0
      | ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

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

fof(f395,plain,
    ( ! [X0] :
        ( ~ ssList(cons(sK3(X0),nil))
        | memberP(nil,sK14(sK3(X0),nil,sK2(X0)))
        | ~ ssList(X0)
        | sK10 != X0
        | nil = X0
        | ~ ssList(sK2(X0)) )
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f394,f171]) ).

fof(f171,plain,
    ! [X0] :
      ( ssItem(sK3(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f394,plain,
    ( ! [X0] :
        ( ~ ssList(cons(sK3(X0),nil))
        | ~ ssItem(sK3(X0))
        | nil = X0
        | sK10 != X0
        | memberP(nil,sK14(sK3(X0),nil,sK2(X0)))
        | ~ ssList(sK2(X0))
        | ~ ssList(X0) )
    | ~ spl16_4 ),
    inference(superposition,[],[f369,f172]) ).

fof(f172,plain,
    ! [X0] :
      ( cons(sK3(X0),sK2(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f369,plain,
    ( ! [X10,X9] :
        ( cons(X9,X10) != sK10
        | ~ ssList(X10)
        | memberP(nil,sK14(X9,nil,X10))
        | ~ ssItem(X9)
        | ~ ssList(cons(X9,nil)) )
    | ~ spl16_4 ),
    inference(duplicate_literal_removal,[],[f345]) ).

fof(f345,plain,
    ( ! [X10,X9] :
        ( ~ ssList(X10)
        | memberP(nil,sK14(X9,nil,X10))
        | ~ ssList(cons(X9,nil))
        | ~ ssItem(X9)
        | cons(X9,X10) != sK10
        | ~ ssList(X10)
        | ~ ssItem(X9) )
    | ~ spl16_4 ),
    inference(superposition,[],[f297,f202]) ).

fof(f202,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f125,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/sandbox/benchmark/theBenchmark.p',ax81) ).

fof(f297,plain,
    ( ! [X8,X9] :
        ( app(cons(X8,nil),X9) != sK10
        | ~ ssItem(X8)
        | ~ ssList(cons(X8,nil))
        | memberP(nil,sK14(X8,nil,X9))
        | ~ ssList(X9) )
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f275,f254]) ).

fof(f254,plain,
    ( ssList(nil)
    | ~ spl16_4 ),
    inference(avatar_component_clause,[],[f253]) ).

fof(f253,plain,
    ( spl16_4
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).

fof(f275,plain,
    ! [X8,X9] :
      ( ~ ssList(nil)
      | app(cons(X8,nil),X9) != sK10
      | ~ ssList(cons(X8,nil))
      | ~ ssList(X9)
      | ~ ssItem(X8)
      | memberP(nil,sK14(X8,nil,X9)) ),
    inference(superposition,[],[f216,f180]) ).

fof(f180,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,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/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f216,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK10
      | ~ ssList(X6)
      | memberP(X5,sK14(X4,X5,X6))
      | ~ ssItem(X4)
      | ~ ssList(X5) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f414,plain,
    ( spl16_2
    | ~ spl16_4
    | spl16_6 ),
    inference(avatar_contradiction_clause,[],[f413]) ).

fof(f413,plain,
    ( $false
    | spl16_2
    | ~ spl16_4
    | spl16_6 ),
    inference(subsumption_resolution,[],[f412,f203]) ).

fof(f412,plain,
    ( ~ ssList(sK10)
    | spl16_2
    | ~ spl16_4
    | spl16_6 ),
    inference(subsumption_resolution,[],[f411,f246]) ).

fof(f411,plain,
    ( nil = sK10
    | ~ ssList(sK10)
    | ~ spl16_4
    | spl16_6 ),
    inference(resolution,[],[f410,f171]) ).

fof(f410,plain,
    ( ~ ssItem(sK3(sK10))
    | ~ spl16_4
    | spl16_6 ),
    inference(subsumption_resolution,[],[f409,f254]) ).

fof(f409,plain,
    ( ~ ssItem(sK3(sK10))
    | ~ ssList(nil)
    | spl16_6 ),
    inference(resolution,[],[f407,f220]) ).

fof(f220,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,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/sandbox/benchmark/theBenchmark.p',ax16) ).

fof(f407,plain,
    ( ~ ssList(cons(sK3(sK10),nil))
    | spl16_6 ),
    inference(avatar_component_clause,[],[f405]) ).

fof(f408,plain,
    ( spl16_5
    | ~ spl16_6
    | spl16_2
    | ~ spl16_4 ),
    inference(avatar_split_clause,[],[f399,f253,f244,f405,f401]) ).

fof(f399,plain,
    ( ~ ssList(cons(sK3(sK10),nil))
    | ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
    | spl16_2
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f398,f203]) ).

fof(f398,plain,
    ( ~ ssList(cons(sK3(sK10),nil))
    | ~ ssList(sK10)
    | ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
    | spl16_2
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f397,f246]) ).

fof(f397,plain,
    ( ssItem(sK14(sK3(sK10),nil,sK2(sK10)))
    | ~ ssList(cons(sK3(sK10),nil))
    | nil = sK10
    | ~ ssList(sK10)
    | ~ spl16_4 ),
    inference(equality_resolution,[],[f381]) ).

fof(f381,plain,
    ( ! [X0] :
        ( sK10 != X0
        | ~ ssList(cons(sK3(X0),nil))
        | ~ ssList(X0)
        | nil = X0
        | ssItem(sK14(sK3(X0),nil,sK2(X0))) )
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f380,f173]) ).

fof(f380,plain,
    ( ! [X0] :
        ( ~ ssList(cons(sK3(X0),nil))
        | ssItem(sK14(sK3(X0),nil,sK2(X0)))
        | ~ ssList(sK2(X0))
        | sK10 != X0
        | nil = X0
        | ~ ssList(X0) )
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f379,f171]) ).

fof(f379,plain,
    ( ! [X0] :
        ( ~ ssList(cons(sK3(X0),nil))
        | ~ ssItem(sK3(X0))
        | ssItem(sK14(sK3(X0),nil,sK2(X0)))
        | ~ ssList(sK2(X0))
        | ~ ssList(X0)
        | nil = X0
        | sK10 != X0 )
    | ~ spl16_4 ),
    inference(superposition,[],[f365,f172]) ).

fof(f365,plain,
    ( ! [X8,X7] :
        ( sK10 != cons(X7,X8)
        | ssItem(sK14(X7,nil,X8))
        | ~ ssItem(X7)
        | ~ ssList(X8)
        | ~ ssList(cons(X7,nil)) )
    | ~ spl16_4 ),
    inference(duplicate_literal_removal,[],[f344]) ).

fof(f344,plain,
    ( ! [X8,X7] :
        ( sK10 != cons(X7,X8)
        | ~ ssList(cons(X7,nil))
        | ~ ssItem(X7)
        | ~ ssList(X8)
        | ssItem(sK14(X7,nil,X8))
        | ~ ssList(X8)
        | ~ ssItem(X7) )
    | ~ spl16_4 ),
    inference(superposition,[],[f295,f202]) ).

fof(f295,plain,
    ( ! [X6,X7] :
        ( app(cons(X6,nil),X7) != sK10
        | ~ ssList(X7)
        | ~ ssItem(X6)
        | ~ ssList(cons(X6,nil))
        | ssItem(sK14(X6,nil,X7)) )
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f274,f254]) ).

fof(f274,plain,
    ! [X6,X7] :
      ( ~ ssList(X7)
      | ~ ssItem(X6)
      | ~ ssList(cons(X6,nil))
      | ~ ssList(nil)
      | app(cons(X6,nil),X7) != sK10
      | ssItem(sK14(X6,nil,X7)) ),
    inference(superposition,[],[f215,f180]) ).

fof(f215,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK10
      | ~ ssList(X6)
      | ~ ssItem(X4)
      | ssItem(sK14(X4,X5,X6))
      | ~ ssList(X5) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f258,plain,
    spl16_4,
    inference(avatar_split_clause,[],[f182,f253]) ).

fof(f182,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f257,plain,
    ~ spl16_2,
    inference(avatar_split_clause,[],[f205,f244]) ).

fof(f205,plain,
    nil != sK10,
    inference(cnf_transformation,[],[f160]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SWC224+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 18:45:49 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.21/0.49  % (27724)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)
% 0.21/0.50  % (27742)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)
% 0.21/0.50  % (27739)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)
% 0.21/0.50  % (27725)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)
% 0.21/0.51  % (27732)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.51  % (27724)Instruction limit reached!
% 0.21/0.51  % (27724)------------------------------
% 0.21/0.51  % (27724)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (27726)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)
% 0.21/0.51  % (27725)Instruction limit reached!
% 0.21/0.51  % (27725)------------------------------
% 0.21/0.51  % (27725)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (27726)First to succeed.
% 0.21/0.52  % (27732)Instruction limit reached!
% 0.21/0.52  % (27732)------------------------------
% 0.21/0.52  % (27732)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (27721)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)
% 0.21/0.52  % (27736)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)
% 0.21/0.52  % (27739)Instruction limit reached!
% 0.21/0.52  % (27739)------------------------------
% 0.21/0.52  % (27739)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (27724)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (27724)Termination reason: Unknown
% 0.21/0.52  % (27724)Termination phase: Saturation
% 0.21/0.52  
% 0.21/0.52  % (27724)Memory used [KB]: 6268
% 0.21/0.52  % (27724)Time elapsed: 0.102 s
% 0.21/0.52  % (27724)Instructions burned: 13 (million)
% 0.21/0.52  % (27724)------------------------------
% 0.21/0.52  % (27724)------------------------------
% 0.21/0.53  % (27739)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (27739)Termination reason: Unknown
% 0.21/0.53  % (27739)Termination phase: Saturation
% 0.21/0.53  
% 0.21/0.53  % (27739)Memory used [KB]: 6396
% 0.21/0.53  % (27739)Time elapsed: 0.112 s
% 0.21/0.53  % (27739)Instructions burned: 12 (million)
% 0.21/0.53  % (27739)------------------------------
% 0.21/0.53  % (27739)------------------------------
% 0.21/0.53  % (27745)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.21/0.53  % (27752)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)
% 0.21/0.53  % (27726)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (27726)------------------------------
% 0.21/0.53  % (27726)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (27726)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (27726)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (27726)Memory used [KB]: 6268
% 0.21/0.53  % (27726)Time elapsed: 0.113 s
% 0.21/0.53  % (27726)Instructions burned: 14 (million)
% 0.21/0.53  % (27726)------------------------------
% 0.21/0.53  % (27726)------------------------------
% 0.21/0.53  % (27715)Success in time 0.178 s
%------------------------------------------------------------------------------