TSTP Solution File: SWC204+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC204+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 : n007.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 18:39:35 EDT 2022

% Result   : Theorem 0.16s 0.51s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   21
% Syntax   : Number of formulae    :  109 (  10 unt;   0 def)
%            Number of atoms       :  502 ( 130 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  648 ( 255   ~; 259   |; 100   &)
%                                         (  11 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;  10 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   96 (  68   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f408,plain,
    $false,
    inference(avatar_sat_refutation,[],[f262,f263,f264,f265,f274,f323,f326,f334,f349,f407]) ).

fof(f407,plain,
    ( ~ spl10_1
    | ~ spl10_5
    | spl10_9
    | ~ spl10_13 ),
    inference(avatar_contradiction_clause,[],[f406]) ).

fof(f406,plain,
    ( $false
    | ~ spl10_1
    | ~ spl10_5
    | spl10_9
    | ~ spl10_13 ),
    inference(subsumption_resolution,[],[f405,f290]) ).

fof(f290,plain,
    ( nil != sK8
    | spl10_9 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f289,plain,
    ( spl10_9
  <=> nil = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_9])]) ).

fof(f405,plain,
    ( nil = sK8
    | ~ spl10_1
    | ~ spl10_5
    | spl10_9
    | ~ spl10_13 ),
    inference(subsumption_resolution,[],[f404,f195]) ).

fof(f195,plain,
    ssList(sK8),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ( ssList(sK5)
    & ssList(sK7)
    & sK6 = sK8
    & ssList(sK8)
    & ( ( ~ neq(sK8,nil)
        & neq(sK6,nil) )
      | ( ! [X4] :
            ( ~ ssList(X4)
            | sK8 = X4
            | ! [X5] :
                ( app(sK7,X5) != X4
                | tl(sK8) != X5
                | ~ ssList(X5)
                | ~ neq(nil,sK8) ) )
        & ~ neq(sK5,nil)
        & neq(sK6,nil) ) )
    & sK7 = sK5
    & ssList(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f131,f152,f151,f150,f149]) ).

fof(f149,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X1 = X3
                    & ssList(X3)
                    & ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | ( ! [X4] :
                            ( ~ ssList(X4)
                            | X3 = X4
                            | ! [X5] :
                                ( app(X2,X5) != X4
                                | tl(X3) != X5
                                | ~ ssList(X5)
                                | ~ neq(nil,X3) ) )
                        & ~ neq(X0,nil)
                        & neq(X1,nil) ) )
                    & X0 = X2 ) )
            & ssList(X1) ) )
   => ( ssList(sK5)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ssList(X3)
                  & ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ! [X4] :
                          ( ~ ssList(X4)
                          | X3 = X4
                          | ! [X5] :
                              ( app(X2,X5) != X4
                              | tl(X3) != X5
                              | ~ ssList(X5)
                              | ~ neq(nil,X3) ) )
                      & ~ neq(sK5,nil)
                      & neq(X1,nil) ) )
                  & sK5 = X2 ) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f150,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( X1 = X3
                & ssList(X3)
                & ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | ( ! [X4] :
                        ( ~ ssList(X4)
                        | X3 = X4
                        | ! [X5] :
                            ( app(X2,X5) != X4
                            | tl(X3) != X5
                            | ~ ssList(X5)
                            | ~ neq(nil,X3) ) )
                    & ~ neq(sK5,nil)
                    & neq(X1,nil) ) )
                & sK5 = X2 ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK6 = X3
              & ssList(X3)
              & ( ( ~ neq(X3,nil)
                  & neq(sK6,nil) )
                | ( ! [X4] :
                      ( ~ ssList(X4)
                      | X3 = X4
                      | ! [X5] :
                          ( app(X2,X5) != X4
                          | tl(X3) != X5
                          | ~ ssList(X5)
                          | ~ neq(nil,X3) ) )
                  & ~ neq(sK5,nil)
                  & neq(sK6,nil) ) )
              & sK5 = X2 ) )
      & ssList(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f151,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK6 = X3
            & ssList(X3)
            & ( ( ~ neq(X3,nil)
                & neq(sK6,nil) )
              | ( ! [X4] :
                    ( ~ ssList(X4)
                    | X3 = X4
                    | ! [X5] :
                        ( app(X2,X5) != X4
                        | tl(X3) != X5
                        | ~ ssList(X5)
                        | ~ neq(nil,X3) ) )
                & ~ neq(sK5,nil)
                & neq(sK6,nil) ) )
            & sK5 = X2 ) )
   => ( ssList(sK7)
      & ? [X3] :
          ( sK6 = X3
          & ssList(X3)
          & ( ( ~ neq(X3,nil)
              & neq(sK6,nil) )
            | ( ! [X4] :
                  ( ~ ssList(X4)
                  | X3 = X4
                  | ! [X5] :
                      ( app(sK7,X5) != X4
                      | tl(X3) != X5
                      | ~ ssList(X5)
                      | ~ neq(nil,X3) ) )
              & ~ neq(sK5,nil)
              & neq(sK6,nil) ) )
          & sK7 = sK5 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f152,plain,
    ( ? [X3] :
        ( sK6 = X3
        & ssList(X3)
        & ( ( ~ neq(X3,nil)
            & neq(sK6,nil) )
          | ( ! [X4] :
                ( ~ ssList(X4)
                | X3 = X4
                | ! [X5] :
                    ( app(sK7,X5) != X4
                    | tl(X3) != X5
                    | ~ ssList(X5)
                    | ~ neq(nil,X3) ) )
            & ~ neq(sK5,nil)
            & neq(sK6,nil) ) )
        & sK7 = sK5 )
   => ( sK6 = sK8
      & ssList(sK8)
      & ( ( ~ neq(sK8,nil)
          & neq(sK6,nil) )
        | ( ! [X4] :
              ( ~ ssList(X4)
              | sK8 = X4
              | ! [X5] :
                  ( app(sK7,X5) != X4
                  | tl(sK8) != X5
                  | ~ ssList(X5)
                  | ~ neq(nil,sK8) ) )
          & ~ neq(sK5,nil)
          & neq(sK6,nil) ) )
      & sK7 = sK5 ) ),
    introduced(choice_axiom,[]) ).

fof(f131,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ssList(X3)
                  & ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ! [X4] :
                          ( ~ ssList(X4)
                          | X3 = X4
                          | ! [X5] :
                              ( app(X2,X5) != X4
                              | tl(X3) != X5
                              | ~ ssList(X5)
                              | ~ neq(nil,X3) ) )
                      & ~ neq(X0,nil)
                      & neq(X1,nil) ) )
                  & X0 = X2 ) )
          & ssList(X1) ) ),
    inference(flattening,[],[f130]) ).

fof(f130,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & X1 = X3
                  & ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ! [X4] :
                          ( ~ ssList(X4)
                          | X3 = X4
                          | ! [X5] :
                              ( app(X2,X5) != X4
                              | tl(X3) != X5
                              | ~ ssList(X5)
                              | ~ neq(nil,X3) ) )
                      & ~ neq(X0,nil)
                      & neq(X1,nil) ) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( X0 != X2
                      | X1 != X3
                      | ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ? [X4] :
                              ( X3 != X4
                              & ssList(X4)
                              & ? [X5] :
                                  ( neq(nil,X3)
                                  & tl(X3) = X5
                                  & ssList(X5)
                                  & app(X2,X5) = X4 ) )
                          | neq(X0,nil)
                          | ~ neq(X1,nil) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X0 != X2
                    | X1 != X3
                    | ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( ? [X4] :
                            ( X3 != X4
                            & ssList(X4)
                            & ? [X5] :
                                ( neq(nil,X3)
                                & tl(X3) = X5
                                & ssList(X5)
                                & app(X2,X5) = X4 ) )
                        | neq(X0,nil)
                        | ~ neq(X1,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f404,plain,
    ( ~ ssList(sK8)
    | nil = sK8
    | ~ spl10_1
    | ~ spl10_5
    | spl10_9
    | ~ spl10_13 ),
    inference(resolution,[],[f403,f182]) ).

fof(f182,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f403,plain,
    ( ~ ssItem(hd(sK8))
    | ~ spl10_1
    | ~ spl10_5
    | spl10_9
    | ~ spl10_13 ),
    inference(subsumption_resolution,[],[f402,f195]) ).

fof(f402,plain,
    ( ~ ssList(sK8)
    | ~ ssItem(hd(sK8))
    | ~ spl10_1
    | ~ spl10_5
    | spl10_9
    | ~ spl10_13 ),
    inference(trivial_inequality_removal,[],[f400]) ).

fof(f400,plain,
    ( ~ ssList(sK8)
    | ~ ssItem(hd(sK8))
    | sK8 != sK8
    | ~ spl10_1
    | ~ spl10_5
    | spl10_9
    | ~ spl10_13 ),
    inference(superposition,[],[f184,f384]) ).

fof(f384,plain,
    ( cons(hd(sK8),sK8) = sK8
    | ~ spl10_1
    | ~ spl10_5
    | spl10_9
    | ~ spl10_13 ),
    inference(subsumption_resolution,[],[f383,f290]) ).

fof(f383,plain,
    ( cons(hd(sK8),sK8) = sK8
    | nil = sK8
    | ~ spl10_1
    | ~ spl10_5
    | ~ spl10_13 ),
    inference(subsumption_resolution,[],[f375,f195]) ).

fof(f375,plain,
    ( cons(hd(sK8),sK8) = sK8
    | ~ ssList(sK8)
    | nil = sK8
    | ~ spl10_1
    | ~ spl10_5
    | ~ spl10_13 ),
    inference(superposition,[],[f162,f357]) ).

fof(f357,plain,
    ( sK8 = tl(sK8)
    | ~ spl10_1
    | ~ spl10_5
    | ~ spl10_13 ),
    inference(subsumption_resolution,[],[f355,f229]) ).

fof(f229,plain,
    ( ssList(tl(sK8))
    | ~ spl10_1 ),
    inference(avatar_component_clause,[],[f228]) ).

fof(f228,plain,
    ( spl10_1
  <=> ssList(tl(sK8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).

fof(f355,plain,
    ( sK8 = tl(sK8)
    | ~ ssList(tl(sK8))
    | ~ spl10_5
    | ~ spl10_13 ),
    inference(superposition,[],[f186,f350]) ).

fof(f350,plain,
    ( sK8 = app(nil,tl(sK8))
    | ~ spl10_5
    | ~ spl10_13 ),
    inference(forward_demodulation,[],[f246,f308]) ).

fof(f308,plain,
    ( nil = sK5
    | ~ spl10_13 ),
    inference(avatar_component_clause,[],[f306]) ).

fof(f306,plain,
    ( spl10_13
  <=> nil = sK5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_13])]) ).

fof(f246,plain,
    ( sK8 = app(sK5,tl(sK8))
    | ~ spl10_5 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f244,plain,
    ( spl10_5
  <=> sK8 = app(sK5,tl(sK8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_5])]) ).

fof(f186,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,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(f162,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f125,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | ~ ssList(X0)
      | nil = X0 ),
    inference(flattening,[],[f124]) ).

fof(f124,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).

fof(f184,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssItem(X1)
          | cons(X1,X0) != X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) != X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).

fof(f349,plain,
    ( ~ spl10_1
    | spl10_3
    | ~ spl10_13 ),
    inference(avatar_contradiction_clause,[],[f348]) ).

fof(f348,plain,
    ( $false
    | ~ spl10_1
    | spl10_3
    | ~ spl10_13 ),
    inference(subsumption_resolution,[],[f344,f229]) ).

fof(f344,plain,
    ( ~ ssList(tl(sK8))
    | spl10_3
    | ~ spl10_13 ),
    inference(duplicate_literal_removal,[],[f343]) ).

fof(f343,plain,
    ( ~ ssList(tl(sK8))
    | ~ ssList(tl(sK8))
    | spl10_3
    | ~ spl10_13 ),
    inference(superposition,[],[f341,f186]) ).

fof(f341,plain,
    ( ~ ssList(app(nil,tl(sK8)))
    | spl10_3
    | ~ spl10_13 ),
    inference(forward_demodulation,[],[f238,f308]) ).

fof(f238,plain,
    ( ~ ssList(app(sK5,tl(sK8)))
    | spl10_3 ),
    inference(avatar_component_clause,[],[f236]) ).

fof(f236,plain,
    ( spl10_3
  <=> ssList(app(sK5,tl(sK8))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).

fof(f334,plain,
    ( ~ spl10_4
    | ~ spl10_7
    | ~ spl10_9 ),
    inference(avatar_contradiction_clause,[],[f333]) ).

fof(f333,plain,
    ( $false
    | ~ spl10_4
    | ~ spl10_7
    | ~ spl10_9 ),
    inference(subsumption_resolution,[],[f332,f254]) ).

fof(f254,plain,
    ( ssList(nil)
    | ~ spl10_7 ),
    inference(avatar_component_clause,[],[f253]) ).

fof(f253,plain,
    ( spl10_7
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).

fof(f332,plain,
    ( ~ ssList(nil)
    | ~ spl10_4
    | ~ spl10_9 ),
    inference(resolution,[],[f327,f224]) ).

fof(f224,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f222]) ).

fof(f222,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f203]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | X0 != X1
      | ~ neq(X0,X1) ),
    inference(cnf_transformation,[],[f156]) ).

fof(f156,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) ) ) ),
    inference(nnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( X0 != X1
          <=> neq(X0,X1) ) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( X0 != X1
          <=> neq(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f327,plain,
    ( neq(nil,nil)
    | ~ spl10_4
    | ~ spl10_9 ),
    inference(backward_demodulation,[],[f242,f291]) ).

fof(f291,plain,
    ( nil = sK8
    | ~ spl10_9 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f242,plain,
    ( neq(sK8,nil)
    | ~ spl10_4 ),
    inference(avatar_component_clause,[],[f240]) ).

fof(f240,plain,
    ( spl10_4
  <=> neq(sK8,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).

fof(f326,plain,
    ( spl10_13
    | ~ spl10_7
    | spl10_8 ),
    inference(avatar_split_clause,[],[f325,f258,f253,f306]) ).

fof(f258,plain,
    ( spl10_8
  <=> neq(sK5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_8])]) ).

fof(f325,plain,
    ( nil = sK5
    | ~ spl10_7
    | spl10_8 ),
    inference(subsumption_resolution,[],[f324,f254]) ).

fof(f324,plain,
    ( ~ ssList(nil)
    | nil = sK5
    | spl10_8 ),
    inference(subsumption_resolution,[],[f315,f198]) ).

fof(f198,plain,
    ssList(sK5),
    inference(cnf_transformation,[],[f153]) ).

fof(f315,plain,
    ( nil = sK5
    | ~ ssList(sK5)
    | ~ ssList(nil)
    | spl10_8 ),
    inference(resolution,[],[f202,f260]) ).

fof(f260,plain,
    ( ~ neq(sK5,nil)
    | spl10_8 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f202,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X0)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f156]) ).

fof(f323,plain,
    ( spl10_9
    | spl10_2
    | ~ spl10_7 ),
    inference(avatar_split_clause,[],[f322,f253,f232,f289]) ).

fof(f232,plain,
    ( spl10_2
  <=> neq(nil,sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).

fof(f322,plain,
    ( nil = sK8
    | spl10_2
    | ~ spl10_7 ),
    inference(subsumption_resolution,[],[f321,f195]) ).

fof(f321,plain,
    ( ~ ssList(sK8)
    | nil = sK8
    | spl10_2
    | ~ spl10_7 ),
    inference(subsumption_resolution,[],[f318,f254]) ).

fof(f318,plain,
    ( ~ ssList(nil)
    | nil = sK8
    | ~ ssList(sK8)
    | spl10_2 ),
    inference(resolution,[],[f202,f234]) ).

fof(f234,plain,
    ( ~ neq(nil,sK8)
    | spl10_2 ),
    inference(avatar_component_clause,[],[f232]) ).

fof(f274,plain,
    ( spl10_1
    | ~ spl10_4
    | ~ spl10_7 ),
    inference(avatar_contradiction_clause,[],[f273]) ).

fof(f273,plain,
    ( $false
    | spl10_1
    | ~ spl10_4
    | ~ spl10_7 ),
    inference(subsumption_resolution,[],[f272,f254]) ).

fof(f272,plain,
    ( ~ ssList(nil)
    | spl10_1
    | ~ spl10_4 ),
    inference(resolution,[],[f268,f224]) ).

fof(f268,plain,
    ( neq(nil,nil)
    | spl10_1
    | ~ spl10_4 ),
    inference(backward_demodulation,[],[f242,f267]) ).

fof(f267,plain,
    ( nil = sK8
    | spl10_1 ),
    inference(subsumption_resolution,[],[f266,f195]) ).

fof(f266,plain,
    ( nil = sK8
    | ~ ssList(sK8)
    | spl10_1 ),
    inference(resolution,[],[f165,f230]) ).

fof(f230,plain,
    ( ~ ssList(tl(sK8))
    | spl10_1 ),
    inference(avatar_component_clause,[],[f228]) ).

fof(f165,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f114]) ).

fof(f114,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(tl(X0))
      | nil = X0 ),
    inference(flattening,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

fof(f265,plain,
    spl10_7,
    inference(avatar_split_clause,[],[f181,f253]) ).

fof(f181,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f264,plain,
    spl10_4,
    inference(avatar_split_clause,[],[f223,f240]) ).

fof(f223,plain,
    neq(sK8,nil),
    inference(duplicate_literal_removal,[],[f213]) ).

fof(f213,plain,
    ( neq(sK8,nil)
    | neq(sK8,nil) ),
    inference(definition_unfolding,[],[f189,f196,f196]) ).

fof(f196,plain,
    sK6 = sK8,
    inference(cnf_transformation,[],[f153]) ).

fof(f189,plain,
    ( neq(sK6,nil)
    | neq(sK6,nil) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f263,plain,
    ( spl10_5
    | ~ spl10_2
    | ~ spl10_4
    | ~ spl10_3
    | ~ spl10_1 ),
    inference(avatar_split_clause,[],[f219,f228,f236,f240,f232,f244]) ).

fof(f219,plain,
    ( ~ ssList(tl(sK8))
    | ~ ssList(app(sK5,tl(sK8)))
    | ~ neq(sK8,nil)
    | ~ neq(nil,sK8)
    | sK8 = app(sK5,tl(sK8)) ),
    inference(equality_resolution,[],[f218]) ).

fof(f218,plain,
    ! [X5] :
      ( ~ neq(sK8,nil)
      | ~ ssList(app(sK5,X5))
      | app(sK5,X5) = sK8
      | tl(sK8) != X5
      | ~ ssList(X5)
      | ~ neq(nil,sK8) ),
    inference(equality_resolution,[],[f209]) ).

fof(f209,plain,
    ! [X4,X5] :
      ( ~ neq(sK8,nil)
      | ~ ssList(X4)
      | sK8 = X4
      | app(sK5,X5) != X4
      | tl(sK8) != X5
      | ~ ssList(X5)
      | ~ neq(nil,sK8) ),
    inference(definition_unfolding,[],[f194,f188]) ).

fof(f188,plain,
    sK7 = sK5,
    inference(cnf_transformation,[],[f153]) ).

fof(f194,plain,
    ! [X4,X5] :
      ( ~ neq(sK8,nil)
      | ~ ssList(X4)
      | sK8 = X4
      | app(sK7,X5) != X4
      | tl(sK8) != X5
      | ~ ssList(X5)
      | ~ neq(nil,sK8) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f262,plain,
    ( ~ spl10_8
    | ~ spl10_4 ),
    inference(avatar_split_clause,[],[f193,f240,f258]) ).

fof(f193,plain,
    ( ~ neq(sK8,nil)
    | ~ neq(sK5,nil) ),
    inference(cnf_transformation,[],[f153]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : SWC204+1 : TPTP v8.1.0. Released v2.4.0.
% 0.02/0.10  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.31  % Computer : n007.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Tue Aug 30 18:19:16 EDT 2022
% 0.10/0.31  % CPUTime    : 
% 0.16/0.44  % (27120)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)
% 0.16/0.44  % (27123)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)
% 0.16/0.45  % (27127)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)
% 0.16/0.45  % (27128)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)
% 0.16/0.46  % (27119)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)
% 0.16/0.46  % (27138)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)
% 0.16/0.46  % (27131)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)
% 0.16/0.47  % (27135)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.16/0.47  % (27125)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.16/0.47  % (27116)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)
% 0.16/0.47  % (27125)Refutation not found, incomplete strategy% (27125)------------------------------
% 0.16/0.47  % (27125)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.47  % (27125)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.47  % (27125)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.47  
% 0.16/0.47  % (27125)Memory used [KB]: 6140
% 0.16/0.47  % (27125)Time elapsed: 0.120 s
% 0.16/0.47  % (27125)Instructions burned: 4 (million)
% 0.16/0.47  % (27125)------------------------------
% 0.16/0.47  % (27125)------------------------------
% 0.16/0.47  % (27122)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)
% 0.16/0.47  % (27127)Instruction limit reached!
% 0.16/0.47  % (27127)------------------------------
% 0.16/0.47  % (27127)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.47  % (27139)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)
% 0.16/0.48  % (27137)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)
% 0.16/0.48  % (27120)Instruction limit reached!
% 0.16/0.48  % (27120)------------------------------
% 0.16/0.48  % (27120)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.48  % (27120)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.48  % (27132)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.48  % (27120)Termination reason: Unknown
% 0.16/0.48  % (27120)Termination phase: Saturation
% 0.16/0.48  
% 0.16/0.48  % (27120)Memory used [KB]: 1663
% 0.16/0.48  % (27120)Time elapsed: 0.095 s
% 0.16/0.48  % (27120)Instructions burned: 15 (million)
% 0.16/0.48  % (27120)------------------------------
% 0.16/0.48  % (27120)------------------------------
% 0.16/0.48  % (27118)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.16/0.48  % (27132)Instruction limit reached!
% 0.16/0.48  % (27132)------------------------------
% 0.16/0.48  % (27132)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.48  % (27115)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.16/0.48  % (27116)Instruction limit reached!
% 0.16/0.48  % (27116)------------------------------
% 0.16/0.48  % (27116)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.48  % (27141)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.16/0.48  % (27129)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)
% 0.16/0.48  % (27130)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.48  % (27144)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)
% 0.16/0.48  % (27124)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)
% 0.16/0.49  % (27119)Instruction limit reached!
% 0.16/0.49  % (27119)------------------------------
% 0.16/0.49  % (27119)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.49  % (27132)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.49  % (27132)Termination reason: Unknown
% 0.16/0.49  % (27132)Termination phase: Preprocessing 3
% 0.16/0.49  
% 0.16/0.49  % (27132)Memory used [KB]: 1663
% 0.16/0.49  % (27132)Time elapsed: 0.003 s
% 0.16/0.49  % (27132)Instructions burned: 3 (million)
% 0.16/0.49  % (27132)------------------------------
% 0.16/0.49  % (27132)------------------------------
% 0.16/0.49  % (27133)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.49  % (27127)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.49  % (27127)Termination reason: Unknown
% 0.16/0.49  % (27127)Termination phase: Saturation
% 0.16/0.49  
% 0.16/0.49  % (27127)Memory used [KB]: 2046
% 0.16/0.49  % (27127)Time elapsed: 0.128 s
% 0.16/0.49  % (27127)Instructions burned: 17 (million)
% 0.16/0.49  % (27127)------------------------------
% 0.16/0.49  % (27127)------------------------------
% 0.16/0.49  % (27119)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.49  % (27119)Termination reason: Unknown
% 0.16/0.49  % (27119)Termination phase: Saturation
% 0.16/0.49  
% 0.16/0.49  % (27119)Memory used [KB]: 6268
% 0.16/0.49  % (27119)Time elapsed: 0.138 s
% 0.16/0.49  % (27119)Instructions burned: 14 (million)
% 0.16/0.49  % (27119)------------------------------
% 0.16/0.49  % (27119)------------------------------
% 0.16/0.50  % (27117)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)
% 0.16/0.50  % (27129)Instruction limit reached!
% 0.16/0.50  % (27129)------------------------------
% 0.16/0.50  % (27129)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.50  % (27129)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.50  % (27129)Termination reason: Unknown
% 0.16/0.50  % (27129)Termination phase: Preprocessing 3
% 0.16/0.50  
% 0.16/0.50  % (27129)Memory used [KB]: 1663
% 0.16/0.50  % (27129)Time elapsed: 0.004 s
% 0.16/0.50  % (27129)Instructions burned: 5 (million)
% 0.16/0.50  % (27129)------------------------------
% 0.16/0.50  % (27129)------------------------------
% 0.16/0.50  % (27116)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.50  % (27116)Termination reason: Unknown
% 0.16/0.50  % (27116)Termination phase: Saturation
% 0.16/0.50  
% 0.16/0.50  % (27116)Memory used [KB]: 6396
% 0.16/0.50  % (27116)Time elapsed: 0.095 s
% 0.16/0.50  % (27116)Instructions burned: 14 (million)
% 0.16/0.50  % (27116)------------------------------
% 0.16/0.50  % (27116)------------------------------
% 0.16/0.50  % (27117)Instruction limit reached!
% 0.16/0.50  % (27117)------------------------------
% 0.16/0.50  % (27117)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.50  % (27117)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.50  % (27117)Termination reason: Unknown
% 0.16/0.50  % (27117)Termination phase: Preprocessing 3
% 0.16/0.50  
% 0.16/0.50  % (27117)Memory used [KB]: 1535
% 0.16/0.50  % (27117)Time elapsed: 0.004 s
% 0.16/0.50  % (27117)Instructions burned: 3 (million)
% 0.16/0.50  % (27117)------------------------------
% 0.16/0.50  % (27117)------------------------------
% 0.16/0.50  % (27130)Instruction limit reached!
% 0.16/0.50  % (27130)------------------------------
% 0.16/0.50  % (27130)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.50  % (27130)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.50  % (27130)Termination reason: Unknown
% 0.16/0.50  % (27130)Termination phase: Function definition elimination
% 0.16/0.50  
% 0.16/0.50  % (27130)Memory used [KB]: 1791
% 0.16/0.50  % (27130)Time elapsed: 0.006 s
% 0.16/0.50  % (27130)Instructions burned: 8 (million)
% 0.16/0.50  % (27130)------------------------------
% 0.16/0.50  % (27130)------------------------------
% 0.16/0.50  % (27121)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)
% 0.16/0.50  % (27126)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.50  % (27136)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)
% 0.16/0.51  % (27143)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.16/0.51  % (27121)First to succeed.
% 0.16/0.51  % (27126)Instruction limit reached!
% 0.16/0.51  % (27126)------------------------------
% 0.16/0.51  % (27126)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.51  % (27126)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.51  % (27126)Termination reason: Unknown
% 0.16/0.51  % (27126)Termination phase: Saturation
% 0.16/0.51  
% 0.16/0.51  % (27126)Memory used [KB]: 6140
% 0.16/0.51  % (27126)Time elapsed: 0.151 s
% 0.16/0.51  % (27126)Instructions burned: 7 (million)
% 0.16/0.51  % (27126)------------------------------
% 0.16/0.51  % (27126)------------------------------
% 0.16/0.51  % (27134)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)
% 0.16/0.51  % (27115)Also succeeded, but the first one will report.
% 0.16/0.51  % (27133)Instruction limit reached!
% 0.16/0.51  % (27133)------------------------------
% 0.16/0.51  % (27133)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.51  % (27133)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.51  % (27133)Termination reason: Unknown
% 0.16/0.51  % (27133)Termination phase: Function definition elimination
% 0.16/0.51  
% 0.16/0.51  % (27133)Memory used [KB]: 1535
% 0.16/0.51  % (27133)Time elapsed: 0.003 s
% 0.16/0.51  % (27133)Instructions burned: 3 (million)
% 0.16/0.51  % (27133)------------------------------
% 0.16/0.51  % (27133)------------------------------
% 0.16/0.51  % (27121)Refutation found. Thanks to Tanya!
% 0.16/0.51  % SZS status Theorem for theBenchmark
% 0.16/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.51  % (27121)------------------------------
% 0.16/0.51  % (27121)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.51  % (27121)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.51  % (27121)Termination reason: Refutation
% 0.16/0.51  
% 0.16/0.51  % (27121)Memory used [KB]: 6140
% 0.16/0.51  % (27121)Time elapsed: 0.115 s
% 0.16/0.51  % (27121)Instructions burned: 9 (million)
% 0.16/0.51  % (27121)------------------------------
% 0.16/0.51  % (27121)------------------------------
% 0.16/0.51  % (27114)Success in time 0.193 s
%------------------------------------------------------------------------------