TSTP Solution File: SWC313+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC313+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 : n019.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 18:40:21 EDT 2022

% Result   : Theorem 1.48s 0.56s
% Output   : Refutation 1.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   66 (   7 unt;   0 def)
%            Number of atoms       :  430 ( 196 equ)
%            Maximal formula atoms :   38 (   6 avg)
%            Number of connectives :  578 ( 214   ~; 197   |; 137   &)
%                                         (   7 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   6 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  146 ( 100   !;  46   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f279,plain,
    $false,
    inference(avatar_sat_refutation,[],[f194,f213,f214,f215,f266,f278]) ).

fof(f278,plain,
    ( ~ spl8_1
    | ~ spl8_4
    | ~ spl8_6 ),
    inference(avatar_contradiction_clause,[],[f277]) ).

fof(f277,plain,
    ( $false
    | ~ spl8_1
    | ~ spl8_4
    | ~ spl8_6 ),
    inference(subsumption_resolution,[],[f276,f201]) ).

fof(f201,plain,
    ( ssList(nil)
    | ~ spl8_4 ),
    inference(avatar_component_clause,[],[f200]) ).

fof(f200,plain,
    ( spl8_4
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

fof(f276,plain,
    ( ~ ssList(nil)
    | ~ spl8_1
    | ~ spl8_6 ),
    inference(resolution,[],[f269,f183]) ).

fof(f183,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f179]) ).

fof(f179,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(equality_resolution,[],[f143]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( neq(X0,X1)
          <=> X0 != X1 ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

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

fof(f269,plain,
    ( neq(nil,nil)
    | ~ spl8_1
    | ~ spl8_6 ),
    inference(backward_demodulation,[],[f211,f188]) ).

fof(f188,plain,
    ( nil = sK5
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f187]) ).

fof(f187,plain,
    ( spl8_1
  <=> nil = sK5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f211,plain,
    ( neq(sK5,nil)
    | ~ spl8_6 ),
    inference(avatar_component_clause,[],[f209]) ).

fof(f209,plain,
    ( spl8_6
  <=> neq(sK5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

fof(f266,plain,
    ( spl8_1
    | ~ spl8_3 ),
    inference(avatar_split_clause,[],[f265,f196,f187]) ).

fof(f196,plain,
    ( spl8_3
  <=> ! [X4,X5] :
        ( app(cons(X4,nil),X5) != sK5
        | ~ ssList(X5)
        | ~ ssItem(X4)
        | app(X5,cons(X4,nil)) != sK4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

fof(f265,plain,
    ( nil = sK5
    | ~ spl8_3 ),
    inference(subsumption_resolution,[],[f261,f157]) ).

fof(f157,plain,
    ssList(sK5),
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ( ssList(sK7)
    & ( ( nil != sK4
        & nil = sK5 )
      | ( ! [X4] :
            ( ! [X5] :
                ( ~ ssList(X5)
                | app(cons(X4,nil),X5) != sK5
                | app(X5,cons(X4,nil)) != sK4 )
            | ~ ssItem(X4) )
        & neq(sK5,nil) ) )
    & ( nil = sK6
      | nil != sK7 )
    & sK6 = sK4
    & ! [X6] :
        ( ~ ssItem(X6)
        | ! [X7] :
            ( app(X7,cons(X6,nil)) = sK6
            | ~ ssList(X7)
            | app(cons(X6,nil),X7) != sK7 ) )
    & sK7 = sK5
    & ssList(sK6)
    & ssList(sK5)
    & ssList(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f117,f134,f133,f132,f131]) ).

fof(f131,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ssList(X3)
                    & ( ( nil != X0
                        & nil = X1 )
                      | ( ! [X4] :
                            ( ! [X5] :
                                ( ~ ssList(X5)
                                | app(cons(X4,nil),X5) != X1
                                | app(X5,cons(X4,nil)) != X0 )
                            | ~ ssItem(X4) )
                        & neq(X1,nil) ) )
                    & ( nil = X2
                      | nil != X3 )
                    & X0 = X2
                    & ! [X6] :
                        ( ~ ssItem(X6)
                        | ! [X7] :
                            ( app(X7,cons(X6,nil)) = X2
                            | ~ ssList(X7)
                            | app(cons(X6,nil),X7) != X3 ) )
                    & X1 = X3 )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & ( ( nil != sK4
                      & nil = X1 )
                    | ( ! [X4] :
                          ( ! [X5] :
                              ( ~ ssList(X5)
                              | app(cons(X4,nil),X5) != X1
                              | app(X5,cons(X4,nil)) != sK4 )
                          | ~ ssItem(X4) )
                      & neq(X1,nil) ) )
                  & ( nil = X2
                    | nil != X3 )
                  & sK4 = X2
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( app(X7,cons(X6,nil)) = X2
                          | ~ ssList(X7)
                          | app(cons(X6,nil),X7) != X3 ) )
                  & X1 = X3 )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ssList(X3)
                & ( ( nil != sK4
                    & nil = X1 )
                  | ( ! [X4] :
                        ( ! [X5] :
                            ( ~ ssList(X5)
                            | app(cons(X4,nil),X5) != X1
                            | app(X5,cons(X4,nil)) != sK4 )
                        | ~ ssItem(X4) )
                    & neq(X1,nil) ) )
                & ( nil = X2
                  | nil != X3 )
                & sK4 = X2
                & ! [X6] :
                    ( ~ ssItem(X6)
                    | ! [X7] :
                        ( app(X7,cons(X6,nil)) = X2
                        | ~ ssList(X7)
                        | app(cons(X6,nil),X7) != X3 ) )
                & X1 = X3 )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ssList(X3)
              & ( ( nil != sK4
                  & nil = sK5 )
                | ( ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | app(cons(X4,nil),X5) != sK5
                          | app(X5,cons(X4,nil)) != sK4 )
                      | ~ ssItem(X4) )
                  & neq(sK5,nil) ) )
              & ( nil = X2
                | nil != X3 )
              & sK4 = X2
              & ! [X6] :
                  ( ~ ssItem(X6)
                  | ! [X7] :
                      ( app(X7,cons(X6,nil)) = X2
                      | ~ ssList(X7)
                      | app(cons(X6,nil),X7) != X3 ) )
              & sK5 = X3 )
          & ssList(X2) )
      & ssList(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ssList(X3)
            & ( ( nil != sK4
                & nil = sK5 )
              | ( ! [X4] :
                    ( ! [X5] :
                        ( ~ ssList(X5)
                        | app(cons(X4,nil),X5) != sK5
                        | app(X5,cons(X4,nil)) != sK4 )
                    | ~ ssItem(X4) )
                & neq(sK5,nil) ) )
            & ( nil = X2
              | nil != X3 )
            & sK4 = X2
            & ! [X6] :
                ( ~ ssItem(X6)
                | ! [X7] :
                    ( app(X7,cons(X6,nil)) = X2
                    | ~ ssList(X7)
                    | app(cons(X6,nil),X7) != X3 ) )
            & sK5 = X3 )
        & ssList(X2) )
   => ( ? [X3] :
          ( ssList(X3)
          & ( ( nil != sK4
              & nil = sK5 )
            | ( ! [X4] :
                  ( ! [X5] :
                      ( ~ ssList(X5)
                      | app(cons(X4,nil),X5) != sK5
                      | app(X5,cons(X4,nil)) != sK4 )
                  | ~ ssItem(X4) )
              & neq(sK5,nil) ) )
          & ( nil = sK6
            | nil != X3 )
          & sK6 = sK4
          & ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( app(X7,cons(X6,nil)) = sK6
                  | ~ ssList(X7)
                  | app(cons(X6,nil),X7) != X3 ) )
          & sK5 = X3 )
      & ssList(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f134,plain,
    ( ? [X3] :
        ( ssList(X3)
        & ( ( nil != sK4
            & nil = sK5 )
          | ( ! [X4] :
                ( ! [X5] :
                    ( ~ ssList(X5)
                    | app(cons(X4,nil),X5) != sK5
                    | app(X5,cons(X4,nil)) != sK4 )
                | ~ ssItem(X4) )
            & neq(sK5,nil) ) )
        & ( nil = sK6
          | nil != X3 )
        & sK6 = sK4
        & ! [X6] :
            ( ~ ssItem(X6)
            | ! [X7] :
                ( app(X7,cons(X6,nil)) = sK6
                | ~ ssList(X7)
                | app(cons(X6,nil),X7) != X3 ) )
        & sK5 = X3 )
   => ( ssList(sK7)
      & ( ( nil != sK4
          & nil = sK5 )
        | ( ! [X4] :
              ( ! [X5] :
                  ( ~ ssList(X5)
                  | app(cons(X4,nil),X5) != sK5
                  | app(X5,cons(X4,nil)) != sK4 )
              | ~ ssItem(X4) )
          & neq(sK5,nil) ) )
      & ( nil = sK6
        | nil != sK7 )
      & sK6 = sK4
      & ! [X6] :
          ( ~ ssItem(X6)
          | ! [X7] :
              ( app(X7,cons(X6,nil)) = sK6
              | ~ ssList(X7)
              | app(cons(X6,nil),X7) != sK7 ) )
      & sK7 = sK5 ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & ( ( nil != X0
                      & nil = X1 )
                    | ( ! [X4] :
                          ( ! [X5] :
                              ( ~ ssList(X5)
                              | app(cons(X4,nil),X5) != X1
                              | app(X5,cons(X4,nil)) != X0 )
                          | ~ ssItem(X4) )
                      & neq(X1,nil) ) )
                  & ( nil = X2
                    | nil != X3 )
                  & X0 = X2
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( app(X7,cons(X6,nil)) = X2
                          | ~ ssList(X7)
                          | app(cons(X6,nil),X7) != X3 ) )
                  & X1 = X3 )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f116]) ).

fof(f116,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( app(X7,cons(X6,nil)) = X2
                          | ~ ssList(X7)
                          | app(cons(X6,nil),X7) != X3 ) )
                  & ( nil = X2
                    | nil != X3 )
                  & X1 = X3
                  & ( ( nil != X0
                      & nil = X1 )
                    | ( ! [X4] :
                          ( ! [X5] :
                              ( ~ ssList(X5)
                              | app(cons(X4,nil),X5) != X1
                              | app(X5,cons(X4,nil)) != X0 )
                          | ~ ssItem(X4) )
                      & neq(X1,nil) ) )
                  & 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)
                   => ( X0 != X2
                      | ? [X6] :
                          ( ? [X7] :
                              ( ssList(X7)
                              & app(X7,cons(X6,nil)) != X2
                              & app(cons(X6,nil),X7) = X3 )
                          & ssItem(X6) )
                      | ( nil = X3
                        & nil != X2 )
                      | X1 != X3
                      | ( ( ~ neq(X1,nil)
                          | ? [X4] :
                              ( ssItem(X4)
                              & ? [X5] :
                                  ( app(cons(X4,nil),X5) = X1
                                  & ssList(X5)
                                  & app(X5,cons(X4,nil)) = X0 ) ) )
                        & ( nil = X0
                          | nil != X1 ) ) ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

fof(f261,plain,
    ( nil = sK5
    | ~ ssList(sK5)
    | ~ spl8_3 ),
    inference(equality_resolution,[],[f260]) ).

fof(f260,plain,
    ( ! [X0] :
        ( sK5 != X0
        | nil = X0
        | ~ ssList(X0) )
    | ~ spl8_3 ),
    inference(subsumption_resolution,[],[f259,f141]) ).

fof(f141,plain,
    ! [X0] :
      ( ssItem(sK3(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ! [X0] :
      ( ( ssItem(sK3(X0))
        & cons(sK3(X0),sK2(X0)) = X0
        & ssList(sK2(X0)) )
      | ~ ssList(X0)
      | nil = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f115,f125,f124]) ).

fof(f124,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ssItem(X2)
              & cons(X2,X1) = X0 )
          & ssList(X1) )
     => ( ? [X2] :
            ( ssItem(X2)
            & cons(X2,sK2(X0)) = X0 )
        & ssList(sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0] :
      ( ? [X2] :
          ( ssItem(X2)
          & cons(X2,sK2(X0)) = X0 )
     => ( ssItem(sK3(X0))
        & cons(sK3(X0),sK2(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ssItem(X2)
              & cons(X2,X1) = X0 )
          & ssList(X1) )
      | ~ ssList(X0)
      | nil = X0 ),
    inference(flattening,[],[f114]) ).

fof(f114,plain,
    ! [X0] :
      ( nil = X0
      | ? [X1] :
          ( ? [X2] :
              ( ssItem(X2)
              & cons(X2,X1) = X0 )
          & ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

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

fof(f259,plain,
    ( ! [X0] :
        ( ~ ssItem(sK3(X0))
        | sK5 != X0
        | ~ ssList(X0)
        | nil = X0 )
    | ~ spl8_3 ),
    inference(subsumption_resolution,[],[f258,f139]) ).

fof(f139,plain,
    ! [X0] :
      ( ssList(sK2(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f258,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sK5 != X0
        | ~ ssList(sK2(X0))
        | ~ ssItem(sK3(X0))
        | nil = X0 )
    | ~ spl8_3 ),
    inference(superposition,[],[f253,f140]) ).

fof(f140,plain,
    ! [X0] :
      ( cons(sK3(X0),sK2(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f253,plain,
    ( ! [X0,X1] :
        ( cons(X0,X1) != sK5
        | ~ ssItem(X0)
        | ~ ssList(X1) )
    | ~ spl8_3 ),
    inference(duplicate_literal_removal,[],[f248]) ).

fof(f248,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X0)
        | ~ ssList(X1)
        | cons(X0,X1) != sK5
        | ~ ssList(X1) )
    | ~ spl8_3 ),
    inference(superposition,[],[f216,f169]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssItem(X1)
          | cons(X1,X0) = app(cons(X1,nil),X0) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).

fof(f216,plain,
    ( ! [X4,X5] :
        ( app(cons(X4,nil),X5) != sK5
        | ~ ssItem(X4)
        | ~ ssList(X5) )
    | ~ spl8_3 ),
    inference(subsumption_resolution,[],[f197,f177]) ).

fof(f177,plain,
    ! [X6,X7] :
      ( app(cons(X6,nil),X7) != sK5
      | app(X7,cons(X6,nil)) = sK4
      | ~ ssList(X7)
      | ~ ssItem(X6) ),
    inference(definition_unfolding,[],[f160,f161,f159]) ).

fof(f159,plain,
    sK7 = sK5,
    inference(cnf_transformation,[],[f135]) ).

fof(f161,plain,
    sK6 = sK4,
    inference(cnf_transformation,[],[f135]) ).

fof(f160,plain,
    ! [X6,X7] :
      ( ~ ssItem(X6)
      | app(X7,cons(X6,nil)) = sK6
      | ~ ssList(X7)
      | app(cons(X6,nil),X7) != sK7 ),
    inference(cnf_transformation,[],[f135]) ).

fof(f197,plain,
    ( ! [X4,X5] :
        ( app(X5,cons(X4,nil)) != sK4
        | ~ ssList(X5)
        | ~ ssItem(X4)
        | app(cons(X4,nil),X5) != sK5 )
    | ~ spl8_3 ),
    inference(avatar_component_clause,[],[f196]) ).

fof(f215,plain,
    ( spl8_1
    | spl8_3 ),
    inference(avatar_split_clause,[],[f164,f196,f187]) ).

fof(f164,plain,
    ! [X4,X5] :
      ( ~ ssItem(X4)
      | nil = sK5
      | app(X5,cons(X4,nil)) != sK4
      | ~ ssList(X5)
      | app(cons(X4,nil),X5) != sK5 ),
    inference(cnf_transformation,[],[f135]) ).

fof(f214,plain,
    ( ~ spl8_2
    | spl8_6 ),
    inference(avatar_split_clause,[],[f165,f209,f191]) ).

fof(f191,plain,
    ( spl8_2
  <=> nil = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f165,plain,
    ( neq(sK5,nil)
    | nil != sK4 ),
    inference(cnf_transformation,[],[f135]) ).

fof(f213,plain,
    spl8_4,
    inference(avatar_split_clause,[],[f174,f200]) ).

fof(f174,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f194,plain,
    ( ~ spl8_1
    | spl8_2 ),
    inference(avatar_split_clause,[],[f176,f191,f187]) ).

fof(f176,plain,
    ( nil = sK4
    | nil != sK5 ),
    inference(definition_unfolding,[],[f162,f161,f159]) ).

fof(f162,plain,
    ( nil = sK6
    | nil != sK7 ),
    inference(cnf_transformation,[],[f135]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SWC313+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13  % 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 : n019.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 18:48:35 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.51  % (11140)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  % (11132)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  % (11132)Instruction limit reached!
% 0.19/0.51  % (11132)------------------------------
% 0.19/0.51  % (11132)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (11132)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (11132)Termination reason: Unknown
% 0.19/0.51  % (11132)Termination phase: Preprocessing 3
% 0.19/0.51  
% 0.19/0.51  % (11132)Memory used [KB]: 1663
% 0.19/0.51  % (11132)Time elapsed: 0.005 s
% 0.19/0.51  % (11132)Instructions burned: 4 (million)
% 0.19/0.51  % (11132)------------------------------
% 0.19/0.51  % (11132)------------------------------
% 0.19/0.52  % (11124)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  % (11119)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)
% 0.19/0.53  % (11121)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)
% 0.19/0.53  % (11131)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)
% 1.35/0.53  % (11147)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)
% 1.35/0.53  % (11134)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)
% 1.35/0.54  % (11145)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 1.35/0.54  % (11128)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)
% 1.35/0.54  % (11126)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)
% 1.35/0.54  % (11136)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)
% 1.35/0.54  % (11139)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)
% 1.35/0.54  % (11122)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)
% 1.35/0.54  % (11120)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)
% 1.35/0.54  % (11125)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)
% 1.35/0.55  % (11118)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 1.35/0.55  % (11120)Instruction limit reached!
% 1.35/0.55  % (11120)------------------------------
% 1.35/0.55  % (11120)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.55  % (11120)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.55  % (11120)Termination reason: Unknown
% 1.35/0.55  % (11120)Termination phase: Naming
% 1.35/0.55  
% 1.35/0.55  % (11120)Memory used [KB]: 1535
% 1.35/0.55  % (11120)Time elapsed: 0.002 s
% 1.35/0.55  % (11120)Instructions burned: 3 (million)
% 1.35/0.55  % (11120)------------------------------
% 1.35/0.55  % (11120)------------------------------
% 1.35/0.55  % (11135)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.35/0.55  % (11138)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)
% 1.35/0.55  % (11124)First to succeed.
% 1.35/0.55  % (11135)Instruction limit reached!
% 1.35/0.55  % (11135)------------------------------
% 1.35/0.55  % (11135)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.55  % (11135)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.55  % (11135)Termination reason: Unknown
% 1.35/0.55  % (11135)Termination phase: Preprocessing 3
% 1.35/0.55  
% 1.35/0.55  % (11135)Memory used [KB]: 1663
% 1.35/0.55  % (11135)Time elapsed: 0.004 s
% 1.35/0.55  % (11135)Instructions burned: 4 (million)
% 1.35/0.55  % (11135)------------------------------
% 1.35/0.55  % (11135)------------------------------
% 1.35/0.55  % (11127)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)
% 1.35/0.55  % (11144)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)
% 1.35/0.55  % (11119)Instruction limit reached!
% 1.35/0.55  % (11119)------------------------------
% 1.35/0.55  % (11119)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.55  % (11143)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 1.48/0.55  % (11141)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)
% 1.48/0.55  % (11119)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.48/0.55  % (11119)Termination reason: Unknown
% 1.48/0.55  % (11119)Termination phase: Saturation
% 1.48/0.55  
% 1.48/0.55  % (11119)Memory used [KB]: 6524
% 1.48/0.55  % (11136)Instruction limit reached!
% 1.48/0.55  % (11136)------------------------------
% 1.48/0.55  % (11136)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.48/0.55  % (11119)Time elapsed: 0.136 s
% 1.48/0.55  % (11119)Instructions burned: 14 (million)
% 1.48/0.55  % (11119)------------------------------
% 1.48/0.55  % (11119)------------------------------
% 1.48/0.55  % (11136)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.48/0.55  % (11136)Termination reason: Unknown
% 1.48/0.55  % (11136)Termination phase: Property scanning
% 1.48/0.55  
% 1.48/0.55  % (11136)Memory used [KB]: 1535
% 1.48/0.55  % (11136)Time elapsed: 0.004 s
% 1.48/0.55  % (11136)Instructions burned: 3 (million)
% 1.48/0.55  % (11136)------------------------------
% 1.48/0.55  % (11136)------------------------------
% 1.48/0.56  % (11142)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)
% 1.48/0.56  % (11129)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)
% 1.48/0.56  % (11124)Refutation found. Thanks to Tanya!
% 1.48/0.56  % SZS status Theorem for theBenchmark
% 1.48/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 1.48/0.56  % (11124)------------------------------
% 1.48/0.56  % (11124)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.48/0.56  % (11124)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.48/0.56  % (11124)Termination reason: Refutation
% 1.48/0.56  
% 1.48/0.56  % (11124)Memory used [KB]: 6140
% 1.48/0.56  % (11124)Time elapsed: 0.116 s
% 1.48/0.56  % (11124)Instructions burned: 6 (million)
% 1.48/0.56  % (11124)------------------------------
% 1.48/0.56  % (11124)------------------------------
% 1.48/0.56  % (11117)Success in time 0.205 s
%------------------------------------------------------------------------------