TSTP Solution File: SWC311+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC311+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 : n029.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 18:40:20 EDT 2022

% Result   : Theorem 0.16s 0.53s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  120 (   7 unt;   0 def)
%            Number of atoms       :  723 ( 253 equ)
%            Maximal formula atoms :   54 (   6 avg)
%            Number of connectives : 1035 ( 432   ~; 433   |; 131   &)
%                                         (  13 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   16 (  14 usr;  12 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  176 ( 140   !;  36   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f733,plain,
    $false,
    inference(avatar_sat_refutation,[],[f232,f236,f261,f266,f267,f278,f292,f296,f299,f303,f330,f688,f732]) ).

fof(f732,plain,
    ( ~ spl10_1
    | ~ spl10_2
    | ~ spl10_12 ),
    inference(avatar_contradiction_clause,[],[f731]) ).

fof(f731,plain,
    ( $false
    | ~ spl10_1
    | ~ spl10_2
    | ~ spl10_12 ),
    inference(subsumption_resolution,[],[f729,f275]) ).

fof(f275,plain,
    ( ssList(nil)
    | ~ spl10_12 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f274,plain,
    ( spl10_12
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_12])]) ).

fof(f729,plain,
    ( ~ ssList(nil)
    | ~ spl10_1
    | ~ spl10_2 ),
    inference(resolution,[],[f702,f223]) ).

fof(f223,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f215]) ).

fof(f215,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(equality_resolution,[],[f172]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

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

fof(f702,plain,
    ( neq(nil,nil)
    | ~ spl10_1
    | ~ spl10_2 ),
    inference(backward_demodulation,[],[f227,f231]) ).

fof(f231,plain,
    ( nil = sK6
    | ~ spl10_2 ),
    inference(avatar_component_clause,[],[f229]) ).

fof(f229,plain,
    ( spl10_2
  <=> nil = sK6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).

fof(f227,plain,
    ( neq(sK6,nil)
    | ~ spl10_1 ),
    inference(avatar_component_clause,[],[f225]) ).

fof(f225,plain,
    ( spl10_1
  <=> neq(sK6,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).

fof(f688,plain,
    ( spl10_2
    | ~ spl10_3
    | ~ spl10_4
    | ~ spl10_8
    | ~ spl10_9 ),
    inference(avatar_contradiction_clause,[],[f687]) ).

fof(f687,plain,
    ( $false
    | spl10_2
    | ~ spl10_3
    | ~ spl10_4
    | ~ spl10_8
    | ~ spl10_9 ),
    inference(subsumption_resolution,[],[f686,f191]) ).

fof(f191,plain,
    ssList(sK6),
    inference(cnf_transformation,[],[f154]) ).

fof(f154,plain,
    ( ssList(sK5)
    & ssList(sK6)
    & ( ! [X4] :
          ( sK7 = X4
          | ~ ssList(X4)
          | ! [X5] :
              ( ~ ssList(X5)
              | ! [X6] :
                  ( ! [X7] :
                      ( hd(sK8) != X7
                      | ~ neq(nil,sK8)
                      | ~ ssItem(X7)
                      | cons(X7,nil) != X6 )
                  | ~ ssList(X6)
                  | ~ neq(nil,sK8)
                  | tl(sK8) != X5
                  | app(X5,X6) != X4 ) ) )
      | ~ neq(sK8,nil) )
    & sK8 = sK6
    & sK7 = sK5
    & ssList(sK8)
    & ( nil = sK7
      | nil != sK8 )
    & ( ( ! [X8] :
            ( ~ ssItem(X8)
            | ! [X9] :
                ( app(X9,cons(X8,nil)) != sK5
                | ~ ssList(X9)
                | app(cons(X8,nil),X9) != sK6 ) )
        & neq(sK6,nil) )
      | ( nil != sK5
        & nil = sK6 ) )
    & ssList(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f116,f153,f152,f151,f150]) ).

fof(f150,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ? [X3] :
                    ( ( ! [X4] :
                          ( X2 = X4
                          | ~ ssList(X4)
                          | ! [X5] :
                              ( ~ ssList(X5)
                              | ! [X6] :
                                  ( ! [X7] :
                                      ( hd(X3) != X7
                                      | ~ neq(nil,X3)
                                      | ~ ssItem(X7)
                                      | cons(X7,nil) != X6 )
                                  | ~ ssList(X6)
                                  | ~ neq(nil,X3)
                                  | tl(X3) != X5
                                  | app(X5,X6) != X4 ) ) )
                      | ~ neq(X3,nil) )
                    & X1 = X3
                    & X0 = X2
                    & ssList(X3)
                    & ( nil = X2
                      | nil != X3 )
                    & ( ( ! [X8] :
                            ( ~ ssItem(X8)
                            | ! [X9] :
                                ( app(X9,cons(X8,nil)) != X0
                                | ~ ssList(X9)
                                | app(cons(X8,nil),X9) != X1 ) )
                        & neq(X1,nil) )
                      | ( nil != X0
                        & nil = X1 ) ) )
                & ssList(X2) ) ) )
   => ( ssList(sK5)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ( ! [X4] :
                        ( X2 = X4
                        | ~ ssList(X4)
                        | ! [X5] :
                            ( ~ ssList(X5)
                            | ! [X6] :
                                ( ! [X7] :
                                    ( hd(X3) != X7
                                    | ~ neq(nil,X3)
                                    | ~ ssItem(X7)
                                    | cons(X7,nil) != X6 )
                                | ~ ssList(X6)
                                | ~ neq(nil,X3)
                                | tl(X3) != X5
                                | app(X5,X6) != X4 ) ) )
                    | ~ neq(X3,nil) )
                  & X1 = X3
                  & sK5 = X2
                  & ssList(X3)
                  & ( nil = X2
                    | nil != X3 )
                  & ( ( ! [X8] :
                          ( ~ ssItem(X8)
                          | ! [X9] :
                              ( app(X9,cons(X8,nil)) != sK5
                              | ~ ssList(X9)
                              | app(cons(X8,nil),X9) != X1 ) )
                      & neq(X1,nil) )
                    | ( nil != sK5
                      & nil = X1 ) ) )
              & ssList(X2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f151,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ? [X3] :
                ( ( ! [X4] :
                      ( X2 = X4
                      | ~ ssList(X4)
                      | ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ! [X7] :
                                  ( hd(X3) != X7
                                  | ~ neq(nil,X3)
                                  | ~ ssItem(X7)
                                  | cons(X7,nil) != X6 )
                              | ~ ssList(X6)
                              | ~ neq(nil,X3)
                              | tl(X3) != X5
                              | app(X5,X6) != X4 ) ) )
                  | ~ neq(X3,nil) )
                & X1 = X3
                & sK5 = X2
                & ssList(X3)
                & ( nil = X2
                  | nil != X3 )
                & ( ( ! [X8] :
                        ( ~ ssItem(X8)
                        | ! [X9] :
                            ( app(X9,cons(X8,nil)) != sK5
                            | ~ ssList(X9)
                            | app(cons(X8,nil),X9) != X1 ) )
                    & neq(X1,nil) )
                  | ( nil != sK5
                    & nil = X1 ) ) )
            & ssList(X2) ) )
   => ( ssList(sK6)
      & ? [X2] :
          ( ? [X3] :
              ( ( ! [X4] :
                    ( X2 = X4
                    | ~ ssList(X4)
                    | ! [X5] :
                        ( ~ ssList(X5)
                        | ! [X6] :
                            ( ! [X7] :
                                ( hd(X3) != X7
                                | ~ neq(nil,X3)
                                | ~ ssItem(X7)
                                | cons(X7,nil) != X6 )
                            | ~ ssList(X6)
                            | ~ neq(nil,X3)
                            | tl(X3) != X5
                            | app(X5,X6) != X4 ) ) )
                | ~ neq(X3,nil) )
              & sK6 = X3
              & sK5 = X2
              & ssList(X3)
              & ( nil = X2
                | nil != X3 )
              & ( ( ! [X8] :
                      ( ~ ssItem(X8)
                      | ! [X9] :
                          ( app(X9,cons(X8,nil)) != sK5
                          | ~ ssList(X9)
                          | app(cons(X8,nil),X9) != sK6 ) )
                  & neq(sK6,nil) )
                | ( nil != sK5
                  & nil = sK6 ) ) )
          & ssList(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f152,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ! [X4] :
                  ( X2 = X4
                  | ~ ssList(X4)
                  | ! [X5] :
                      ( ~ ssList(X5)
                      | ! [X6] :
                          ( ! [X7] :
                              ( hd(X3) != X7
                              | ~ neq(nil,X3)
                              | ~ ssItem(X7)
                              | cons(X7,nil) != X6 )
                          | ~ ssList(X6)
                          | ~ neq(nil,X3)
                          | tl(X3) != X5
                          | app(X5,X6) != X4 ) ) )
              | ~ neq(X3,nil) )
            & sK6 = X3
            & sK5 = X2
            & ssList(X3)
            & ( nil = X2
              | nil != X3 )
            & ( ( ! [X8] :
                    ( ~ ssItem(X8)
                    | ! [X9] :
                        ( app(X9,cons(X8,nil)) != sK5
                        | ~ ssList(X9)
                        | app(cons(X8,nil),X9) != sK6 ) )
                & neq(sK6,nil) )
              | ( nil != sK5
                & nil = sK6 ) ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ! [X4] :
                ( sK7 = X4
                | ~ ssList(X4)
                | ! [X5] :
                    ( ~ ssList(X5)
                    | ! [X6] :
                        ( ! [X7] :
                            ( hd(X3) != X7
                            | ~ neq(nil,X3)
                            | ~ ssItem(X7)
                            | cons(X7,nil) != X6 )
                        | ~ ssList(X6)
                        | ~ neq(nil,X3)
                        | tl(X3) != X5
                        | app(X5,X6) != X4 ) ) )
            | ~ neq(X3,nil) )
          & sK6 = X3
          & sK7 = sK5
          & ssList(X3)
          & ( nil = sK7
            | nil != X3 )
          & ( ( ! [X8] :
                  ( ~ ssItem(X8)
                  | ! [X9] :
                      ( app(X9,cons(X8,nil)) != sK5
                      | ~ ssList(X9)
                      | app(cons(X8,nil),X9) != sK6 ) )
              & neq(sK6,nil) )
            | ( nil != sK5
              & nil = sK6 ) ) )
      & ssList(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f153,plain,
    ( ? [X3] :
        ( ( ! [X4] :
              ( sK7 = X4
              | ~ ssList(X4)
              | ! [X5] :
                  ( ~ ssList(X5)
                  | ! [X6] :
                      ( ! [X7] :
                          ( hd(X3) != X7
                          | ~ neq(nil,X3)
                          | ~ ssItem(X7)
                          | cons(X7,nil) != X6 )
                      | ~ ssList(X6)
                      | ~ neq(nil,X3)
                      | tl(X3) != X5
                      | app(X5,X6) != X4 ) ) )
          | ~ neq(X3,nil) )
        & sK6 = X3
        & sK7 = sK5
        & ssList(X3)
        & ( nil = sK7
          | nil != X3 )
        & ( ( ! [X8] :
                ( ~ ssItem(X8)
                | ! [X9] :
                    ( app(X9,cons(X8,nil)) != sK5
                    | ~ ssList(X9)
                    | app(cons(X8,nil),X9) != sK6 ) )
            & neq(sK6,nil) )
          | ( nil != sK5
            & nil = sK6 ) ) )
   => ( ( ! [X4] :
            ( sK7 = X4
            | ~ ssList(X4)
            | ! [X5] :
                ( ~ ssList(X5)
                | ! [X6] :
                    ( ! [X7] :
                        ( hd(sK8) != X7
                        | ~ neq(nil,sK8)
                        | ~ ssItem(X7)
                        | cons(X7,nil) != X6 )
                    | ~ ssList(X6)
                    | ~ neq(nil,sK8)
                    | tl(sK8) != X5
                    | app(X5,X6) != X4 ) ) )
        | ~ neq(sK8,nil) )
      & sK8 = sK6
      & sK7 = sK5
      & ssList(sK8)
      & ( nil = sK7
        | nil != sK8 )
      & ( ( ! [X8] :
              ( ~ ssItem(X8)
              | ! [X9] :
                  ( app(X9,cons(X8,nil)) != sK5
                  | ~ ssList(X9)
                  | app(cons(X8,nil),X9) != sK6 ) )
          & neq(sK6,nil) )
        | ( nil != sK5
          & nil = sK6 ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f116,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ( ! [X4] :
                        ( X2 = X4
                        | ~ ssList(X4)
                        | ! [X5] :
                            ( ~ ssList(X5)
                            | ! [X6] :
                                ( ! [X7] :
                                    ( hd(X3) != X7
                                    | ~ neq(nil,X3)
                                    | ~ ssItem(X7)
                                    | cons(X7,nil) != X6 )
                                | ~ ssList(X6)
                                | ~ neq(nil,X3)
                                | tl(X3) != X5
                                | app(X5,X6) != X4 ) ) )
                    | ~ neq(X3,nil) )
                  & X1 = X3
                  & X0 = X2
                  & ssList(X3)
                  & ( nil = X2
                    | nil != X3 )
                  & ( ( ! [X8] :
                          ( ~ ssItem(X8)
                          | ! [X9] :
                              ( app(X9,cons(X8,nil)) != X0
                              | ~ ssList(X9)
                              | app(cons(X8,nil),X9) != X1 ) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) ) )
              & ssList(X2) ) ) ),
    inference(flattening,[],[f115]) ).

fof(f115,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & ( ! [X4] :
                        ( X2 = X4
                        | ~ ssList(X4)
                        | ! [X5] :
                            ( ~ ssList(X5)
                            | ! [X6] :
                                ( ! [X7] :
                                    ( hd(X3) != X7
                                    | ~ neq(nil,X3)
                                    | ~ ssItem(X7)
                                    | cons(X7,nil) != X6 )
                                | ~ ssList(X6)
                                | ~ neq(nil,X3)
                                | tl(X3) != X5
                                | app(X5,X6) != X4 ) ) )
                    | ~ neq(X3,nil) )
                  & X1 = X3
                  & ( ( ! [X8] :
                          ( ~ ssItem(X8)
                          | ! [X9] :
                              ( app(X9,cons(X8,nil)) != X0
                              | ~ ssList(X9)
                              | app(cons(X8,nil),X9) != X1 ) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( nil = X2
                    | nil != X3 )
                  & 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
                      | ( ? [X4] :
                            ( ? [X5] :
                                ( ? [X6] :
                                    ( neq(nil,X3)
                                    & app(X5,X6) = X4
                                    & ? [X7] :
                                        ( ssItem(X7)
                                        & neq(nil,X3)
                                        & cons(X7,nil) = X6
                                        & hd(X3) = X7 )
                                    & ssList(X6)
                                    & tl(X3) = X5 )
                                & ssList(X5) )
                            & X2 != X4
                            & ssList(X4) )
                        & neq(X3,nil) )
                      | X1 != X3
                      | ( ( nil != X1
                          | nil = X0 )
                        & ( ? [X8] :
                              ( ssItem(X8)
                              & ? [X9] :
                                  ( app(X9,cons(X8,nil)) = X0
                                  & app(cons(X8,nil),X9) = X1
                                  & ssList(X9) ) )
                          | ~ neq(X1,nil) ) )
                      | ( nil != X2
                        & nil = X3 ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f686,plain,
    ( ~ ssList(sK6)
    | spl10_2
    | ~ spl10_3
    | ~ spl10_4
    | ~ spl10_8
    | ~ spl10_9 ),
    inference(subsumption_resolution,[],[f685,f230]) ).

fof(f230,plain,
    ( nil != sK6
    | spl10_2 ),
    inference(avatar_component_clause,[],[f229]) ).

fof(f685,plain,
    ( nil = sK6
    | ~ ssList(sK6)
    | ~ spl10_3
    | ~ spl10_4
    | ~ spl10_8
    | ~ spl10_9 ),
    inference(trivial_inequality_removal,[],[f684]) ).

fof(f684,plain,
    ( nil = sK6
    | sK6 != sK6
    | ~ ssList(sK6)
    | ~ spl10_3
    | ~ spl10_4
    | ~ spl10_8
    | ~ spl10_9 ),
    inference(superposition,[],[f683,f201]) ).

fof(f201,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f104]) ).

fof(f104,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/sandbox/benchmark/theBenchmark.p',ax78) ).

fof(f683,plain,
    ( sK6 != cons(hd(sK6),tl(sK6))
    | ~ spl10_3
    | ~ spl10_4
    | ~ spl10_8
    | ~ spl10_9 ),
    inference(subsumption_resolution,[],[f682,f239]) ).

fof(f239,plain,
    ( ssList(tl(sK6))
    | ~ spl10_4 ),
    inference(avatar_component_clause,[],[f238]) ).

fof(f238,plain,
    ( spl10_4
  <=> ssList(tl(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).

fof(f682,plain,
    ( sK6 != cons(hd(sK6),tl(sK6))
    | ~ ssList(tl(sK6))
    | ~ spl10_3
    | ~ spl10_8
    | ~ spl10_9 ),
    inference(subsumption_resolution,[],[f681,f259]) ).

fof(f259,plain,
    ( ssItem(hd(sK6))
    | ~ spl10_9 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f258,plain,
    ( spl10_9
  <=> ssItem(hd(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_9])]) ).

fof(f681,plain,
    ( sK6 != cons(hd(sK6),tl(sK6))
    | ~ ssItem(hd(sK6))
    | ~ ssList(tl(sK6))
    | ~ spl10_3
    | ~ spl10_8 ),
    inference(trivial_inequality_removal,[],[f678]) ).

fof(f678,plain,
    ( sK6 != cons(hd(sK6),tl(sK6))
    | ~ ssList(tl(sK6))
    | ~ ssItem(hd(sK6))
    | sK5 != sK5
    | ~ spl10_3
    | ~ spl10_8 ),
    inference(superposition,[],[f406,f256]) ).

fof(f256,plain,
    ( app(tl(sK6),cons(hd(sK6),nil)) = sK5
    | ~ spl10_8 ),
    inference(avatar_component_clause,[],[f254]) ).

fof(f254,plain,
    ( spl10_8
  <=> app(tl(sK6),cons(hd(sK6),nil)) = sK5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_8])]) ).

fof(f406,plain,
    ( ! [X0,X1] :
        ( app(X1,cons(X0,nil)) != sK5
        | ~ ssList(X1)
        | cons(X0,X1) != sK6
        | ~ ssItem(X0) )
    | ~ spl10_3 ),
    inference(duplicate_literal_removal,[],[f402]) ).

fof(f402,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(X0)
        | ~ ssItem(X0)
        | cons(X0,X1) != sK6
        | ~ ssList(X1)
        | app(X1,cons(X0,nil)) != sK5
        | ~ ssList(X1) )
    | ~ spl10_3 ),
    inference(superposition,[],[f235,f203]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,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(f235,plain,
    ( ! [X8,X9] :
        ( app(cons(X8,nil),X9) != sK6
        | app(X9,cons(X8,nil)) != sK5
        | ~ ssItem(X8)
        | ~ ssList(X9) )
    | ~ spl10_3 ),
    inference(avatar_component_clause,[],[f234]) ).

fof(f234,plain,
    ( spl10_3
  <=> ! [X9,X8] :
        ( app(cons(X8,nil),X9) != sK6
        | app(X9,cons(X8,nil)) != sK5
        | ~ ssItem(X8)
        | ~ ssList(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).

fof(f330,plain,
    ( spl10_2
    | spl10_6
    | ~ spl10_12 ),
    inference(avatar_contradiction_clause,[],[f329]) ).

fof(f329,plain,
    ( $false
    | spl10_2
    | spl10_6
    | ~ spl10_12 ),
    inference(subsumption_resolution,[],[f328,f275]) ).

fof(f328,plain,
    ( ~ ssList(nil)
    | spl10_2
    | spl10_6 ),
    inference(subsumption_resolution,[],[f327,f191]) ).

fof(f327,plain,
    ( ~ ssList(sK6)
    | ~ ssList(nil)
    | spl10_2
    | spl10_6 ),
    inference(subsumption_resolution,[],[f324,f230]) ).

fof(f324,plain,
    ( nil = sK6
    | ~ ssList(nil)
    | ~ ssList(sK6)
    | spl10_6 ),
    inference(resolution,[],[f173,f248]) ).

fof(f248,plain,
    ( ~ neq(nil,sK6)
    | spl10_6 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f246,plain,
    ( spl10_6
  <=> neq(nil,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_6])]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X0)
      | X0 = X1
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f303,plain,
    ( spl10_5
    | ~ spl10_9
    | ~ spl10_12 ),
    inference(avatar_contradiction_clause,[],[f302]) ).

fof(f302,plain,
    ( $false
    | spl10_5
    | ~ spl10_9
    | ~ spl10_12 ),
    inference(subsumption_resolution,[],[f301,f259]) ).

fof(f301,plain,
    ( ~ ssItem(hd(sK6))
    | spl10_5
    | ~ spl10_12 ),
    inference(subsumption_resolution,[],[f300,f275]) ).

fof(f300,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sK6))
    | spl10_5 ),
    inference(resolution,[],[f197,f244]) ).

fof(f244,plain,
    ( ~ ssList(cons(hd(sK6),nil))
    | spl10_5 ),
    inference(avatar_component_clause,[],[f242]) ).

fof(f242,plain,
    ( spl10_5
  <=> ssList(cons(hd(sK6),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_5])]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssList(X0)
      | ~ ssItem(X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

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

fof(f299,plain,
    ( ~ spl10_5
    | ~ spl10_4
    | spl10_7 ),
    inference(avatar_split_clause,[],[f298,f250,f238,f242]) ).

fof(f250,plain,
    ( spl10_7
  <=> ssList(app(tl(sK6),cons(hd(sK6),nil))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).

fof(f298,plain,
    ( ~ ssList(cons(hd(sK6),nil))
    | ~ spl10_4
    | spl10_7 ),
    inference(subsumption_resolution,[],[f297,f239]) ).

fof(f297,plain,
    ( ~ ssList(tl(sK6))
    | ~ ssList(cons(hd(sK6),nil))
    | spl10_7 ),
    inference(resolution,[],[f252,f195]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X0)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ssList(app(X0,X1)) ) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).

fof(f252,plain,
    ( ~ ssList(app(tl(sK6),cons(hd(sK6),nil)))
    | spl10_7 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f296,plain,
    ( spl10_2
    | spl10_4 ),
    inference(avatar_contradiction_clause,[],[f295]) ).

fof(f295,plain,
    ( $false
    | spl10_2
    | spl10_4 ),
    inference(subsumption_resolution,[],[f294,f230]) ).

fof(f294,plain,
    ( nil = sK6
    | spl10_4 ),
    inference(subsumption_resolution,[],[f293,f191]) ).

fof(f293,plain,
    ( ~ ssList(sK6)
    | nil = sK6
    | spl10_4 ),
    inference(resolution,[],[f240,f167]) ).

fof(f167,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,plain,
    ! [X0] :
      ( nil = X0
      | ssList(tl(X0))
      | ~ ssList(X0) ),
    inference(flattening,[],[f132]) ).

fof(f132,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/sandbox/benchmark/theBenchmark.p',ax24) ).

fof(f240,plain,
    ( ~ ssList(tl(sK6))
    | spl10_4 ),
    inference(avatar_component_clause,[],[f238]) ).

fof(f292,plain,
    ( spl10_2
    | spl10_9 ),
    inference(avatar_contradiction_clause,[],[f291]) ).

fof(f291,plain,
    ( $false
    | spl10_2
    | spl10_9 ),
    inference(subsumption_resolution,[],[f290,f230]) ).

fof(f290,plain,
    ( nil = sK6
    | spl10_9 ),
    inference(subsumption_resolution,[],[f289,f191]) ).

fof(f289,plain,
    ( ~ ssList(sK6)
    | nil = sK6
    | spl10_9 ),
    inference(resolution,[],[f196,f260]) ).

fof(f260,plain,
    ( ~ ssItem(hd(sK6))
    | spl10_9 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f196,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f114]) ).

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

fof(f113,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/sandbox/benchmark/theBenchmark.p',ax22) ).

fof(f278,plain,
    spl10_12,
    inference(avatar_split_clause,[],[f168,f274]) ).

fof(f168,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f267,plain,
    ( spl10_1
    | ~ spl10_10 ),
    inference(avatar_split_clause,[],[f183,f263,f225]) ).

fof(f263,plain,
    ( spl10_10
  <=> nil = sK5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_10])]) ).

fof(f183,plain,
    ( nil != sK5
    | neq(sK6,nil) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f266,plain,
    ( spl10_10
    | ~ spl10_2 ),
    inference(avatar_split_clause,[],[f210,f229,f263]) ).

fof(f210,plain,
    ( nil != sK6
    | nil = sK5 ),
    inference(definition_unfolding,[],[f186,f188,f189]) ).

fof(f189,plain,
    sK8 = sK6,
    inference(cnf_transformation,[],[f154]) ).

fof(f188,plain,
    sK7 = sK5,
    inference(cnf_transformation,[],[f154]) ).

fof(f186,plain,
    ( nil = sK7
    | nil != sK8 ),
    inference(cnf_transformation,[],[f154]) ).

fof(f261,plain,
    ( ~ spl10_4
    | ~ spl10_5
    | ~ spl10_6
    | ~ spl10_7
    | ~ spl10_1
    | spl10_8
    | ~ spl10_9 ),
    inference(avatar_split_clause,[],[f222,f258,f254,f225,f250,f246,f242,f238]) ).

fof(f222,plain,
    ( ~ ssItem(hd(sK6))
    | app(tl(sK6),cons(hd(sK6),nil)) = sK5
    | ~ neq(sK6,nil)
    | ~ ssList(app(tl(sK6),cons(hd(sK6),nil)))
    | ~ neq(nil,sK6)
    | ~ ssList(cons(hd(sK6),nil))
    | ~ ssList(tl(sK6)) ),
    inference(duplicate_literal_removal,[],[f219]) ).

fof(f219,plain,
    ( app(tl(sK6),cons(hd(sK6),nil)) = sK5
    | ~ neq(nil,sK6)
    | ~ ssList(app(tl(sK6),cons(hd(sK6),nil)))
    | ~ neq(nil,sK6)
    | ~ ssItem(hd(sK6))
    | ~ ssList(cons(hd(sK6),nil))
    | ~ ssList(tl(sK6))
    | ~ neq(sK6,nil) ),
    inference(equality_resolution,[],[f218]) ).

fof(f218,plain,
    ! [X4] :
      ( sK5 = X4
      | ~ ssList(X4)
      | ~ ssList(tl(sK6))
      | ~ neq(nil,sK6)
      | ~ ssItem(hd(sK6))
      | ~ ssList(cons(hd(sK6),nil))
      | ~ neq(nil,sK6)
      | app(tl(sK6),cons(hd(sK6),nil)) != X4
      | ~ neq(sK6,nil) ),
    inference(equality_resolution,[],[f217]) ).

fof(f217,plain,
    ! [X4,X5] :
      ( sK5 = X4
      | ~ ssList(X4)
      | ~ ssList(X5)
      | ~ neq(nil,sK6)
      | ~ ssItem(hd(sK6))
      | ~ ssList(cons(hd(sK6),nil))
      | ~ neq(nil,sK6)
      | tl(sK6) != X5
      | app(X5,cons(hd(sK6),nil)) != X4
      | ~ neq(sK6,nil) ),
    inference(equality_resolution,[],[f216]) ).

fof(f216,plain,
    ! [X6,X4,X5] :
      ( sK5 = X4
      | ~ ssList(X4)
      | ~ ssList(X5)
      | ~ neq(nil,sK6)
      | ~ ssItem(hd(sK6))
      | cons(hd(sK6),nil) != X6
      | ~ ssList(X6)
      | ~ neq(nil,sK6)
      | tl(sK6) != X5
      | app(X5,X6) != X4
      | ~ neq(sK6,nil) ),
    inference(equality_resolution,[],[f208]) ).

fof(f208,plain,
    ! [X6,X7,X4,X5] :
      ( sK5 = X4
      | ~ ssList(X4)
      | ~ ssList(X5)
      | hd(sK6) != X7
      | ~ neq(nil,sK6)
      | ~ ssItem(X7)
      | cons(X7,nil) != X6
      | ~ ssList(X6)
      | ~ neq(nil,sK6)
      | tl(sK6) != X5
      | app(X5,X6) != X4
      | ~ neq(sK6,nil) ),
    inference(definition_unfolding,[],[f190,f188,f189,f189,f189,f189,f189]) ).

fof(f190,plain,
    ! [X6,X7,X4,X5] :
      ( sK7 = X4
      | ~ ssList(X4)
      | ~ ssList(X5)
      | hd(sK8) != X7
      | ~ neq(nil,sK8)
      | ~ ssItem(X7)
      | cons(X7,nil) != X6
      | ~ ssList(X6)
      | ~ neq(nil,sK8)
      | tl(sK8) != X5
      | app(X5,X6) != X4
      | ~ neq(sK8,nil) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f236,plain,
    ( spl10_2
    | spl10_3 ),
    inference(avatar_split_clause,[],[f184,f234,f229]) ).

fof(f184,plain,
    ! [X8,X9] :
      ( app(cons(X8,nil),X9) != sK6
      | ~ ssList(X9)
      | ~ ssItem(X8)
      | nil = sK6
      | app(X9,cons(X8,nil)) != sK5 ),
    inference(cnf_transformation,[],[f154]) ).

fof(f232,plain,
    ( spl10_1
    | spl10_2 ),
    inference(avatar_split_clause,[],[f182,f229,f225]) ).

fof(f182,plain,
    ( nil = sK6
    | neq(sK6,nil) ),
    inference(cnf_transformation,[],[f154]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SWC311+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.32  % Computer : n029.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Aug 30 18:55:27 EDT 2022
% 0.11/0.32  % CPUTime    : 
% 0.16/0.48  % (29035)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)
% 0.16/0.49  % (29053)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)
% 0.16/0.49  % (29052)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)
% 0.16/0.49  % (29044)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)
% 0.16/0.51  % (29036)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)
% 0.16/0.51  % (29042)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)
% 0.16/0.51  % (29044)Instruction limit reached!
% 0.16/0.51  % (29044)------------------------------
% 0.16/0.51  % (29044)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.51  % (29044)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.51  % (29044)Termination reason: Unknown
% 0.16/0.51  % (29044)Termination phase: Function definition elimination
% 0.16/0.51  
% 0.16/0.51  % (29044)Memory used [KB]: 1791
% 0.16/0.51  % (29044)Time elapsed: 0.012 s
% 0.16/0.51  % (29044)Instructions burned: 8 (million)
% 0.16/0.51  % (29044)------------------------------
% 0.16/0.51  % (29044)------------------------------
% 0.16/0.52  % (29033)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)
% 0.16/0.52  % (29035)First to succeed.
% 0.16/0.52  % (29030)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)
% 0.16/0.52  % (29032)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)
% 0.16/0.52  % (29031)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)
% 0.16/0.52  % (29034)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)
% 0.16/0.52  % (29031)Instruction limit reached!
% 0.16/0.52  % (29031)------------------------------
% 0.16/0.52  % (29031)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.52  % (29031)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.52  % (29031)Termination reason: Unknown
% 0.16/0.52  % (29031)Termination phase: Naming
% 0.16/0.52  
% 0.16/0.52  % (29031)Memory used [KB]: 1535
% 0.16/0.52  % (29031)Time elapsed: 0.003 s
% 0.16/0.52  % (29031)Instructions burned: 3 (million)
% 0.16/0.52  % (29031)------------------------------
% 0.16/0.52  % (29031)------------------------------
% 0.16/0.53  % (29035)Refutation found. Thanks to Tanya!
% 0.16/0.53  % SZS status Theorem for theBenchmark
% 0.16/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.53  % (29035)------------------------------
% 0.16/0.53  % (29035)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.53  % (29035)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.53  % (29035)Termination reason: Refutation
% 0.16/0.53  
% 0.16/0.53  % (29035)Memory used [KB]: 6396
% 0.16/0.53  % (29035)Time elapsed: 0.124 s
% 0.16/0.53  % (29035)Instructions burned: 19 (million)
% 0.16/0.53  % (29035)------------------------------
% 0.16/0.53  % (29035)------------------------------
% 0.16/0.53  % (29028)Success in time 0.195 s
%------------------------------------------------------------------------------