TSTP Solution File: SWC339+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC339+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_sat --cores 0 -t %d %s

% Computer : n010.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 18:43:14 EDT 2022

% Result   : Theorem 2.45s 0.69s
% Output   : Refutation 2.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   46 (  13 unt;   0 def)
%            Number of atoms       :  559 ( 162 equ)
%            Maximal formula atoms :   56 (  12 avg)
%            Number of connectives :  823 ( 310   ~; 271   |; 210   &)
%                                         (   4 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (  10 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  249 ( 165   !;  84   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f744,plain,
    $false,
    inference(avatar_sat_refutation,[],[f609,f633,f741]) ).

fof(f741,plain,
    spl59_1,
    inference(avatar_contradiction_clause,[],[f740]) ).

fof(f740,plain,
    ( $false
    | spl59_1 ),
    inference(subsumption_resolution,[],[f739,f565]) ).

fof(f565,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f553,f542]) ).

fof(f542,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f347]) ).

fof(f347,plain,
    ( ssList(sK53)
    & ssList(sK54)
    & ssList(sK55)
    & ssList(sK57)
    & ! [X6] :
        ( ! [X7] :
            ( ~ ssList(X7)
            | ! [X8] :
                ( ! [X9] :
                    ( sK55 != app(X9,cons(X8,nil))
                    | ~ leq(X8,X6)
                    | ~ ssList(X9) )
                | ~ ssItem(X8) )
            | app(cons(X6,nil),X7) != sK58 )
        | ~ ssItem(X6) )
    & ssList(sK58)
    & app(app(sK57,sK55),sK58) = sK56
    & ! [X10] :
        ( ~ ssItem(X10)
        | ! [X11] :
            ( ! [X12] :
                ( ! [X13] :
                    ( sK55 != app(cons(X12,nil),X13)
                    | ~ leq(X10,X12)
                    | ~ ssList(X13) )
                | ~ ssItem(X12) )
            | ~ ssList(X11)
            | app(X11,cons(X10,nil)) != sK57 ) )
    & totalorderedP(sK55)
    & ( nil != sK55
      | nil = sK56 )
    & ( ~ segmentP(sK54,sK53)
      | ~ totalorderedP(sK53) )
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f205,f346,f345,f344,f343,f342,f341]) ).

fof(f341,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ? [X4] :
                        ( ssList(X4)
                        & ? [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( ~ ssList(X7)
                                    | ! [X8] :
                                        ( ! [X9] :
                                            ( app(X9,cons(X8,nil)) != X2
                                            | ~ leq(X8,X6)
                                            | ~ ssList(X9) )
                                        | ~ ssItem(X8) )
                                    | app(cons(X6,nil),X7) != X5 )
                                | ~ ssItem(X6) )
                            & ssList(X5)
                            & app(app(X4,X2),X5) = X3
                            & ! [X10] :
                                ( ~ ssItem(X10)
                                | ! [X11] :
                                    ( ! [X12] :
                                        ( ! [X13] :
                                            ( app(cons(X12,nil),X13) != X2
                                            | ~ leq(X10,X12)
                                            | ~ ssList(X13) )
                                        | ~ ssItem(X12) )
                                    | ~ ssList(X11)
                                    | app(X11,cons(X10,nil)) != X4 ) )
                            & totalorderedP(X2) ) )
                    & ( nil != X2
                      | nil = X3 )
                    & ( ~ segmentP(X1,X0)
                      | ~ totalorderedP(X0) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) ) ) ) )
   => ( ssList(sK53)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ~ ssList(X7)
                                  | ! [X8] :
                                      ( ! [X9] :
                                          ( app(X9,cons(X8,nil)) != X2
                                          | ~ leq(X8,X6)
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5 )
                              | ~ ssItem(X6) )
                          & ssList(X5)
                          & app(app(X4,X2),X5) = X3
                          & ! [X10] :
                              ( ~ ssItem(X10)
                              | ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( app(cons(X12,nil),X13) != X2
                                          | ~ leq(X10,X12)
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | ~ ssList(X11)
                                  | app(X11,cons(X10,nil)) != X4 ) )
                          & totalorderedP(X2) ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ( ~ segmentP(X1,sK53)
                    | ~ totalorderedP(sK53) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f342,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ? [X4] :
                    ( ssList(X4)
                    & ? [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ~ ssList(X7)
                                | ! [X8] :
                                    ( ! [X9] :
                                        ( app(X9,cons(X8,nil)) != X2
                                        | ~ leq(X8,X6)
                                        | ~ ssList(X9) )
                                    | ~ ssItem(X8) )
                                | app(cons(X6,nil),X7) != X5 )
                            | ~ ssItem(X6) )
                        & ssList(X5)
                        & app(app(X4,X2),X5) = X3
                        & ! [X10] :
                            ( ~ ssItem(X10)
                            | ! [X11] :
                                ( ! [X12] :
                                    ( ! [X13] :
                                        ( app(cons(X12,nil),X13) != X2
                                        | ~ leq(X10,X12)
                                        | ~ ssList(X13) )
                                    | ~ ssItem(X12) )
                                | ~ ssList(X11)
                                | app(X11,cons(X10,nil)) != X4 ) )
                        & totalorderedP(X2) ) )
                & ( nil != X2
                  | nil = X3 )
                & ( ~ segmentP(X1,sK53)
                  | ~ totalorderedP(sK53) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) ) ) )
   => ( ssList(sK54)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ? [X4] :
                  ( ssList(X4)
                  & ? [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ~ ssList(X7)
                              | ! [X8] :
                                  ( ! [X9] :
                                      ( app(X9,cons(X8,nil)) != X2
                                      | ~ leq(X8,X6)
                                      | ~ ssList(X9) )
                                  | ~ ssItem(X8) )
                              | app(cons(X6,nil),X7) != X5 )
                          | ~ ssItem(X6) )
                      & ssList(X5)
                      & app(app(X4,X2),X5) = X3
                      & ! [X10] :
                          ( ~ ssItem(X10)
                          | ! [X11] :
                              ( ! [X12] :
                                  ( ! [X13] :
                                      ( app(cons(X12,nil),X13) != X2
                                      | ~ leq(X10,X12)
                                      | ~ ssList(X13) )
                                  | ~ ssItem(X12) )
                              | ~ ssList(X11)
                              | app(X11,cons(X10,nil)) != X4 ) )
                      & totalorderedP(X2) ) )
              & ( nil != X2
                | nil = X3 )
              & ( ~ segmentP(sK54,sK53)
                | ~ totalorderedP(sK53) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f343,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ? [X4] :
                ( ssList(X4)
                & ? [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ~ ssList(X7)
                            | ! [X8] :
                                ( ! [X9] :
                                    ( app(X9,cons(X8,nil)) != X2
                                    | ~ leq(X8,X6)
                                    | ~ ssList(X9) )
                                | ~ ssItem(X8) )
                            | app(cons(X6,nil),X7) != X5 )
                        | ~ ssItem(X6) )
                    & ssList(X5)
                    & app(app(X4,X2),X5) = X3
                    & ! [X10] :
                        ( ~ ssItem(X10)
                        | ! [X11] :
                            ( ! [X12] :
                                ( ! [X13] :
                                    ( app(cons(X12,nil),X13) != X2
                                    | ~ leq(X10,X12)
                                    | ~ ssList(X13) )
                                | ~ ssItem(X12) )
                            | ~ ssList(X11)
                            | app(X11,cons(X10,nil)) != X4 ) )
                    & totalorderedP(X2) ) )
            & ( nil != X2
              | nil = X3 )
            & ( ~ segmentP(sK54,sK53)
              | ~ totalorderedP(sK53) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) ) )
   => ( ssList(sK55)
      & ? [X3] :
          ( ? [X4] :
              ( ssList(X4)
              & ? [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ~ ssList(X7)
                          | ! [X8] :
                              ( ! [X9] :
                                  ( sK55 != app(X9,cons(X8,nil))
                                  | ~ leq(X8,X6)
                                  | ~ ssList(X9) )
                              | ~ ssItem(X8) )
                          | app(cons(X6,nil),X7) != X5 )
                      | ~ ssItem(X6) )
                  & ssList(X5)
                  & app(app(X4,sK55),X5) = X3
                  & ! [X10] :
                      ( ~ ssItem(X10)
                      | ! [X11] :
                          ( ! [X12] :
                              ( ! [X13] :
                                  ( sK55 != app(cons(X12,nil),X13)
                                  | ~ leq(X10,X12)
                                  | ~ ssList(X13) )
                              | ~ ssItem(X12) )
                          | ~ ssList(X11)
                          | app(X11,cons(X10,nil)) != X4 ) )
                  & totalorderedP(sK55) ) )
          & ( nil != sK55
            | nil = X3 )
          & ( ~ segmentP(sK54,sK53)
            | ~ totalorderedP(sK53) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( ssList(X4)
            & ? [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ~ ssList(X7)
                        | ! [X8] :
                            ( ! [X9] :
                                ( sK55 != app(X9,cons(X8,nil))
                                | ~ leq(X8,X6)
                                | ~ ssList(X9) )
                            | ~ ssItem(X8) )
                        | app(cons(X6,nil),X7) != X5 )
                    | ~ ssItem(X6) )
                & ssList(X5)
                & app(app(X4,sK55),X5) = X3
                & ! [X10] :
                    ( ~ ssItem(X10)
                    | ! [X11] :
                        ( ! [X12] :
                            ( ! [X13] :
                                ( sK55 != app(cons(X12,nil),X13)
                                | ~ leq(X10,X12)
                                | ~ ssList(X13) )
                            | ~ ssItem(X12) )
                        | ~ ssList(X11)
                        | app(X11,cons(X10,nil)) != X4 ) )
                & totalorderedP(sK55) ) )
        & ( nil != sK55
          | nil = X3 )
        & ( ~ segmentP(sK54,sK53)
          | ~ totalorderedP(sK53) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ? [X4] :
          ( ssList(X4)
          & ? [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ~ ssList(X7)
                      | ! [X8] :
                          ( ! [X9] :
                              ( sK55 != app(X9,cons(X8,nil))
                              | ~ leq(X8,X6)
                              | ~ ssList(X9) )
                          | ~ ssItem(X8) )
                      | app(cons(X6,nil),X7) != X5 )
                  | ~ ssItem(X6) )
              & ssList(X5)
              & sK56 = app(app(X4,sK55),X5)
              & ! [X10] :
                  ( ~ ssItem(X10)
                  | ! [X11] :
                      ( ! [X12] :
                          ( ! [X13] :
                              ( sK55 != app(cons(X12,nil),X13)
                              | ~ leq(X10,X12)
                              | ~ ssList(X13) )
                          | ~ ssItem(X12) )
                      | ~ ssList(X11)
                      | app(X11,cons(X10,nil)) != X4 ) )
              & totalorderedP(sK55) ) )
      & ( nil != sK55
        | nil = sK56 )
      & ( ~ segmentP(sK54,sK53)
        | ~ totalorderedP(sK53) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X4] :
        ( ssList(X4)
        & ? [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ~ ssList(X7)
                    | ! [X8] :
                        ( ! [X9] :
                            ( sK55 != app(X9,cons(X8,nil))
                            | ~ leq(X8,X6)
                            | ~ ssList(X9) )
                        | ~ ssItem(X8) )
                    | app(cons(X6,nil),X7) != X5 )
                | ~ ssItem(X6) )
            & ssList(X5)
            & sK56 = app(app(X4,sK55),X5)
            & ! [X10] :
                ( ~ ssItem(X10)
                | ! [X11] :
                    ( ! [X12] :
                        ( ! [X13] :
                            ( sK55 != app(cons(X12,nil),X13)
                            | ~ leq(X10,X12)
                            | ~ ssList(X13) )
                        | ~ ssItem(X12) )
                    | ~ ssList(X11)
                    | app(X11,cons(X10,nil)) != X4 ) )
            & totalorderedP(sK55) ) )
   => ( ssList(sK57)
      & ? [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ~ ssList(X7)
                  | ! [X8] :
                      ( ! [X9] :
                          ( sK55 != app(X9,cons(X8,nil))
                          | ~ leq(X8,X6)
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  | app(cons(X6,nil),X7) != X5 )
              | ~ ssItem(X6) )
          & ssList(X5)
          & sK56 = app(app(sK57,sK55),X5)
          & ! [X10] :
              ( ~ ssItem(X10)
              | ! [X11] :
                  ( ! [X12] :
                      ( ! [X13] :
                          ( sK55 != app(cons(X12,nil),X13)
                          | ~ leq(X10,X12)
                          | ~ ssList(X13) )
                      | ~ ssItem(X12) )
                  | ~ ssList(X11)
                  | app(X11,cons(X10,nil)) != sK57 ) )
          & totalorderedP(sK55) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ~ ssList(X7)
                | ! [X8] :
                    ( ! [X9] :
                        ( sK55 != app(X9,cons(X8,nil))
                        | ~ leq(X8,X6)
                        | ~ ssList(X9) )
                    | ~ ssItem(X8) )
                | app(cons(X6,nil),X7) != X5 )
            | ~ ssItem(X6) )
        & ssList(X5)
        & sK56 = app(app(sK57,sK55),X5)
        & ! [X10] :
            ( ~ ssItem(X10)
            | ! [X11] :
                ( ! [X12] :
                    ( ! [X13] :
                        ( sK55 != app(cons(X12,nil),X13)
                        | ~ leq(X10,X12)
                        | ~ ssList(X13) )
                    | ~ ssItem(X12) )
                | ~ ssList(X11)
                | app(X11,cons(X10,nil)) != sK57 ) )
        & totalorderedP(sK55) )
   => ( ! [X6] :
          ( ! [X7] :
              ( ~ ssList(X7)
              | ! [X8] :
                  ( ! [X9] :
                      ( sK55 != app(X9,cons(X8,nil))
                      | ~ leq(X8,X6)
                      | ~ ssList(X9) )
                  | ~ ssItem(X8) )
              | app(cons(X6,nil),X7) != sK58 )
          | ~ ssItem(X6) )
      & ssList(sK58)
      & app(app(sK57,sK55),sK58) = sK56
      & ! [X10] :
          ( ~ ssItem(X10)
          | ! [X11] :
              ( ! [X12] :
                  ( ! [X13] :
                      ( sK55 != app(cons(X12,nil),X13)
                      | ~ leq(X10,X12)
                      | ~ ssList(X13) )
                  | ~ ssItem(X12) )
              | ~ ssList(X11)
              | app(X11,cons(X10,nil)) != sK57 ) )
      & totalorderedP(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f205,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ~ ssList(X7)
                                  | ! [X8] :
                                      ( ! [X9] :
                                          ( app(X9,cons(X8,nil)) != X2
                                          | ~ leq(X8,X6)
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5 )
                              | ~ ssItem(X6) )
                          & ssList(X5)
                          & app(app(X4,X2),X5) = X3
                          & ! [X10] :
                              ( ~ ssItem(X10)
                              | ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( app(cons(X12,nil),X13) != X2
                                          | ~ leq(X10,X12)
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | ~ ssList(X11)
                                  | app(X11,cons(X10,nil)) != X4 ) )
                          & totalorderedP(X2) ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ( ~ segmentP(X1,X0)
                    | ~ totalorderedP(X0) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) ) ) ) ),
    inference(flattening,[],[f204]) ).

fof(f204,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X2
                    | nil = X3 )
                  & X0 = X2
                  & X1 = X3
                  & ? [X4] :
                      ( ? [X5] :
                          ( totalorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ! [X10] :
                              ( ~ ssItem(X10)
                              | ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( app(cons(X12,nil),X13) != X2
                                          | ~ leq(X10,X12)
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | ~ ssList(X11)
                                  | app(X11,cons(X10,nil)) != X4 ) )
                          & ! [X6] :
                              ( ! [X7] :
                                  ( ~ ssList(X7)
                                  | ! [X8] :
                                      ( ! [X9] :
                                          ( app(X9,cons(X8,nil)) != X2
                                          | ~ leq(X8,X6)
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5 )
                              | ~ ssItem(X6) )
                          & ssList(X5) )
                      & ssList(X4) )
                  & ( ~ segmentP(X1,X0)
                    | ~ totalorderedP(X0) )
                  & 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)
                   => ( ( nil = X2
                        & nil != X3 )
                      | X0 != X2
                      | X1 != X3
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( ~ totalorderedP(X2)
                                | app(app(X4,X2),X5) != X3
                                | ? [X10] :
                                    ( ssItem(X10)
                                    & ? [X11] :
                                        ( ? [X12] :
                                            ( ? [X13] :
                                                ( ssList(X13)
                                                & app(cons(X12,nil),X13) = X2
                                                & leq(X10,X12) )
                                            & ssItem(X12) )
                                        & app(X11,cons(X10,nil)) = X4
                                        & ssList(X11) ) )
                                | ? [X6] :
                                    ( ssItem(X6)
                                    & ? [X7] :
                                        ( ssList(X7)
                                        & ? [X8] :
                                            ( ssItem(X8)
                                            & ? [X9] :
                                                ( app(X9,cons(X8,nil)) = X2
                                                & ssList(X9)
                                                & leq(X8,X6) ) )
                                        & app(cons(X6,nil),X7) = X5 ) ) ) ) )
                      | ( totalorderedP(X0)
                        & segmentP(X1,X0) ) ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( X1 != X3
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( ~ totalorderedP(X2)
                                | ? [X10] :
                                    ( ssItem(X10)
                                    & ? [X11] :
                                        ( ? [X12] :
                                            ( ? [X13] :
                                                ( leq(X12,X10)
                                                & ssList(X13)
                                                & app(X13,cons(X12,nil)) = X2 )
                                            & ssItem(X12) )
                                        & app(cons(X10,nil),X11) = X5
                                        & ssList(X11) ) )
                                | app(app(X4,X2),X5) != X3
                                | ? [X6] :
                                    ( ssItem(X6)
                                    & ? [X7] :
                                        ( ? [X8] :
                                            ( ? [X9] :
                                                ( app(cons(X8,nil),X9) = X2
                                                & ssList(X9)
                                                & leq(X6,X8) )
                                            & ssItem(X8) )
                                        & app(X7,cons(X6,nil)) = X4
                                        & ssList(X7) ) ) ) ) )
                      | ( totalorderedP(X0)
                        & segmentP(X1,X0) )
                      | X0 != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X1 != X3
                    | ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( ~ totalorderedP(X2)
                              | ? [X10] :
                                  ( ssItem(X10)
                                  & ? [X11] :
                                      ( ? [X12] :
                                          ( ? [X13] :
                                              ( leq(X12,X10)
                                              & ssList(X13)
                                              & app(X13,cons(X12,nil)) = X2 )
                                          & ssItem(X12) )
                                      & app(cons(X10,nil),X11) = X5
                                      & ssList(X11) ) )
                              | app(app(X4,X2),X5) != X3
                              | ? [X6] :
                                  ( ssItem(X6)
                                  & ? [X7] :
                                      ( ? [X8] :
                                          ( ? [X9] :
                                              ( app(cons(X8,nil),X9) = X2
                                              & ssList(X9)
                                              & leq(X6,X8) )
                                          & ssItem(X8) )
                                      & app(X7,cons(X6,nil)) = X4
                                      & ssList(X7) ) ) ) ) )
                    | ( totalorderedP(X0)
                      & segmentP(X1,X0) )
                    | X0 != X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f553,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f347]) ).

fof(f739,plain,
    ( ~ ssList(sK56)
    | spl59_1 ),
    inference(subsumption_resolution,[],[f738,f549]) ).

fof(f549,plain,
    ssList(sK58),
    inference(cnf_transformation,[],[f347]) ).

fof(f738,plain,
    ( ~ ssList(sK58)
    | ~ ssList(sK56)
    | spl59_1 ),
    inference(subsumption_resolution,[],[f737,f564]) ).

fof(f564,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f554,f543]) ).

fof(f543,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f347]) ).

fof(f554,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f347]) ).

fof(f737,plain,
    ( ~ ssList(sK55)
    | ~ ssList(sK56)
    | ~ ssList(sK58)
    | spl59_1 ),
    inference(subsumption_resolution,[],[f736,f551]) ).

fof(f551,plain,
    ssList(sK57),
    inference(cnf_transformation,[],[f347]) ).

fof(f736,plain,
    ( ~ ssList(sK57)
    | ~ ssList(sK58)
    | ~ ssList(sK56)
    | ~ ssList(sK55)
    | spl59_1 ),
    inference(subsumption_resolution,[],[f734,f604]) ).

fof(f604,plain,
    ( ~ segmentP(sK56,sK55)
    | spl59_1 ),
    inference(avatar_component_clause,[],[f602]) ).

fof(f602,plain,
    ( spl59_1
  <=> segmentP(sK56,sK55) ),
    introduced(avatar_definition,[new_symbols(naming,[spl59_1])]) ).

fof(f734,plain,
    ( segmentP(sK56,sK55)
    | ~ ssList(sK56)
    | ~ ssList(sK57)
    | ~ ssList(sK55)
    | ~ ssList(sK58) ),
    inference(superposition,[],[f587,f548]) ).

fof(f548,plain,
    app(app(sK57,sK55),sK58) = sK56,
    inference(cnf_transformation,[],[f347]) ).

fof(f587,plain,
    ! [X2,X3,X1] :
      ( segmentP(app(app(X2,X1),X3),X1)
      | ~ ssList(X2)
      | ~ ssList(app(app(X2,X1),X3))
      | ~ ssList(X1)
      | ~ ssList(X3) ),
    inference(equality_resolution,[],[f507]) ).

fof(f507,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X0)
      | segmentP(X0,X1)
      | ~ ssList(X3)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X2)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f323]) ).

fof(f323,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( ~ ssList(X3)
                      | app(app(X2,X1),X3) != X0 )
                  | ~ ssList(X2) ) )
            & ( ( ssList(sK44(X0,X1))
                & app(app(sK43(X0,X1),X1),sK44(X0,X1)) = X0
                & ssList(sK43(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44])],[f320,f322,f321]) ).

fof(f321,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( ssList(X5)
              & app(app(X4,X1),X5) = X0 )
          & ssList(X4) )
     => ( ? [X5] :
            ( ssList(X5)
            & app(app(sK43(X0,X1),X1),X5) = X0 )
        & ssList(sK43(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f322,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ssList(X5)
          & app(app(sK43(X0,X1),X1),X5) = X0 )
     => ( ssList(sK44(X0,X1))
        & app(app(sK43(X0,X1),X1),sK44(X0,X1)) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f320,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( ~ ssList(X3)
                      | app(app(X2,X1),X3) != X0 )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( ssList(X5)
                      & app(app(X4,X1),X5) = X0 )
                  & ssList(X4) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) ) ),
    inference(rectify,[],[f319]) ).

fof(f319,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( ~ ssList(X3)
                      | app(app(X2,X1),X3) != X0 )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( ssList(X3)
                      & app(app(X2,X1),X3) = X0 )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) ) ),
    inference(nnf_transformation,[],[f141]) ).

fof(f141,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( ssList(X3)
                    & app(app(X2,X1),X3) = X0 )
                & ssList(X2) ) )
          | ~ ssList(X1) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( ssList(X3)
                    & app(app(X2,X1),X3) = X0 )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).

fof(f633,plain,
    spl59_2,
    inference(avatar_split_clause,[],[f546,f606]) ).

fof(f606,plain,
    ( spl59_2
  <=> totalorderedP(sK55) ),
    introduced(avatar_definition,[new_symbols(naming,[spl59_2])]) ).

fof(f546,plain,
    totalorderedP(sK55),
    inference(cnf_transformation,[],[f347]) ).

fof(f609,plain,
    ( ~ spl59_1
    | ~ spl59_2 ),
    inference(avatar_split_clause,[],[f566,f606,f602]) ).

fof(f566,plain,
    ( ~ totalorderedP(sK55)
    | ~ segmentP(sK56,sK55) ),
    inference(definition_unfolding,[],[f544,f542,f543,f543]) ).

fof(f544,plain,
    ( ~ segmentP(sK54,sK53)
    | ~ totalorderedP(sK53) ),
    inference(cnf_transformation,[],[f347]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC339+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 18:40:44 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.55  % (18557)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.55  % (18556)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.56  % (18572)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.56  % (18573)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.21/0.56  % (18565)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.21/0.56  % (18564)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.57  % (18557)Instruction limit reached!
% 0.21/0.57  % (18557)------------------------------
% 0.21/0.57  % (18557)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.58  % (18557)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.58  % (18557)Termination reason: Unknown
% 0.21/0.58  % (18557)Termination phase: Property scanning
% 0.21/0.58  
% 0.21/0.58  % (18557)Memory used [KB]: 1279
% 0.21/0.58  % (18557)Time elapsed: 0.007 s
% 0.21/0.58  % (18557)Instructions burned: 7 (million)
% 0.21/0.58  % (18557)------------------------------
% 0.21/0.58  % (18557)------------------------------
% 0.21/0.60  TRYING [1]
% 0.21/0.61  % (18554)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.61  % (18552)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.61  % (18555)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.21/0.61  % (18553)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.61  % (18551)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.62  TRYING [2]
% 0.21/0.62  % (18560)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.62  % (18574)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.21/0.62  % (18575)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.21/0.62  % (18579)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.21/0.62  % (18570)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.21/0.62  % (18550)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.21/0.62  % (18568)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.62  % (18571)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.62  % (18569)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.62  % (18562)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.62  % (18567)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.21/0.63  % (18576)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.63  % (18566)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.63  % (18561)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.63  % (18563)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.63  % (18559)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.63  % (18558)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.63  % (18558)Instruction limit reached!
% 0.21/0.63  % (18558)------------------------------
% 0.21/0.63  % (18558)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.63  % (18558)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.63  % (18558)Termination reason: Unknown
% 0.21/0.63  % (18558)Termination phase: Preprocessing 2
% 0.21/0.63  
% 0.21/0.63  % (18558)Memory used [KB]: 1023
% 0.21/0.63  % (18558)Time elapsed: 0.004 s
% 0.21/0.63  % (18558)Instructions burned: 3 (million)
% 0.21/0.63  % (18558)------------------------------
% 0.21/0.63  % (18558)------------------------------
% 0.21/0.64  % (18577)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.21/0.64  % (18578)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.64  % (18556)Instruction limit reached!
% 0.21/0.64  % (18556)------------------------------
% 0.21/0.64  % (18556)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.07/0.65  % (18556)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.07/0.65  % (18556)Termination reason: Unknown
% 2.07/0.65  % (18556)Termination phase: Finite model building SAT solving
% 2.07/0.65  
% 2.07/0.65  % (18556)Memory used [KB]: 7164
% 2.07/0.65  % (18556)Time elapsed: 0.205 s
% 2.07/0.65  % (18556)Instructions burned: 52 (million)
% 2.07/0.65  % (18556)------------------------------
% 2.07/0.65  % (18556)------------------------------
% 2.45/0.67  % (18551)First to succeed.
% 2.45/0.67  TRYING [1]
% 2.45/0.67  TRYING [1]
% 2.45/0.68  TRYING [2]
% 2.45/0.68  % (18552)Instruction limit reached!
% 2.45/0.68  % (18552)------------------------------
% 2.45/0.68  % (18552)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.45/0.69  % (18551)Refutation found. Thanks to Tanya!
% 2.45/0.69  % SZS status Theorem for theBenchmark
% 2.45/0.69  % SZS output start Proof for theBenchmark
% See solution above
% 2.45/0.69  % (18551)------------------------------
% 2.45/0.69  % (18551)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.45/0.69  % (18551)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.45/0.69  % (18551)Termination reason: Refutation
% 2.45/0.69  
% 2.45/0.69  % (18551)Memory used [KB]: 6268
% 2.45/0.69  % (18551)Time elapsed: 0.205 s
% 2.45/0.69  % (18551)Instructions burned: 25 (million)
% 2.45/0.69  % (18551)------------------------------
% 2.45/0.69  % (18551)------------------------------
% 2.45/0.69  % (18549)Success in time 0.332 s
%------------------------------------------------------------------------------