TSTP Solution File: SWC181+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC181+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 : n022.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 18:42:14 EDT 2022

% Result   : Theorem 2.19s 0.65s
% Output   : Refutation 2.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   74 (  15 unt;   0 def)
%            Number of atoms       :  822 ( 221 equ)
%            Maximal formula atoms :   54 (  11 avg)
%            Number of connectives : 1170 ( 422   ~; 370   |; 323   &)
%                                         (   6 <=>;  49  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (  11 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;   7 con; 0-2 aty)
%            Number of variables   :  396 ( 248   !; 148   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1958,plain,
    $false,
    inference(subsumption_resolution,[],[f1948,f645]) ).

fof(f645,plain,
    ssItem(sK37(sK9)),
    inference(subsumption_resolution,[],[f644,f373]) ).

fof(f373,plain,
    ssList(sK9),
    inference(cnf_transformation,[],[f248]) ).

fof(f248,plain,
    ( ssList(sK10)
    & ssList(sK12)
    & ssList(sK13)
    & ! [X6] :
        ( ~ ssItem(X6)
        | ! [X7] :
            ( ! [X8] :
                ( ! [X9] :
                    ( ~ lt(X6,X8)
                    | app(cons(X8,nil),X9) != sK11
                    | ~ ssList(X9) )
                | ~ ssItem(X8) )
            | app(X7,cons(X6,nil)) != sK13
            | ~ ssList(X7) ) )
    & ssList(sK14)
    & app(app(sK13,sK11),sK14) = sK12
    & ! [X10] :
        ( ~ ssItem(X10)
        | ! [X11] :
            ( app(cons(X10,nil),X11) != sK14
            | ~ ssList(X11)
            | ! [X12] :
                ( ! [X13] :
                    ( ~ lt(X12,X10)
                    | app(X13,cons(X12,nil)) != sK11
                    | ~ ssList(X13) )
                | ~ ssItem(X12) ) ) )
    & strictorderedP(sK11)
    & ~ duplicatefreeP(sK9)
    & sK11 = sK9
    & sK10 = sK12
    & ( nil != sK11
      | nil = sK12 )
    & ssList(sK11)
    & ssList(sK9) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13,sK14])],[f241,f247,f246,f245,f244,f243,f242]) ).

fof(f242,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ? [X3] :
                    ( ssList(X3)
                    & ? [X4] :
                        ( ssList(X4)
                        & ? [X5] :
                            ( ! [X6] :
                                ( ~ ssItem(X6)
                                | ! [X7] :
                                    ( ! [X8] :
                                        ( ! [X9] :
                                            ( ~ lt(X6,X8)
                                            | app(cons(X8,nil),X9) != X2
                                            | ~ ssList(X9) )
                                        | ~ ssItem(X8) )
                                    | app(X7,cons(X6,nil)) != X4
                                    | ~ ssList(X7) ) )
                            & ssList(X5)
                            & app(app(X4,X2),X5) = X3
                            & ! [X10] :
                                ( ~ ssItem(X10)
                                | ! [X11] :
                                    ( app(cons(X10,nil),X11) != X5
                                    | ~ ssList(X11)
                                    | ! [X12] :
                                        ( ! [X13] :
                                            ( ~ lt(X12,X10)
                                            | app(X13,cons(X12,nil)) != X2
                                            | ~ ssList(X13) )
                                        | ~ ssItem(X12) ) ) )
                            & strictorderedP(X2) ) )
                    & ~ duplicatefreeP(X0)
                    & X0 = X2
                    & X1 = X3
                    & ( nil != X2
                      | nil = X3 ) )
                & ssList(X2) ) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ! [X6] :
                              ( ~ ssItem(X6)
                              | ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X6,X8)
                                          | app(cons(X8,nil),X9) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(X7,cons(X6,nil)) != X4
                                  | ~ ssList(X7) ) )
                          & ssList(X5)
                          & app(app(X4,X2),X5) = X3
                          & ! [X10] :
                              ( ~ ssItem(X10)
                              | ! [X11] :
                                  ( app(cons(X10,nil),X11) != X5
                                  | ~ ssList(X11)
                                  | ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X12,X10)
                                          | app(X13,cons(X12,nil)) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) ) ) )
                          & strictorderedP(X2) ) )
                  & ~ duplicatefreeP(sK9)
                  & sK9 = X2
                  & X1 = X3
                  & ( nil != X2
                    | nil = X3 ) )
              & ssList(X2) ) )
      & ssList(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f243,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & ? [X5] :
                        ( ! [X6] :
                            ( ~ ssItem(X6)
                            | ! [X7] :
                                ( ! [X8] :
                                    ( ! [X9] :
                                        ( ~ lt(X6,X8)
                                        | app(cons(X8,nil),X9) != X2
                                        | ~ ssList(X9) )
                                    | ~ ssItem(X8) )
                                | app(X7,cons(X6,nil)) != X4
                                | ~ ssList(X7) ) )
                        & ssList(X5)
                        & app(app(X4,X2),X5) = X3
                        & ! [X10] :
                            ( ~ ssItem(X10)
                            | ! [X11] :
                                ( app(cons(X10,nil),X11) != X5
                                | ~ ssList(X11)
                                | ! [X12] :
                                    ( ! [X13] :
                                        ( ~ lt(X12,X10)
                                        | app(X13,cons(X12,nil)) != X2
                                        | ~ ssList(X13) )
                                    | ~ ssItem(X12) ) ) )
                        & strictorderedP(X2) ) )
                & ~ duplicatefreeP(sK9)
                & sK9 = X2
                & X1 = X3
                & ( nil != X2
                  | nil = X3 ) )
            & ssList(X2) ) )
   => ( ssList(sK10)
      & ? [X2] :
          ( ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & ? [X5] :
                      ( ! [X6] :
                          ( ~ ssItem(X6)
                          | ! [X7] :
                              ( ! [X8] :
                                  ( ! [X9] :
                                      ( ~ lt(X6,X8)
                                      | app(cons(X8,nil),X9) != X2
                                      | ~ ssList(X9) )
                                  | ~ ssItem(X8) )
                              | app(X7,cons(X6,nil)) != X4
                              | ~ ssList(X7) ) )
                      & ssList(X5)
                      & app(app(X4,X2),X5) = X3
                      & ! [X10] :
                          ( ~ ssItem(X10)
                          | ! [X11] :
                              ( app(cons(X10,nil),X11) != X5
                              | ~ ssList(X11)
                              | ! [X12] :
                                  ( ! [X13] :
                                      ( ~ lt(X12,X10)
                                      | app(X13,cons(X12,nil)) != X2
                                      | ~ ssList(X13) )
                                  | ~ ssItem(X12) ) ) )
                      & strictorderedP(X2) ) )
              & ~ duplicatefreeP(sK9)
              & sK9 = X2
              & sK10 = X3
              & ( nil != X2
                | nil = X3 ) )
          & ssList(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f244,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ssList(X3)
            & ? [X4] :
                ( ssList(X4)
                & ? [X5] :
                    ( ! [X6] :
                        ( ~ ssItem(X6)
                        | ! [X7] :
                            ( ! [X8] :
                                ( ! [X9] :
                                    ( ~ lt(X6,X8)
                                    | app(cons(X8,nil),X9) != X2
                                    | ~ ssList(X9) )
                                | ~ ssItem(X8) )
                            | app(X7,cons(X6,nil)) != X4
                            | ~ ssList(X7) ) )
                    & ssList(X5)
                    & app(app(X4,X2),X5) = X3
                    & ! [X10] :
                        ( ~ ssItem(X10)
                        | ! [X11] :
                            ( app(cons(X10,nil),X11) != X5
                            | ~ ssList(X11)
                            | ! [X12] :
                                ( ! [X13] :
                                    ( ~ lt(X12,X10)
                                    | app(X13,cons(X12,nil)) != X2
                                    | ~ ssList(X13) )
                                | ~ ssItem(X12) ) ) )
                    & strictorderedP(X2) ) )
            & ~ duplicatefreeP(sK9)
            & sK9 = X2
            & sK10 = X3
            & ( nil != X2
              | nil = X3 ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ssList(X3)
          & ? [X4] :
              ( ssList(X4)
              & ? [X5] :
                  ( ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( ! [X8] :
                              ( ! [X9] :
                                  ( ~ lt(X6,X8)
                                  | app(cons(X8,nil),X9) != sK11
                                  | ~ ssList(X9) )
                              | ~ ssItem(X8) )
                          | app(X7,cons(X6,nil)) != X4
                          | ~ ssList(X7) ) )
                  & ssList(X5)
                  & app(app(X4,sK11),X5) = X3
                  & ! [X10] :
                      ( ~ ssItem(X10)
                      | ! [X11] :
                          ( app(cons(X10,nil),X11) != X5
                          | ~ ssList(X11)
                          | ! [X12] :
                              ( ! [X13] :
                                  ( ~ lt(X12,X10)
                                  | app(X13,cons(X12,nil)) != sK11
                                  | ~ ssList(X13) )
                              | ~ ssItem(X12) ) ) )
                  & strictorderedP(sK11) ) )
          & ~ duplicatefreeP(sK9)
          & sK11 = sK9
          & sK10 = X3
          & ( nil != sK11
            | nil = X3 ) )
      & ssList(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f245,plain,
    ( ? [X3] :
        ( ssList(X3)
        & ? [X4] :
            ( ssList(X4)
            & ? [X5] :
                ( ! [X6] :
                    ( ~ ssItem(X6)
                    | ! [X7] :
                        ( ! [X8] :
                            ( ! [X9] :
                                ( ~ lt(X6,X8)
                                | app(cons(X8,nil),X9) != sK11
                                | ~ ssList(X9) )
                            | ~ ssItem(X8) )
                        | app(X7,cons(X6,nil)) != X4
                        | ~ ssList(X7) ) )
                & ssList(X5)
                & app(app(X4,sK11),X5) = X3
                & ! [X10] :
                    ( ~ ssItem(X10)
                    | ! [X11] :
                        ( app(cons(X10,nil),X11) != X5
                        | ~ ssList(X11)
                        | ! [X12] :
                            ( ! [X13] :
                                ( ~ lt(X12,X10)
                                | app(X13,cons(X12,nil)) != sK11
                                | ~ ssList(X13) )
                            | ~ ssItem(X12) ) ) )
                & strictorderedP(sK11) ) )
        & ~ duplicatefreeP(sK9)
        & sK11 = sK9
        & sK10 = X3
        & ( nil != sK11
          | nil = X3 ) )
   => ( ssList(sK12)
      & ? [X4] :
          ( ssList(X4)
          & ? [X5] :
              ( ! [X6] :
                  ( ~ ssItem(X6)
                  | ! [X7] :
                      ( ! [X8] :
                          ( ! [X9] :
                              ( ~ lt(X6,X8)
                              | app(cons(X8,nil),X9) != sK11
                              | ~ ssList(X9) )
                          | ~ ssItem(X8) )
                      | app(X7,cons(X6,nil)) != X4
                      | ~ ssList(X7) ) )
              & ssList(X5)
              & app(app(X4,sK11),X5) = sK12
              & ! [X10] :
                  ( ~ ssItem(X10)
                  | ! [X11] :
                      ( app(cons(X10,nil),X11) != X5
                      | ~ ssList(X11)
                      | ! [X12] :
                          ( ! [X13] :
                              ( ~ lt(X12,X10)
                              | app(X13,cons(X12,nil)) != sK11
                              | ~ ssList(X13) )
                          | ~ ssItem(X12) ) ) )
              & strictorderedP(sK11) ) )
      & ~ duplicatefreeP(sK9)
      & sK11 = sK9
      & sK10 = sK12
      & ( nil != sK11
        | nil = sK12 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f246,plain,
    ( ? [X4] :
        ( ssList(X4)
        & ? [X5] :
            ( ! [X6] :
                ( ~ ssItem(X6)
                | ! [X7] :
                    ( ! [X8] :
                        ( ! [X9] :
                            ( ~ lt(X6,X8)
                            | app(cons(X8,nil),X9) != sK11
                            | ~ ssList(X9) )
                        | ~ ssItem(X8) )
                    | app(X7,cons(X6,nil)) != X4
                    | ~ ssList(X7) ) )
            & ssList(X5)
            & app(app(X4,sK11),X5) = sK12
            & ! [X10] :
                ( ~ ssItem(X10)
                | ! [X11] :
                    ( app(cons(X10,nil),X11) != X5
                    | ~ ssList(X11)
                    | ! [X12] :
                        ( ! [X13] :
                            ( ~ lt(X12,X10)
                            | app(X13,cons(X12,nil)) != sK11
                            | ~ ssList(X13) )
                        | ~ ssItem(X12) ) ) )
            & strictorderedP(sK11) ) )
   => ( ssList(sK13)
      & ? [X5] :
          ( ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ~ lt(X6,X8)
                          | app(cons(X8,nil),X9) != sK11
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  | app(X7,cons(X6,nil)) != sK13
                  | ~ ssList(X7) ) )
          & ssList(X5)
          & app(app(sK13,sK11),X5) = sK12
          & ! [X10] :
              ( ~ ssItem(X10)
              | ! [X11] :
                  ( app(cons(X10,nil),X11) != X5
                  | ~ ssList(X11)
                  | ! [X12] :
                      ( ! [X13] :
                          ( ~ lt(X12,X10)
                          | app(X13,cons(X12,nil)) != sK11
                          | ~ ssList(X13) )
                      | ~ ssItem(X12) ) ) )
          & strictorderedP(sK11) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f247,plain,
    ( ? [X5] :
        ( ! [X6] :
            ( ~ ssItem(X6)
            | ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ~ lt(X6,X8)
                        | app(cons(X8,nil),X9) != sK11
                        | ~ ssList(X9) )
                    | ~ ssItem(X8) )
                | app(X7,cons(X6,nil)) != sK13
                | ~ ssList(X7) ) )
        & ssList(X5)
        & app(app(sK13,sK11),X5) = sK12
        & ! [X10] :
            ( ~ ssItem(X10)
            | ! [X11] :
                ( app(cons(X10,nil),X11) != X5
                | ~ ssList(X11)
                | ! [X12] :
                    ( ! [X13] :
                        ( ~ lt(X12,X10)
                        | app(X13,cons(X12,nil)) != sK11
                        | ~ ssList(X13) )
                    | ~ ssItem(X12) ) ) )
        & strictorderedP(sK11) )
   => ( ! [X6] :
          ( ~ ssItem(X6)
          | ! [X7] :
              ( ! [X8] :
                  ( ! [X9] :
                      ( ~ lt(X6,X8)
                      | app(cons(X8,nil),X9) != sK11
                      | ~ ssList(X9) )
                  | ~ ssItem(X8) )
              | app(X7,cons(X6,nil)) != sK13
              | ~ ssList(X7) ) )
      & ssList(sK14)
      & app(app(sK13,sK11),sK14) = sK12
      & ! [X10] :
          ( ~ ssItem(X10)
          | ! [X11] :
              ( app(cons(X10,nil),X11) != sK14
              | ~ ssList(X11)
              | ! [X12] :
                  ( ! [X13] :
                      ( ~ lt(X12,X10)
                      | app(X13,cons(X12,nil)) != sK11
                      | ~ ssList(X13) )
                  | ~ ssItem(X12) ) ) )
      & strictorderedP(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f241,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ! [X6] :
                              ( ~ ssItem(X6)
                              | ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X6,X8)
                                          | app(cons(X8,nil),X9) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(X7,cons(X6,nil)) != X4
                                  | ~ ssList(X7) ) )
                          & ssList(X5)
                          & app(app(X4,X2),X5) = X3
                          & ! [X10] :
                              ( ~ ssItem(X10)
                              | ! [X11] :
                                  ( app(cons(X10,nil),X11) != X5
                                  | ~ ssList(X11)
                                  | ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X12,X10)
                                          | app(X13,cons(X12,nil)) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) ) ) )
                          & strictorderedP(X2) ) )
                  & ~ duplicatefreeP(X0)
                  & X0 = X2
                  & X1 = X3
                  & ( nil != X2
                    | nil = X3 ) )
              & ssList(X2) ) )
      & ssList(X0) ),
    inference(rectify,[],[f167]) ).

fof(f167,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ! [X10] :
                              ( ~ ssItem(X10)
                              | ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) ) )
                          & ssList(X5)
                          & app(app(X4,X2),X5) = X3
                          & ! [X6] :
                              ( ~ ssItem(X6)
                              | ! [X7] :
                                  ( app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7)
                                  | ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) ) ) )
                          & strictorderedP(X2) ) )
                  & ~ duplicatefreeP(X0)
                  & X0 = X2
                  & X1 = X3
                  & ( nil != X2
                    | nil = X3 ) )
              & ssList(X2) ) )
      & ssList(X0) ),
    inference(flattening,[],[f166]) ).

fof(f166,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ duplicatefreeP(X0)
                  & X0 = X2
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ~ ssItem(X6)
                              | ! [X7] :
                                  ( app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7)
                                  | ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) ) ) )
                          & ! [X10] :
                              ( ~ ssItem(X10)
                              | ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) ) )
                          & app(app(X4,X2),X5) = X3
                          & strictorderedP(X2)
                          & ssList(X5) )
                      & ssList(X4) )
                  & ( nil != X2
                    | nil = X3 )
                  & X1 = X3
                  & 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)
                   => ( duplicatefreeP(X0)
                      | X0 != X2
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( ? [X6] :
                                    ( ssItem(X6)
                                    & ? [X7] :
                                        ( app(cons(X6,nil),X7) = X5
                                        & ssList(X7)
                                        & ? [X8] :
                                            ( ssItem(X8)
                                            & ? [X9] :
                                                ( ssList(X9)
                                                & lt(X8,X6)
                                                & app(X9,cons(X8,nil)) = X2 ) ) ) )
                                | ? [X10] :
                                    ( ? [X11] :
                                        ( app(X11,cons(X10,nil)) = X4
                                        & ? [X12] :
                                            ( ssItem(X12)
                                            & ? [X13] :
                                                ( lt(X10,X12)
                                                & ssList(X13)
                                                & app(cons(X12,nil),X13) = X2 ) )
                                        & ssList(X11) )
                                    & ssItem(X10) )
                                | app(app(X4,X2),X5) != X3
                                | ~ strictorderedP(X2) ) ) )
                      | ( nil != X3
                        & nil = X2 )
                      | X1 != X3 ) ) ) ) ),
    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
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( app(app(X4,X2),X5) != X3
                                | ~ strictorderedP(X2)
                                | ? [X10] :
                                    ( ? [X11] :
                                        ( app(cons(X10,nil),X11) = X5
                                        & ? [X12] :
                                            ( ? [X13] :
                                                ( lt(X12,X10)
                                                & ssList(X13)
                                                & app(X13,cons(X12,nil)) = X2 )
                                            & ssItem(X12) )
                                        & ssList(X11) )
                                    & ssItem(X10) )
                                | ? [X6] :
                                    ( ssItem(X6)
                                    & ? [X7] :
                                        ( ? [X8] :
                                            ( ssItem(X8)
                                            & ? [X9] :
                                                ( lt(X6,X8)
                                                & app(cons(X8,nil),X9) = X2
                                                & ssList(X9) ) )
                                        & ssList(X7)
                                        & app(X7,cons(X6,nil)) = X4 ) ) ) ) )
                      | duplicatefreeP(X0) ) ) ) ) ),
    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
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X4,X2),X5) != X3
                              | ~ strictorderedP(X2)
                              | ? [X10] :
                                  ( ? [X11] :
                                      ( app(cons(X10,nil),X11) = X5
                                      & ? [X12] :
                                          ( ? [X13] :
                                              ( lt(X12,X10)
                                              & ssList(X13)
                                              & app(X13,cons(X12,nil)) = X2 )
                                          & ssItem(X12) )
                                      & ssList(X11) )
                                  & ssItem(X10) )
                              | ? [X6] :
                                  ( ssItem(X6)
                                  & ? [X7] :
                                      ( ? [X8] :
                                          ( ssItem(X8)
                                          & ? [X9] :
                                              ( lt(X6,X8)
                                              & app(cons(X8,nil),X9) = X2
                                              & ssList(X9) ) )
                                      & ssList(X7)
                                      & app(X7,cons(X6,nil)) = X4 ) ) ) ) )
                    | duplicatefreeP(X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f644,plain,
    ( ssItem(sK37(sK9))
    | ~ ssList(sK9) ),
    inference(resolution,[],[f486,f378]) ).

fof(f378,plain,
    ~ duplicatefreeP(sK9),
    inference(cnf_transformation,[],[f248]) ).

fof(f486,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ssItem(sK37(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f308,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( duplicatefreeP(X0)
          | ( ssList(sK39(X0))
            & sK37(X0) = sK38(X0)
            & ssList(sK41(X0))
            & app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),sK41(X0))) = X0
            & ssList(sK40(X0))
            & ssItem(sK38(X0))
            & ssItem(sK37(X0)) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ~ ssList(X8)
                      | ! [X9] :
                          ( ! [X10] :
                              ( X6 != X7
                              | ~ ssList(X10)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0 )
                          | ~ ssList(X9) ) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ duplicatefreeP(X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38,sK39,sK40,sK41])],[f302,f307,f306,f305,f304,f303]) ).

fof(f303,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & ? [X4] :
                      ( ? [X5] :
                          ( X1 = X2
                          & ssList(X5)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0 )
                      & ssList(X4) ) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ? [X5] :
                        ( sK37(X0) = X2
                        & ssList(X5)
                        & app(app(X3,cons(sK37(X0),X4)),cons(X2,X5)) = X0 )
                    & ssList(X4) ) )
            & ssItem(X2) )
        & ssItem(sK37(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f304,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ? [X5] :
                      ( sK37(X0) = X2
                      & ssList(X5)
                      & app(app(X3,cons(sK37(X0),X4)),cons(X2,X5)) = X0 )
                  & ssList(X4) ) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ssList(X3)
            & ? [X4] :
                ( ? [X5] :
                    ( sK37(X0) = sK38(X0)
                    & ssList(X5)
                    & app(app(X3,cons(sK37(X0),X4)),cons(sK38(X0),X5)) = X0 )
                & ssList(X4) ) )
        & ssItem(sK38(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f305,plain,
    ! [X0] :
      ( ? [X3] :
          ( ssList(X3)
          & ? [X4] :
              ( ? [X5] :
                  ( sK37(X0) = sK38(X0)
                  & ssList(X5)
                  & app(app(X3,cons(sK37(X0),X4)),cons(sK38(X0),X5)) = X0 )
              & ssList(X4) ) )
     => ( ssList(sK39(X0))
        & ? [X4] :
            ( ? [X5] :
                ( sK37(X0) = sK38(X0)
                & ssList(X5)
                & app(app(sK39(X0),cons(sK37(X0),X4)),cons(sK38(X0),X5)) = X0 )
            & ssList(X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f306,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( sK37(X0) = sK38(X0)
              & ssList(X5)
              & app(app(sK39(X0),cons(sK37(X0),X4)),cons(sK38(X0),X5)) = X0 )
          & ssList(X4) )
     => ( ? [X5] :
            ( sK37(X0) = sK38(X0)
            & ssList(X5)
            & app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),X5)) = X0 )
        & ssList(sK40(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f307,plain,
    ! [X0] :
      ( ? [X5] :
          ( sK37(X0) = sK38(X0)
          & ssList(X5)
          & app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),X5)) = X0 )
     => ( sK37(X0) = sK38(X0)
        & ssList(sK41(X0))
        & app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),sK41(X0))) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f302,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( duplicatefreeP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ssList(X3)
                      & ? [X4] :
                          ( ? [X5] :
                              ( X1 = X2
                              & ssList(X5)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0 )
                          & ssList(X4) ) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ~ ssList(X8)
                      | ! [X9] :
                          ( ! [X10] :
                              ( X6 != X7
                              | ~ ssList(X10)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0 )
                          | ~ ssList(X9) ) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ duplicatefreeP(X0) ) ) ),
    inference(rectify,[],[f301]) ).

fof(f301,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( duplicatefreeP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ssList(X3)
                      & ? [X4] :
                          ( ? [X5] :
                              ( X1 = X2
                              & ssList(X5)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0 )
                          & ssList(X4) ) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X1] :
              ( ! [X2] :
                  ( ! [X3] :
                      ( ~ ssList(X3)
                      | ! [X4] :
                          ( ! [X5] :
                              ( X1 != X2
                              | ~ ssList(X5)
                              | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0 )
                          | ~ ssList(X4) ) )
                  | ~ ssItem(X2) )
              | ~ ssItem(X1) )
          | ~ duplicatefreeP(X0) ) ) ),
    inference(nnf_transformation,[],[f218]) ).

fof(f218,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ~ ssList(X3)
                    | ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | ~ ssList(X5)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0 )
                        | ~ ssList(X4) ) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) ) ),
    inference(flattening,[],[f217]) ).

fof(f217,plain,
    ! [X0] :
      ( ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
      <=> duplicatefreeP(X0) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => X1 != X2 ) ) ) ) ) )
      <=> duplicatefreeP(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).

fof(f1948,plain,
    ~ ssItem(sK37(sK9)),
    inference(resolution,[],[f1739,f550]) ).

fof(f550,plain,
    ! [X0] :
      ( ~ lt(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f165,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ lt(X0,X0) ),
    inference(ennf_transformation,[],[f90]) ).

fof(f90,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ lt(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).

fof(f1739,plain,
    lt(sK37(sK9),sK37(sK9)),
    inference(subsumption_resolution,[],[f1738,f645]) ).

fof(f1738,plain,
    ( lt(sK37(sK9),sK37(sK9))
    | ~ ssItem(sK37(sK9)) ),
    inference(subsumption_resolution,[],[f1737,f569]) ).

fof(f569,plain,
    strictorderedP(sK9),
    inference(definition_unfolding,[],[f379,f377]) ).

fof(f377,plain,
    sK11 = sK9,
    inference(cnf_transformation,[],[f248]) ).

fof(f379,plain,
    strictorderedP(sK11),
    inference(cnf_transformation,[],[f248]) ).

fof(f1737,plain,
    ( lt(sK37(sK9),sK37(sK9))
    | ~ strictorderedP(sK9)
    | ~ ssItem(sK37(sK9)) ),
    inference(subsumption_resolution,[],[f1736,f956]) ).

fof(f956,plain,
    ssList(sK41(sK9)),
    inference(subsumption_resolution,[],[f948,f373]) ).

fof(f948,plain,
    ( ~ ssList(sK9)
    | ssList(sK41(sK9)) ),
    inference(resolution,[],[f378,f490]) ).

fof(f490,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ~ ssList(X0)
      | ssList(sK41(X0)) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f1736,plain,
    ( ~ ssList(sK41(sK9))
    | lt(sK37(sK9),sK37(sK9))
    | ~ strictorderedP(sK9)
    | ~ ssItem(sK37(sK9)) ),
    inference(subsumption_resolution,[],[f1735,f649]) ).

fof(f649,plain,
    ssList(sK40(sK9)),
    inference(subsumption_resolution,[],[f648,f373]) ).

fof(f648,plain,
    ( ssList(sK40(sK9))
    | ~ ssList(sK9) ),
    inference(resolution,[],[f488,f378]) ).

fof(f488,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ~ ssList(X0)
      | ssList(sK40(X0)) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f1735,plain,
    ( ~ ssList(sK40(sK9))
    | ~ ssItem(sK37(sK9))
    | ~ ssList(sK41(sK9))
    | lt(sK37(sK9),sK37(sK9))
    | ~ strictorderedP(sK9) ),
    inference(subsumption_resolution,[],[f1734,f373]) ).

fof(f1734,plain,
    ( ~ ssList(sK9)
    | ~ strictorderedP(sK9)
    | ~ ssList(sK40(sK9))
    | ~ ssItem(sK37(sK9))
    | ~ ssList(sK41(sK9))
    | lt(sK37(sK9),sK37(sK9)) ),
    inference(subsumption_resolution,[],[f1733,f954]) ).

fof(f954,plain,
    ssList(sK39(sK9)),
    inference(subsumption_resolution,[],[f947,f373]) ).

fof(f947,plain,
    ( ssList(sK39(sK9))
    | ~ ssList(sK9) ),
    inference(resolution,[],[f378,f492]) ).

fof(f492,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ~ ssList(X0)
      | ssList(sK39(X0)) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f1733,plain,
    ( ~ ssList(sK39(sK9))
    | ~ ssItem(sK37(sK9))
    | ~ ssList(sK9)
    | ~ strictorderedP(sK9)
    | ~ ssList(sK40(sK9))
    | ~ ssList(sK41(sK9))
    | lt(sK37(sK9),sK37(sK9)) ),
    inference(duplicate_literal_removal,[],[f1730]) ).

fof(f1730,plain,
    ( ~ ssItem(sK37(sK9))
    | ~ ssList(sK40(sK9))
    | ~ ssList(sK9)
    | ~ strictorderedP(sK9)
    | ~ ssList(sK39(sK9))
    | lt(sK37(sK9),sK37(sK9))
    | ~ ssItem(sK37(sK9))
    | ~ ssList(sK41(sK9)) ),
    inference(superposition,[],[f580,f1706]) ).

fof(f1706,plain,
    sK9 = app(app(sK39(sK9),cons(sK37(sK9),sK40(sK9))),cons(sK37(sK9),sK41(sK9))),
    inference(forward_demodulation,[],[f1154,f750]) ).

fof(f750,plain,
    sK37(sK9) = sK38(sK9),
    inference(subsumption_resolution,[],[f749,f373]) ).

fof(f749,plain,
    ( ~ ssList(sK9)
    | sK37(sK9) = sK38(sK9) ),
    inference(resolution,[],[f491,f378]) ).

fof(f491,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ~ ssList(X0)
      | sK37(X0) = sK38(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f1154,plain,
    sK9 = app(app(sK39(sK9),cons(sK37(sK9),sK40(sK9))),cons(sK38(sK9),sK41(sK9))),
    inference(subsumption_resolution,[],[f1153,f373]) ).

fof(f1153,plain,
    ( sK9 = app(app(sK39(sK9),cons(sK37(sK9),sK40(sK9))),cons(sK38(sK9),sK41(sK9)))
    | ~ ssList(sK9) ),
    inference(resolution,[],[f489,f378]) ).

fof(f489,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),sK41(X0))) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f580,plain,
    ! [X10,X8,X6,X9,X7] :
      ( ~ ssList(app(app(X8,cons(X6,X9)),cons(X7,X10)))
      | ~ ssList(X8)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssItem(X6)
      | ~ strictorderedP(app(app(X8,cons(X6,X9)),cons(X7,X10)))
      | ~ ssItem(X7)
      | lt(X6,X7) ),
    inference(equality_resolution,[],[f408]) ).

fof(f408,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( ~ ssList(X0)
      | ~ ssItem(X6)
      | ~ ssItem(X7)
      | ~ ssList(X8)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | lt(X6,X7)
      | ~ ssList(X9)
      | ~ strictorderedP(X0) ),
    inference(cnf_transformation,[],[f266]) ).

fof(f266,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( strictorderedP(X0)
          | ( ssItem(sK17(X0))
            & ssItem(sK18(X0))
            & ssList(sK19(X0))
            & app(app(sK19(X0),cons(sK17(X0),sK20(X0))),cons(sK18(X0),sK21(X0))) = X0
            & ssList(sK21(X0))
            & ~ lt(sK17(X0),sK18(X0))
            & ssList(sK20(X0)) ) )
        & ( ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( ~ ssItem(X7)
                  | ! [X8] :
                      ( ~ ssList(X8)
                      | ! [X9] :
                          ( ! [X10] :
                              ( app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10)
                              | lt(X6,X7) )
                          | ~ ssList(X9) ) ) ) )
          | ~ strictorderedP(X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20,sK21])],[f260,f265,f264,f263,f262,f261]) ).

fof(f261,plain,
    ! [X0] :
      ( ? [X1] :
          ( ssItem(X1)
          & ? [X2] :
              ( ssItem(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ? [X4] :
                      ( ? [X5] :
                          ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5)
                          & ~ lt(X1,X2) )
                      & ssList(X4) ) ) ) )
     => ( ssItem(sK17(X0))
        & ? [X2] :
            ( ssItem(X2)
            & ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ? [X5] :
                        ( app(app(X3,cons(sK17(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5)
                        & ~ lt(sK17(X0),X2) )
                    & ssList(X4) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f262,plain,
    ! [X0] :
      ( ? [X2] :
          ( ssItem(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ? [X5] :
                      ( app(app(X3,cons(sK17(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5)
                      & ~ lt(sK17(X0),X2) )
                  & ssList(X4) ) ) )
     => ( ssItem(sK18(X0))
        & ? [X3] :
            ( ssList(X3)
            & ? [X4] :
                ( ? [X5] :
                    ( app(app(X3,cons(sK17(X0),X4)),cons(sK18(X0),X5)) = X0
                    & ssList(X5)
                    & ~ lt(sK17(X0),sK18(X0)) )
                & ssList(X4) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f263,plain,
    ! [X0] :
      ( ? [X3] :
          ( ssList(X3)
          & ? [X4] :
              ( ? [X5] :
                  ( app(app(X3,cons(sK17(X0),X4)),cons(sK18(X0),X5)) = X0
                  & ssList(X5)
                  & ~ lt(sK17(X0),sK18(X0)) )
              & ssList(X4) ) )
     => ( ssList(sK19(X0))
        & ? [X4] :
            ( ? [X5] :
                ( app(app(sK19(X0),cons(sK17(X0),X4)),cons(sK18(X0),X5)) = X0
                & ssList(X5)
                & ~ lt(sK17(X0),sK18(X0)) )
            & ssList(X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f264,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(sK19(X0),cons(sK17(X0),X4)),cons(sK18(X0),X5)) = X0
              & ssList(X5)
              & ~ lt(sK17(X0),sK18(X0)) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK19(X0),cons(sK17(X0),sK20(X0))),cons(sK18(X0),X5)) = X0
            & ssList(X5)
            & ~ lt(sK17(X0),sK18(X0)) )
        & ssList(sK20(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f265,plain,
    ! [X0] :
      ( ? [X5] :
          ( app(app(sK19(X0),cons(sK17(X0),sK20(X0))),cons(sK18(X0),X5)) = X0
          & ssList(X5)
          & ~ lt(sK17(X0),sK18(X0)) )
     => ( app(app(sK19(X0),cons(sK17(X0),sK20(X0))),cons(sK18(X0),sK21(X0))) = X0
        & ssList(sK21(X0))
        & ~ lt(sK17(X0),sK18(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f260,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( strictorderedP(X0)
          | ? [X1] :
              ( ssItem(X1)
              & ? [X2] :
                  ( ssItem(X2)
                  & ? [X3] :
                      ( ssList(X3)
                      & ? [X4] :
                          ( ? [X5] :
                              ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5)
                              & ~ lt(X1,X2) )
                          & ssList(X4) ) ) ) ) )
        & ( ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( ~ ssItem(X7)
                  | ! [X8] :
                      ( ~ ssList(X8)
                      | ! [X9] :
                          ( ! [X10] :
                              ( app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10)
                              | lt(X6,X7) )
                          | ~ ssList(X9) ) ) ) )
          | ~ strictorderedP(X0) ) ) ),
    inference(rectify,[],[f259]) ).

fof(f259,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( strictorderedP(X0)
          | ? [X1] :
              ( ssItem(X1)
              & ? [X2] :
                  ( ssItem(X2)
                  & ? [X3] :
                      ( ssList(X3)
                      & ? [X4] :
                          ( ? [X5] :
                              ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5)
                              & ~ lt(X1,X2) )
                          & ssList(X4) ) ) ) ) )
        & ( ! [X1] :
              ( ~ ssItem(X1)
              | ! [X2] :
                  ( ~ ssItem(X2)
                  | ! [X3] :
                      ( ~ ssList(X3)
                      | ! [X4] :
                          ( ! [X5] :
                              ( app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                              | ~ ssList(X5)
                              | lt(X1,X2) )
                          | ~ ssList(X4) ) ) ) )
          | ~ strictorderedP(X0) ) ) ),
    inference(nnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( strictorderedP(X0)
      <=> ! [X1] :
            ( ~ ssItem(X1)
            | ! [X2] :
                ( ~ ssItem(X2)
                | ! [X3] :
                    ( ~ ssList(X3)
                    | ! [X4] :
                        ( ! [X5] :
                            ( app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5)
                            | lt(X1,X2) )
                        | ~ ssList(X4) ) ) ) ) ) ),
    inference(flattening,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
      <=> strictorderedP(X0) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => lt(X1,X2) ) ) ) ) ) )
      <=> strictorderedP(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC181+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
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 18:32:41 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.49  % (19032)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)
% 0.21/0.49  % (19046)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)
% 0.21/0.50  % (19045)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)
% 0.21/0.50  % (19038)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.50  % (19038)Instruction limit reached!
% 0.21/0.50  % (19038)------------------------------
% 0.21/0.50  % (19038)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50  % (19038)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50  % (19038)Termination reason: Unknown
% 0.21/0.50  % (19038)Termination phase: Preprocessing 1
% 0.21/0.50  
% 0.21/0.50  % (19038)Memory used [KB]: 1023
% 0.21/0.50  % (19038)Time elapsed: 0.004 s
% 0.21/0.50  % (19038)Instructions burned: 2 (million)
% 0.21/0.50  % (19038)------------------------------
% 0.21/0.50  % (19038)------------------------------
% 0.21/0.50  % (19040)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.50  % (19054)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.21/0.50  % (19048)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.51  % (19037)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.51  % (19037)Instruction limit reached!
% 0.21/0.51  % (19037)------------------------------
% 0.21/0.51  % (19037)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (19053)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)
% 0.21/0.52  % (19037)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (19037)Termination reason: Unknown
% 0.21/0.52  % (19037)Termination phase: Property scanning
% 0.21/0.52  
% 0.21/0.52  % (19037)Memory used [KB]: 1279
% 0.21/0.52  % (19037)Time elapsed: 0.006 s
% 0.21/0.52  % (19037)Instructions burned: 7 (million)
% 0.21/0.52  % (19037)------------------------------
% 0.21/0.52  % (19037)------------------------------
% 0.21/0.53  % (19043)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.37/0.53  % (19039)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)
% 1.37/0.54  % (19055)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.37/0.54  % (19059)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)
% 1.37/0.54  % (19035)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)
% 1.37/0.55  % (19031)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)
% 1.37/0.55  % (19032)Instruction limit reached!
% 1.37/0.55  % (19032)------------------------------
% 1.37/0.55  % (19032)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.37/0.55  % (19032)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.37/0.55  % (19032)Termination reason: Unknown
% 1.37/0.55  % (19032)Termination phase: Saturation
% 1.37/0.55  
% 1.37/0.55  % (19032)Memory used [KB]: 1791
% 1.37/0.55  % (19032)Time elapsed: 0.131 s
% 1.37/0.55  % (19032)Instructions burned: 37 (million)
% 1.37/0.55  % (19032)------------------------------
% 1.37/0.55  % (19032)------------------------------
% 1.37/0.55  % (19034)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.37/0.55  % (19047)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.55/0.56  % (19051)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.55/0.58  % (19030)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)
% 1.55/0.59  % (19040)Instruction limit reached!
% 1.55/0.59  % (19040)------------------------------
% 1.55/0.59  % (19040)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.55/0.59  % (19040)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.55/0.59  % (19040)Termination reason: Unknown
% 1.55/0.59  % (19040)Termination phase: Saturation
% 1.55/0.59  
% 1.55/0.59  % (19040)Memory used [KB]: 6524
% 1.55/0.59  % (19040)Time elapsed: 0.168 s
% 1.55/0.59  % (19040)Instructions burned: 50 (million)
% 1.55/0.59  % (19040)------------------------------
% 1.55/0.59  % (19040)------------------------------
% 1.55/0.59  % (19050)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)
% 1.55/0.60  % (19042)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.55/0.61  % (19044)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)
% 1.55/0.61  % (19058)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.55/0.62  TRYING [1]
% 1.55/0.62  % (19045)Instruction limit reached!
% 1.55/0.62  % (19045)------------------------------
% 1.55/0.62  % (19045)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.55/0.62  % (19052)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)
% 1.55/0.62  % (19033)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)
% 1.55/0.63  % (19045)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.55/0.63  % (19045)Termination reason: Unknown
% 1.55/0.63  % (19045)Termination phase: Saturation
% 1.55/0.63  
% 1.55/0.63  % (19045)Memory used [KB]: 2430
% 1.55/0.63  % (19045)Time elapsed: 0.199 s
% 1.55/0.63  % (19045)Instructions burned: 75 (million)
% 1.55/0.63  % (19045)------------------------------
% 1.55/0.63  % (19045)------------------------------
% 1.55/0.63  % (19031)Refutation not found, incomplete strategy% (19031)------------------------------
% 1.55/0.63  % (19031)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.55/0.63  % (19031)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.55/0.63  % (19031)Termination reason: Refutation not found, incomplete strategy
% 1.55/0.63  
% 1.55/0.63  % (19031)Memory used [KB]: 6140
% 1.55/0.63  % (19031)Time elapsed: 0.185 s
% 1.55/0.63  % (19031)Instructions burned: 24 (million)
% 1.55/0.63  % (19031)------------------------------
% 1.55/0.63  % (19031)------------------------------
% 1.55/0.63  TRYING [2]
% 1.55/0.64  % (19041)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)
% 1.55/0.64  % (19053)First to succeed.
% 1.55/0.64  % (19056)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)
% 1.55/0.64  % (19036)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)
% 1.55/0.64  % (19049)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)
% 2.19/0.65  % (19057)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)
% 2.19/0.65  % (19053)Refutation found. Thanks to Tanya!
% 2.19/0.65  % SZS status Theorem for theBenchmark
% 2.19/0.65  % SZS output start Proof for theBenchmark
% See solution above
% 2.19/0.65  % (19053)------------------------------
% 2.19/0.65  % (19053)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.19/0.65  % (19053)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.19/0.65  % (19053)Termination reason: Refutation
% 2.19/0.65  
% 2.19/0.65  % (19053)Memory used [KB]: 6780
% 2.19/0.65  % (19053)Time elapsed: 0.238 s
% 2.19/0.65  % (19053)Instructions burned: 67 (million)
% 2.19/0.65  % (19053)------------------------------
% 2.19/0.65  % (19053)------------------------------
% 2.19/0.65  % (19029)Success in time 0.293 s
%------------------------------------------------------------------------------