TSTP Solution File: SWC118+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC118+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 : n017.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 18:41:50 EDT 2022

% Result   : Theorem 0.20s 0.59s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   62 (  13 unt;   0 def)
%            Number of atoms       :  602 ( 193 equ)
%            Maximal formula atoms :   60 (   9 avg)
%            Number of connectives :  887 ( 347   ~; 297   |; 210   &)
%                                         (   9 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (   8 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   6 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  243 ( 167   !;  76   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f721,plain,
    $false,
    inference(avatar_sat_refutation,[],[f610,f626,f635,f641,f655,f720]) ).

fof(f720,plain,
    spl59_1,
    inference(avatar_contradiction_clause,[],[f719]) ).

fof(f719,plain,
    ( $false
    | spl59_1 ),
    inference(subsumption_resolution,[],[f718,f443]) ).

fof(f443,plain,
    ssList(sK23),
    inference(cnf_transformation,[],[f276]) ).

fof(f276,plain,
    ( ssList(sK20)
    & ssList(sK22)
    & ( ~ neq(sK20,nil)
      | ~ segmentP(sK21,sK20) )
    & ( nil = sK23
      | nil != sK22 )
    & ( nil != sK20
      | nil != sK21 )
    & sK21 = sK23
    & sK20 = sK22
    & ssList(sK24)
    & ! [X6] :
        ( ~ ssItem(X6)
        | ! [X7] :
            ( app(X7,cons(X6,nil)) != sK24
            | ~ ssList(X7)
            | ! [X8] :
                ( ~ ssItem(X8)
                | ! [X9] :
                    ( ~ ssList(X9)
                    | app(cons(X8,nil),X9) != sK22
                    | ~ leq(X6,X8) ) ) ) )
    & totalorderedP(sK22)
    & app(app(sK24,sK22),sK25) = sK23
    & ssList(sK25)
    & ! [X10] :
        ( ! [X11] :
            ( app(cons(X10,nil),X11) != sK25
            | ! [X12] :
                ( ! [X13] :
                    ( app(X13,cons(X12,nil)) != sK22
                    | ~ ssList(X13)
                    | ~ leq(X12,X10) )
                | ~ ssItem(X12) )
            | ~ ssList(X11) )
        | ~ ssItem(X10) )
    & ssList(sK23)
    & ssList(sK21) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25])],[f208,f275,f274,f273,f272,f271,f270]) ).

fof(f270,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ( ~ neq(X0,nil)
                      | ~ segmentP(X1,X0) )
                    & ( nil = X3
                      | nil != X2 )
                    & ( nil != X0
                      | nil != X1 )
                    & X1 = X3
                    & X0 = X2
                    & ? [X4] :
                        ( ssList(X4)
                        & ? [X5] :
                            ( ! [X6] :
                                ( ~ ssItem(X6)
                                | ! [X7] :
                                    ( app(X7,cons(X6,nil)) != X4
                                    | ~ ssList(X7)
                                    | ! [X8] :
                                        ( ~ ssItem(X8)
                                        | ! [X9] :
                                            ( ~ ssList(X9)
                                            | app(cons(X8,nil),X9) != X2
                                            | ~ leq(X6,X8) ) ) ) )
                            & totalorderedP(X2)
                            & app(app(X4,X2),X5) = X3
                            & ssList(X5)
                            & ! [X10] :
                                ( ! [X11] :
                                    ( app(cons(X10,nil),X11) != X5
                                    | ! [X12] :
                                        ( ! [X13] :
                                            ( app(X13,cons(X12,nil)) != X2
                                            | ~ ssList(X13)
                                            | ~ leq(X12,X10) )
                                        | ~ ssItem(X12) )
                                    | ~ ssList(X11) )
                                | ~ ssItem(X10) ) ) )
                    & ssList(X3) ) )
            & ssList(X1) ) )
   => ( ssList(sK20)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ( ~ neq(sK20,nil)
                    | ~ segmentP(X1,sK20) )
                  & ( nil = X3
                    | nil != X2 )
                  & ( nil != sK20
                    | nil != X1 )
                  & X1 = X3
                  & sK20 = X2
                  & ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ! [X6] :
                              ( ~ ssItem(X6)
                              | ! [X7] :
                                  ( app(X7,cons(X6,nil)) != X4
                                  | ~ ssList(X7)
                                  | ! [X8] :
                                      ( ~ ssItem(X8)
                                      | ! [X9] :
                                          ( ~ ssList(X9)
                                          | app(cons(X8,nil),X9) != X2
                                          | ~ leq(X6,X8) ) ) ) )
                          & totalorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5)
                          & ! [X10] :
                              ( ! [X11] :
                                  ( app(cons(X10,nil),X11) != X5
                                  | ! [X12] :
                                      ( ! [X13] :
                                          ( app(X13,cons(X12,nil)) != X2
                                          | ~ ssList(X13)
                                          | ~ leq(X12,X10) )
                                      | ~ ssItem(X12) )
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) ) ) )
                  & ssList(X3) ) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f271,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ( ~ neq(sK20,nil)
                  | ~ segmentP(X1,sK20) )
                & ( nil = X3
                  | nil != X2 )
                & ( nil != sK20
                  | nil != X1 )
                & X1 = X3
                & sK20 = X2
                & ? [X4] :
                    ( ssList(X4)
                    & ? [X5] :
                        ( ! [X6] :
                            ( ~ ssItem(X6)
                            | ! [X7] :
                                ( app(X7,cons(X6,nil)) != X4
                                | ~ ssList(X7)
                                | ! [X8] :
                                    ( ~ ssItem(X8)
                                    | ! [X9] :
                                        ( ~ ssList(X9)
                                        | app(cons(X8,nil),X9) != X2
                                        | ~ leq(X6,X8) ) ) ) )
                        & totalorderedP(X2)
                        & app(app(X4,X2),X5) = X3
                        & ssList(X5)
                        & ! [X10] :
                            ( ! [X11] :
                                ( app(cons(X10,nil),X11) != X5
                                | ! [X12] :
                                    ( ! [X13] :
                                        ( app(X13,cons(X12,nil)) != X2
                                        | ~ ssList(X13)
                                        | ~ leq(X12,X10) )
                                    | ~ ssItem(X12) )
                                | ~ ssList(X11) )
                            | ~ ssItem(X10) ) ) )
                & ssList(X3) ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ( ~ neq(sK20,nil)
                | ~ segmentP(sK21,sK20) )
              & ( nil = X3
                | nil != X2 )
              & ( nil != sK20
                | nil != sK21 )
              & sK21 = X3
              & sK20 = X2
              & ? [X4] :
                  ( ssList(X4)
                  & ? [X5] :
                      ( ! [X6] :
                          ( ~ ssItem(X6)
                          | ! [X7] :
                              ( app(X7,cons(X6,nil)) != X4
                              | ~ ssList(X7)
                              | ! [X8] :
                                  ( ~ ssItem(X8)
                                  | ! [X9] :
                                      ( ~ ssList(X9)
                                      | app(cons(X8,nil),X9) != X2
                                      | ~ leq(X6,X8) ) ) ) )
                      & totalorderedP(X2)
                      & app(app(X4,X2),X5) = X3
                      & ssList(X5)
                      & ! [X10] :
                          ( ! [X11] :
                              ( app(cons(X10,nil),X11) != X5
                              | ! [X12] :
                                  ( ! [X13] :
                                      ( app(X13,cons(X12,nil)) != X2
                                      | ~ ssList(X13)
                                      | ~ leq(X12,X10) )
                                  | ~ ssItem(X12) )
                              | ~ ssList(X11) )
                          | ~ ssItem(X10) ) ) )
              & ssList(X3) ) )
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f272,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ( ~ neq(sK20,nil)
              | ~ segmentP(sK21,sK20) )
            & ( nil = X3
              | nil != X2 )
            & ( nil != sK20
              | nil != sK21 )
            & sK21 = X3
            & sK20 = X2
            & ? [X4] :
                ( ssList(X4)
                & ? [X5] :
                    ( ! [X6] :
                        ( ~ ssItem(X6)
                        | ! [X7] :
                            ( app(X7,cons(X6,nil)) != X4
                            | ~ ssList(X7)
                            | ! [X8] :
                                ( ~ ssItem(X8)
                                | ! [X9] :
                                    ( ~ ssList(X9)
                                    | app(cons(X8,nil),X9) != X2
                                    | ~ leq(X6,X8) ) ) ) )
                    & totalorderedP(X2)
                    & app(app(X4,X2),X5) = X3
                    & ssList(X5)
                    & ! [X10] :
                        ( ! [X11] :
                            ( app(cons(X10,nil),X11) != X5
                            | ! [X12] :
                                ( ! [X13] :
                                    ( app(X13,cons(X12,nil)) != X2
                                    | ~ ssList(X13)
                                    | ~ leq(X12,X10) )
                                | ~ ssItem(X12) )
                            | ~ ssList(X11) )
                        | ~ ssItem(X10) ) ) )
            & ssList(X3) ) )
   => ( ssList(sK22)
      & ? [X3] :
          ( ( ~ neq(sK20,nil)
            | ~ segmentP(sK21,sK20) )
          & ( nil = X3
            | nil != sK22 )
          & ( nil != sK20
            | nil != sK21 )
          & sK21 = X3
          & sK20 = sK22
          & ? [X4] :
              ( ssList(X4)
              & ? [X5] :
                  ( ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( app(X7,cons(X6,nil)) != X4
                          | ~ ssList(X7)
                          | ! [X8] :
                              ( ~ ssItem(X8)
                              | ! [X9] :
                                  ( ~ ssList(X9)
                                  | app(cons(X8,nil),X9) != sK22
                                  | ~ leq(X6,X8) ) ) ) )
                  & totalorderedP(sK22)
                  & app(app(X4,sK22),X5) = X3
                  & ssList(X5)
                  & ! [X10] :
                      ( ! [X11] :
                          ( app(cons(X10,nil),X11) != X5
                          | ! [X12] :
                              ( ! [X13] :
                                  ( app(X13,cons(X12,nil)) != sK22
                                  | ~ ssList(X13)
                                  | ~ leq(X12,X10) )
                              | ~ ssItem(X12) )
                          | ~ ssList(X11) )
                      | ~ ssItem(X10) ) ) )
          & ssList(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f273,plain,
    ( ? [X3] :
        ( ( ~ neq(sK20,nil)
          | ~ segmentP(sK21,sK20) )
        & ( nil = X3
          | nil != sK22 )
        & ( nil != sK20
          | nil != sK21 )
        & sK21 = X3
        & sK20 = sK22
        & ? [X4] :
            ( ssList(X4)
            & ? [X5] :
                ( ! [X6] :
                    ( ~ ssItem(X6)
                    | ! [X7] :
                        ( app(X7,cons(X6,nil)) != X4
                        | ~ ssList(X7)
                        | ! [X8] :
                            ( ~ ssItem(X8)
                            | ! [X9] :
                                ( ~ ssList(X9)
                                | app(cons(X8,nil),X9) != sK22
                                | ~ leq(X6,X8) ) ) ) )
                & totalorderedP(sK22)
                & app(app(X4,sK22),X5) = X3
                & ssList(X5)
                & ! [X10] :
                    ( ! [X11] :
                        ( app(cons(X10,nil),X11) != X5
                        | ! [X12] :
                            ( ! [X13] :
                                ( app(X13,cons(X12,nil)) != sK22
                                | ~ ssList(X13)
                                | ~ leq(X12,X10) )
                            | ~ ssItem(X12) )
                        | ~ ssList(X11) )
                    | ~ ssItem(X10) ) ) )
        & ssList(X3) )
   => ( ( ~ neq(sK20,nil)
        | ~ segmentP(sK21,sK20) )
      & ( nil = sK23
        | nil != sK22 )
      & ( nil != sK20
        | nil != sK21 )
      & sK21 = sK23
      & sK20 = sK22
      & ? [X4] :
          ( ssList(X4)
          & ? [X5] :
              ( ! [X6] :
                  ( ~ ssItem(X6)
                  | ! [X7] :
                      ( app(X7,cons(X6,nil)) != X4
                      | ~ ssList(X7)
                      | ! [X8] :
                          ( ~ ssItem(X8)
                          | ! [X9] :
                              ( ~ ssList(X9)
                              | app(cons(X8,nil),X9) != sK22
                              | ~ leq(X6,X8) ) ) ) )
              & totalorderedP(sK22)
              & app(app(X4,sK22),X5) = sK23
              & ssList(X5)
              & ! [X10] :
                  ( ! [X11] :
                      ( app(cons(X10,nil),X11) != X5
                      | ! [X12] :
                          ( ! [X13] :
                              ( app(X13,cons(X12,nil)) != sK22
                              | ~ ssList(X13)
                              | ~ leq(X12,X10) )
                          | ~ ssItem(X12) )
                      | ~ ssList(X11) )
                  | ~ ssItem(X10) ) ) )
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f274,plain,
    ( ? [X4] :
        ( ssList(X4)
        & ? [X5] :
            ( ! [X6] :
                ( ~ ssItem(X6)
                | ! [X7] :
                    ( app(X7,cons(X6,nil)) != X4
                    | ~ ssList(X7)
                    | ! [X8] :
                        ( ~ ssItem(X8)
                        | ! [X9] :
                            ( ~ ssList(X9)
                            | app(cons(X8,nil),X9) != sK22
                            | ~ leq(X6,X8) ) ) ) )
            & totalorderedP(sK22)
            & app(app(X4,sK22),X5) = sK23
            & ssList(X5)
            & ! [X10] :
                ( ! [X11] :
                    ( app(cons(X10,nil),X11) != X5
                    | ! [X12] :
                        ( ! [X13] :
                            ( app(X13,cons(X12,nil)) != sK22
                            | ~ ssList(X13)
                            | ~ leq(X12,X10) )
                        | ~ ssItem(X12) )
                    | ~ ssList(X11) )
                | ~ ssItem(X10) ) ) )
   => ( ssList(sK24)
      & ? [X5] :
          ( ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( app(X7,cons(X6,nil)) != sK24
                  | ~ ssList(X7)
                  | ! [X8] :
                      ( ~ ssItem(X8)
                      | ! [X9] :
                          ( ~ ssList(X9)
                          | app(cons(X8,nil),X9) != sK22
                          | ~ leq(X6,X8) ) ) ) )
          & totalorderedP(sK22)
          & app(app(sK24,sK22),X5) = sK23
          & ssList(X5)
          & ! [X10] :
              ( ! [X11] :
                  ( app(cons(X10,nil),X11) != X5
                  | ! [X12] :
                      ( ! [X13] :
                          ( app(X13,cons(X12,nil)) != sK22
                          | ~ ssList(X13)
                          | ~ leq(X12,X10) )
                      | ~ ssItem(X12) )
                  | ~ ssList(X11) )
              | ~ ssItem(X10) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f275,plain,
    ( ? [X5] :
        ( ! [X6] :
            ( ~ ssItem(X6)
            | ! [X7] :
                ( app(X7,cons(X6,nil)) != sK24
                | ~ ssList(X7)
                | ! [X8] :
                    ( ~ ssItem(X8)
                    | ! [X9] :
                        ( ~ ssList(X9)
                        | app(cons(X8,nil),X9) != sK22
                        | ~ leq(X6,X8) ) ) ) )
        & totalorderedP(sK22)
        & app(app(sK24,sK22),X5) = sK23
        & ssList(X5)
        & ! [X10] :
            ( ! [X11] :
                ( app(cons(X10,nil),X11) != X5
                | ! [X12] :
                    ( ! [X13] :
                        ( app(X13,cons(X12,nil)) != sK22
                        | ~ ssList(X13)
                        | ~ leq(X12,X10) )
                    | ~ ssItem(X12) )
                | ~ ssList(X11) )
            | ~ ssItem(X10) ) )
   => ( ! [X6] :
          ( ~ ssItem(X6)
          | ! [X7] :
              ( app(X7,cons(X6,nil)) != sK24
              | ~ ssList(X7)
              | ! [X8] :
                  ( ~ ssItem(X8)
                  | ! [X9] :
                      ( ~ ssList(X9)
                      | app(cons(X8,nil),X9) != sK22
                      | ~ leq(X6,X8) ) ) ) )
      & totalorderedP(sK22)
      & app(app(sK24,sK22),sK25) = sK23
      & ssList(sK25)
      & ! [X10] :
          ( ! [X11] :
              ( app(cons(X10,nil),X11) != sK25
              | ! [X12] :
                  ( ! [X13] :
                      ( app(X13,cons(X12,nil)) != sK22
                      | ~ ssList(X13)
                      | ~ leq(X12,X10) )
                  | ~ ssItem(X12) )
              | ~ ssList(X11) )
          | ~ ssItem(X10) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f208,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ( ~ neq(X0,nil)
                    | ~ segmentP(X1,X0) )
                  & ( nil = X3
                    | nil != X2 )
                  & ( nil != X0
                    | nil != X1 )
                  & X1 = X3
                  & X0 = X2
                  & ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ! [X6] :
                              ( ~ ssItem(X6)
                              | ! [X7] :
                                  ( app(X7,cons(X6,nil)) != X4
                                  | ~ ssList(X7)
                                  | ! [X8] :
                                      ( ~ ssItem(X8)
                                      | ! [X9] :
                                          ( ~ ssList(X9)
                                          | app(cons(X8,nil),X9) != X2
                                          | ~ leq(X6,X8) ) ) ) )
                          & totalorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5)
                          & ! [X10] :
                              ( ! [X11] :
                                  ( app(cons(X10,nil),X11) != X5
                                  | ! [X12] :
                                      ( ! [X13] :
                                          ( app(X13,cons(X12,nil)) != X2
                                          | ~ ssList(X13)
                                          | ~ leq(X12,X10) )
                                      | ~ ssItem(X12) )
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) ) ) )
                  & ssList(X3) ) )
          & ssList(X1) ) ),
    inference(flattening,[],[f207]) ).

fof(f207,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & ( ~ neq(X0,nil)
                    | ~ segmentP(X1,X0) )
                  & ( nil != X0
                    | nil != X1 )
                  & ( nil = X3
                    | nil != X2 )
                  & X1 = X3
                  & ? [X4] :
                      ( ? [X5] :
                          ( totalorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ! [X10] :
                              ( ! [X11] :
                                  ( app(cons(X10,nil),X11) != X5
                                  | ! [X12] :
                                      ( ! [X13] :
                                          ( app(X13,cons(X12,nil)) != X2
                                          | ~ ssList(X13)
                                          | ~ leq(X12,X10) )
                                      | ~ ssItem(X12) )
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & ! [X6] :
                              ( ~ ssItem(X6)
                              | ! [X7] :
                                  ( app(X7,cons(X6,nil)) != X4
                                  | ~ ssList(X7)
                                  | ! [X8] :
                                      ( ~ ssItem(X8)
                                      | ! [X9] :
                                          ( ~ ssList(X9)
                                          | app(cons(X8,nil),X9) != X2
                                          | ~ leq(X6,X8) ) ) ) )
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

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

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

fof(f718,plain,
    ( ~ ssList(sK23)
    | spl59_1 ),
    inference(subsumption_resolution,[],[f717,f449]) ).

fof(f449,plain,
    ssList(sK24),
    inference(cnf_transformation,[],[f276]) ).

fof(f717,plain,
    ( ~ ssList(sK24)
    | ~ ssList(sK23)
    | spl59_1 ),
    inference(subsumption_resolution,[],[f716,f605]) ).

fof(f605,plain,
    ( ~ segmentP(sK23,sK22)
    | spl59_1 ),
    inference(avatar_component_clause,[],[f603]) ).

fof(f603,plain,
    ( spl59_1
  <=> segmentP(sK23,sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl59_1])]) ).

fof(f716,plain,
    ( segmentP(sK23,sK22)
    | ~ ssList(sK23)
    | ~ ssList(sK24) ),
    inference(subsumption_resolution,[],[f715,f564]) ).

fof(f564,plain,
    ssList(sK22),
    inference(definition_unfolding,[],[f456,f450]) ).

fof(f450,plain,
    sK20 = sK22,
    inference(cnf_transformation,[],[f276]) ).

fof(f456,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f276]) ).

fof(f715,plain,
    ( ~ ssList(sK22)
    | segmentP(sK23,sK22)
    | ~ ssList(sK24)
    | ~ ssList(sK23) ),
    inference(subsumption_resolution,[],[f712,f445]) ).

fof(f445,plain,
    ssList(sK25),
    inference(cnf_transformation,[],[f276]) ).

fof(f712,plain,
    ( ~ ssList(sK25)
    | ~ ssList(sK23)
    | ~ ssList(sK22)
    | ~ ssList(sK24)
    | segmentP(sK23,sK22) ),
    inference(superposition,[],[f587,f446]) ).

fof(f446,plain,
    app(app(sK24,sK22),sK25) = sK23,
    inference(cnf_transformation,[],[f276]) ).

fof(f587,plain,
    ! [X1,X4,X5] :
      ( segmentP(app(app(X4,X1),X5),X1)
      | ~ ssList(X1)
      | ~ ssList(X4)
      | ~ ssList(X5)
      | ~ ssList(app(app(X4,X1),X5)) ),
    inference(equality_resolution,[],[f525]) ).

fof(f525,plain,
    ! [X0,X1,X4,X5] :
      ( ~ ssList(X0)
      | segmentP(X0,X1)
      | app(app(X4,X1),X5) != X0
      | ~ ssList(X5)
      | ~ ssList(X4)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f323]) ).

fof(f323,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( ( app(app(sK47(X0,X1),X1),sK48(X0,X1)) = X0
                & ssList(sK48(X0,X1))
                & ssList(sK47(X0,X1)) )
              | ~ segmentP(X0,X1) )
            & ( segmentP(X0,X1)
              | ! [X4] :
                  ( ! [X5] :
                      ( app(app(X4,X1),X5) != X0
                      | ~ ssList(X5) )
                  | ~ ssList(X4) ) ) )
          | ~ ssList(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48])],[f320,f322,f321]) ).

fof(f321,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( app(app(X2,X1),X3) = X0
              & ssList(X3) )
          & ssList(X2) )
     => ( ? [X3] :
            ( app(app(sK47(X0,X1),X1),X3) = X0
            & ssList(X3) )
        & ssList(sK47(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f322,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(app(sK47(X0,X1),X1),X3) = X0
          & ssList(X3) )
     => ( app(app(sK47(X0,X1),X1),sK48(X0,X1)) = X0
        & ssList(sK48(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f319,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) )
            & ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) ) )
          | ~ ssList(X1) ) ),
    inference(nnf_transformation,[],[f154]) ).

fof(f154,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) )
          <=> segmentP(X0,X1) )
          | ~ ssList(X1) ) ),
    inference(ennf_transformation,[],[f7]) ).

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

fof(f655,plain,
    ( spl59_2
    | ~ spl59_3
    | spl59_6 ),
    inference(avatar_contradiction_clause,[],[f654]) ).

fof(f654,plain,
    ( $false
    | spl59_2
    | ~ spl59_3
    | spl59_6 ),
    inference(unit_resulting_resolution,[],[f614,f564,f630,f609,f391]) ).

fof(f391,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f251]) ).

fof(f251,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( neq(X0,X1)
          <=> X0 != X1 ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

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

fof(f609,plain,
    ( ~ neq(sK22,nil)
    | spl59_2 ),
    inference(avatar_component_clause,[],[f607]) ).

fof(f607,plain,
    ( spl59_2
  <=> neq(sK22,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl59_2])]) ).

fof(f630,plain,
    ( nil != sK22
    | spl59_6 ),
    inference(avatar_component_clause,[],[f628]) ).

fof(f628,plain,
    ( spl59_6
  <=> nil = sK22 ),
    introduced(avatar_definition,[new_symbols(naming,[spl59_6])]) ).

fof(f614,plain,
    ( ssList(nil)
    | ~ spl59_3 ),
    inference(avatar_component_clause,[],[f613]) ).

fof(f613,plain,
    ( spl59_3
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl59_3])]) ).

fof(f641,plain,
    ( ~ spl59_6
    | spl59_7 ),
    inference(avatar_split_clause,[],[f453,f632,f628]) ).

fof(f632,plain,
    ( spl59_7
  <=> nil = sK23 ),
    introduced(avatar_definition,[new_symbols(naming,[spl59_7])]) ).

fof(f453,plain,
    ( nil = sK23
    | nil != sK22 ),
    inference(cnf_transformation,[],[f276]) ).

fof(f635,plain,
    ( ~ spl59_6
    | ~ spl59_7 ),
    inference(avatar_split_clause,[],[f566,f632,f628]) ).

fof(f566,plain,
    ( nil != sK23
    | nil != sK22 ),
    inference(definition_unfolding,[],[f452,f450,f451]) ).

fof(f451,plain,
    sK21 = sK23,
    inference(cnf_transformation,[],[f276]) ).

fof(f452,plain,
    ( nil != sK20
    | nil != sK21 ),
    inference(cnf_transformation,[],[f276]) ).

fof(f626,plain,
    spl59_3,
    inference(avatar_split_clause,[],[f385,f613]) ).

fof(f385,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f610,plain,
    ( ~ spl59_1
    | ~ spl59_2 ),
    inference(avatar_split_clause,[],[f565,f607,f603]) ).

fof(f565,plain,
    ( ~ neq(sK22,nil)
    | ~ segmentP(sK23,sK22) ),
    inference(definition_unfolding,[],[f454,f450,f451,f450]) ).

fof(f454,plain,
    ( ~ neq(sK20,nil)
    | ~ segmentP(sK21,sK20) ),
    inference(cnf_transformation,[],[f276]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC118+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
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 17:42:35 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.52  % (5723)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)
% 0.20/0.52  % (5735)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)
% 0.20/0.52  % (5744)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)
% 0.20/0.52  % (5733)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52  % (5734)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)
% 0.20/0.52  % (5722)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)
% 0.20/0.53  % (5725)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)
% 0.20/0.53  % (5720)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)
% 0.20/0.53  % (5727)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53  % (5738)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.53  % (5721)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)
% 0.20/0.53  % (5726)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)
% 0.20/0.54  % (5728)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.54  % (5728)Instruction limit reached!
% 0.20/0.54  % (5728)------------------------------
% 0.20/0.54  % (5728)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (5728)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (5728)Termination reason: Unknown
% 0.20/0.54  % (5728)Termination phase: Preprocessing 2
% 0.20/0.54  
% 0.20/0.54  % (5728)Memory used [KB]: 1023
% 0.20/0.54  % (5728)Time elapsed: 0.002 s
% 0.20/0.54  % (5728)Instructions burned: 3 (million)
% 0.20/0.54  % (5728)------------------------------
% 0.20/0.54  % (5728)------------------------------
% 0.20/0.54  % (5724)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (5731)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)
% 0.20/0.54  % (5727)Instruction limit reached!
% 0.20/0.54  % (5727)------------------------------
% 0.20/0.54  % (5727)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (5727)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (5727)Termination reason: Unknown
% 0.20/0.54  % (5727)Termination phase: Function definition elimination
% 0.20/0.54  
% 0.20/0.54  % (5727)Memory used [KB]: 1279
% 0.20/0.54  % (5727)Time elapsed: 0.009 s
% 0.20/0.54  % (5727)Instructions burned: 8 (million)
% 0.20/0.54  % (5727)------------------------------
% 0.20/0.54  % (5727)------------------------------
% 0.20/0.54  % (5730)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54  % (5732)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.54  % (5741)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)
% 0.20/0.54  % (5740)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)
% 0.20/0.54  % (5745)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.55  % (5729)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)
% 0.20/0.55  % (5737)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)
% 0.20/0.55  % (5742)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.55  % (5748)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)
% 0.20/0.55  % (5747)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)
% 0.20/0.55  % (5750)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)
% 0.20/0.55  % (5739)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.56  % (5746)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.56  % (5749)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.56  % (5721)First to succeed.
% 0.20/0.57  % (5743)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)
% 0.20/0.58  TRYING [1]
% 0.20/0.58  TRYING [1]
% 0.20/0.58  TRYING [2]
% 0.20/0.58  TRYING [1]
% 0.20/0.58  TRYING [2]
% 0.20/0.58  TRYING [2]
% 0.20/0.59  % (5722)Instruction limit reached!
% 0.20/0.59  % (5722)------------------------------
% 0.20/0.59  % (5722)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.59  % (5722)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.59  % (5722)Termination reason: Unknown
% 0.20/0.59  % (5722)Termination phase: Saturation
% 0.20/0.59  
% 0.20/0.59  % (5722)Memory used [KB]: 1791
% 0.20/0.59  % (5722)Time elapsed: 0.175 s
% 0.20/0.59  % (5722)Instructions burned: 38 (million)
% 0.20/0.59  % (5722)------------------------------
% 0.20/0.59  % (5722)------------------------------
% 0.20/0.59  % (5721)Refutation found. Thanks to Tanya!
% 0.20/0.59  % SZS status Theorem for theBenchmark
% 0.20/0.59  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.59  % (5721)------------------------------
% 0.20/0.59  % (5721)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.59  % (5721)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.59  % (5721)Termination reason: Refutation
% 0.20/0.59  
% 0.20/0.59  % (5721)Memory used [KB]: 6140
% 0.20/0.59  % (5721)Time elapsed: 0.155 s
% 0.20/0.59  % (5721)Instructions burned: 22 (million)
% 0.20/0.59  % (5721)------------------------------
% 0.20/0.59  % (5721)------------------------------
% 0.20/0.59  % (5716)Success in time 0.234 s
%------------------------------------------------------------------------------