TSTP Solution File: SWC239+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC239+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 : n002.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 18:42:37 EDT 2022

% Result   : Theorem 0.16s 0.54s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   53 (  10 unt;   0 def)
%            Number of atoms       :  463 ( 159 equ)
%            Maximal formula atoms :   50 (   8 avg)
%            Number of connectives :  614 ( 204   ~; 179   |; 210   &)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   8 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-3 aty)
%            Number of variables   :  154 (  94   !;  60   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f757,plain,
    $false,
    inference(subsumption_resolution,[],[f756,f561]) ).

fof(f561,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f756,plain,
    ~ ssList(nil),
    inference(trivial_inequality_removal,[],[f755]) ).

fof(f755,plain,
    ( sK16 != sK16
    | ~ ssList(nil) ),
    inference(superposition,[],[f749,f693]) ).

fof(f693,plain,
    app(sK16,nil) = sK16,
    inference(resolution,[],[f374,f376]) ).

fof(f376,plain,
    ssList(sK16),
    inference(cnf_transformation,[],[f256]) ).

fof(f256,plain,
    ( nil != sK16
    & sK19 = sK17
    & ssList(sK19)
    & ( ( nil = sK19
        & nil = sK18 )
      | ( ssItem(sK20)
        & ! [X5] :
            ( ~ ssItem(X5)
            | ~ memberP(sK19,X5)
            | ~ leq(sK20,X5)
            | sK20 = X5 )
        & sK18 = cons(sK20,nil)
        & memberP(sK19,sK20) ) )
    & sK18 = sK16
    & ! [X6] :
        ( ~ ssItem(X6)
        | ! [X7] :
            ( ~ ssList(X7)
            | ! [X8] :
                ( ( memberP(X8,sK21(X6,X7,X8))
                  & lt(X6,sK21(X6,X7,X8))
                  & memberP(X7,sK21(X6,X7,X8))
                  & ssItem(sK21(X6,X7,X8))
                  & ~ leq(X6,sK21(X6,X7,X8)) )
                | ~ ssList(X8)
                | app(app(X7,cons(X6,nil)),X8) != sK16 ) ) )
    & ssList(sK18)
    & ssList(sK17)
    & ssList(sK16) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19,sK20,sK21])],[f249,f255,f254,f253,f252,f251,f250]) ).

fof(f250,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( nil != X0
                    & X1 = X3
                    & ssList(X3)
                    & ( ( nil = X3
                        & nil = X2 )
                      | ? [X4] :
                          ( ssItem(X4)
                          & ! [X5] :
                              ( ~ ssItem(X5)
                              | ~ memberP(X3,X5)
                              | ~ leq(X4,X5)
                              | X4 = X5 )
                          & cons(X4,nil) = X2
                          & memberP(X3,X4) ) )
                    & X0 = X2
                    & ! [X6] :
                        ( ~ ssItem(X6)
                        | ! [X7] :
                            ( ~ ssList(X7)
                            | ! [X8] :
                                ( ? [X9] :
                                    ( memberP(X8,X9)
                                    & lt(X6,X9)
                                    & memberP(X7,X9)
                                    & ssItem(X9)
                                    & ~ leq(X6,X9) )
                                | ~ ssList(X8)
                                | app(app(X7,cons(X6,nil)),X8) != X0 ) ) ) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( nil != sK16
                  & X1 = X3
                  & ssList(X3)
                  & ( ( nil = X3
                      & nil = X2 )
                    | ? [X4] :
                        ( ssItem(X4)
                        & ! [X5] :
                            ( ~ ssItem(X5)
                            | ~ memberP(X3,X5)
                            | ~ leq(X4,X5)
                            | X4 = X5 )
                        & cons(X4,nil) = X2
                        & memberP(X3,X4) ) )
                  & sK16 = X2
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( ~ ssList(X7)
                          | ! [X8] :
                              ( ? [X9] :
                                  ( memberP(X8,X9)
                                  & lt(X6,X9)
                                  & memberP(X7,X9)
                                  & ssItem(X9)
                                  & ~ leq(X6,X9) )
                              | ~ ssList(X8)
                              | app(app(X7,cons(X6,nil)),X8) != sK16 ) ) ) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK16) ) ),
    introduced(choice_axiom,[]) ).

fof(f251,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( nil != sK16
                & X1 = X3
                & ssList(X3)
                & ( ( nil = X3
                    & nil = X2 )
                  | ? [X4] :
                      ( ssItem(X4)
                      & ! [X5] :
                          ( ~ ssItem(X5)
                          | ~ memberP(X3,X5)
                          | ~ leq(X4,X5)
                          | X4 = X5 )
                      & cons(X4,nil) = X2
                      & memberP(X3,X4) ) )
                & sK16 = X2
                & ! [X6] :
                    ( ~ ssItem(X6)
                    | ! [X7] :
                        ( ~ ssList(X7)
                        | ! [X8] :
                            ( ? [X9] :
                                ( memberP(X8,X9)
                                & lt(X6,X9)
                                & memberP(X7,X9)
                                & ssItem(X9)
                                & ~ leq(X6,X9) )
                            | ~ ssList(X8)
                            | app(app(X7,cons(X6,nil)),X8) != sK16 ) ) ) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( nil != sK16
              & sK17 = X3
              & ssList(X3)
              & ( ( nil = X3
                  & nil = X2 )
                | ? [X4] :
                    ( ssItem(X4)
                    & ! [X5] :
                        ( ~ ssItem(X5)
                        | ~ memberP(X3,X5)
                        | ~ leq(X4,X5)
                        | X4 = X5 )
                    & cons(X4,nil) = X2
                    & memberP(X3,X4) ) )
              & sK16 = X2
              & ! [X6] :
                  ( ~ ssItem(X6)
                  | ! [X7] :
                      ( ~ ssList(X7)
                      | ! [X8] :
                          ( ? [X9] :
                              ( memberP(X8,X9)
                              & lt(X6,X9)
                              & memberP(X7,X9)
                              & ssItem(X9)
                              & ~ leq(X6,X9) )
                          | ~ ssList(X8)
                          | app(app(X7,cons(X6,nil)),X8) != sK16 ) ) ) )
          & ssList(X2) )
      & ssList(sK17) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( nil != sK16
            & sK17 = X3
            & ssList(X3)
            & ( ( nil = X3
                & nil = X2 )
              | ? [X4] :
                  ( ssItem(X4)
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ~ memberP(X3,X5)
                      | ~ leq(X4,X5)
                      | X4 = X5 )
                  & cons(X4,nil) = X2
                  & memberP(X3,X4) ) )
            & sK16 = X2
            & ! [X6] :
                ( ~ ssItem(X6)
                | ! [X7] :
                    ( ~ ssList(X7)
                    | ! [X8] :
                        ( ? [X9] :
                            ( memberP(X8,X9)
                            & lt(X6,X9)
                            & memberP(X7,X9)
                            & ssItem(X9)
                            & ~ leq(X6,X9) )
                        | ~ ssList(X8)
                        | app(app(X7,cons(X6,nil)),X8) != sK16 ) ) ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( nil != sK16
          & sK17 = X3
          & ssList(X3)
          & ( ( nil = X3
              & nil = sK18 )
            | ? [X4] :
                ( ssItem(X4)
                & ! [X5] :
                    ( ~ ssItem(X5)
                    | ~ memberP(X3,X5)
                    | ~ leq(X4,X5)
                    | X4 = X5 )
                & cons(X4,nil) = sK18
                & memberP(X3,X4) ) )
          & sK18 = sK16
          & ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( ~ ssList(X7)
                  | ! [X8] :
                      ( ? [X9] :
                          ( memberP(X8,X9)
                          & lt(X6,X9)
                          & memberP(X7,X9)
                          & ssItem(X9)
                          & ~ leq(X6,X9) )
                      | ~ ssList(X8)
                      | app(app(X7,cons(X6,nil)),X8) != sK16 ) ) ) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X3] :
        ( nil != sK16
        & sK17 = X3
        & ssList(X3)
        & ( ( nil = X3
            & nil = sK18 )
          | ? [X4] :
              ( ssItem(X4)
              & ! [X5] :
                  ( ~ ssItem(X5)
                  | ~ memberP(X3,X5)
                  | ~ leq(X4,X5)
                  | X4 = X5 )
              & cons(X4,nil) = sK18
              & memberP(X3,X4) ) )
        & sK18 = sK16
        & ! [X6] :
            ( ~ ssItem(X6)
            | ! [X7] :
                ( ~ ssList(X7)
                | ! [X8] :
                    ( ? [X9] :
                        ( memberP(X8,X9)
                        & lt(X6,X9)
                        & memberP(X7,X9)
                        & ssItem(X9)
                        & ~ leq(X6,X9) )
                    | ~ ssList(X8)
                    | app(app(X7,cons(X6,nil)),X8) != sK16 ) ) ) )
   => ( nil != sK16
      & sK19 = sK17
      & ssList(sK19)
      & ( ( nil = sK19
          & nil = sK18 )
        | ? [X4] :
            ( ssItem(X4)
            & ! [X5] :
                ( ~ ssItem(X5)
                | ~ memberP(sK19,X5)
                | ~ leq(X4,X5)
                | X4 = X5 )
            & cons(X4,nil) = sK18
            & memberP(sK19,X4) ) )
      & sK18 = sK16
      & ! [X6] :
          ( ~ ssItem(X6)
          | ! [X7] :
              ( ~ ssList(X7)
              | ! [X8] :
                  ( ? [X9] :
                      ( memberP(X8,X9)
                      & lt(X6,X9)
                      & memberP(X7,X9)
                      & ssItem(X9)
                      & ~ leq(X6,X9) )
                  | ~ ssList(X8)
                  | app(app(X7,cons(X6,nil)),X8) != sK16 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f254,plain,
    ( ? [X4] :
        ( ssItem(X4)
        & ! [X5] :
            ( ~ ssItem(X5)
            | ~ memberP(sK19,X5)
            | ~ leq(X4,X5)
            | X4 = X5 )
        & cons(X4,nil) = sK18
        & memberP(sK19,X4) )
   => ( ssItem(sK20)
      & ! [X5] :
          ( ~ ssItem(X5)
          | ~ memberP(sK19,X5)
          | ~ leq(sK20,X5)
          | sK20 = X5 )
      & sK18 = cons(sK20,nil)
      & memberP(sK19,sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f255,plain,
    ! [X6,X7,X8] :
      ( ? [X9] :
          ( memberP(X8,X9)
          & lt(X6,X9)
          & memberP(X7,X9)
          & ssItem(X9)
          & ~ leq(X6,X9) )
     => ( memberP(X8,sK21(X6,X7,X8))
        & lt(X6,sK21(X6,X7,X8))
        & memberP(X7,sK21(X6,X7,X8))
        & ssItem(sK21(X6,X7,X8))
        & ~ leq(X6,sK21(X6,X7,X8)) ) ),
    introduced(choice_axiom,[]) ).

fof(f249,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( nil != X0
                  & X1 = X3
                  & ssList(X3)
                  & ( ( nil = X3
                      & nil = X2 )
                    | ? [X4] :
                        ( ssItem(X4)
                        & ! [X5] :
                            ( ~ ssItem(X5)
                            | ~ memberP(X3,X5)
                            | ~ leq(X4,X5)
                            | X4 = X5 )
                        & cons(X4,nil) = X2
                        & memberP(X3,X4) ) )
                  & X0 = X2
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( ~ ssList(X7)
                          | ! [X8] :
                              ( ? [X9] :
                                  ( memberP(X8,X9)
                                  & lt(X6,X9)
                                  & memberP(X7,X9)
                                  & ssItem(X9)
                                  & ~ leq(X6,X9) )
                              | ~ ssList(X8)
                              | app(app(X7,cons(X6,nil)),X8) != X0 ) ) ) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(rectify,[],[f143]) ).

fof(f143,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( nil != X0
                  & X1 = X3
                  & ssList(X3)
                  & ( ( nil = X3
                      & nil = X2 )
                    | ? [X8] :
                        ( ssItem(X8)
                        & ! [X9] :
                            ( ~ ssItem(X9)
                            | ~ memberP(X3,X9)
                            | ~ leq(X8,X9)
                            | X8 = X9 )
                        & cons(X8,nil) = X2
                        & memberP(X3,X8) ) )
                  & X0 = X2
                  & ! [X4] :
                      ( ~ ssItem(X4)
                      | ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ? [X7] :
                                  ( memberP(X6,X7)
                                  & lt(X4,X7)
                                  & memberP(X5,X7)
                                  & ssItem(X7)
                                  & ~ leq(X4,X7) )
                              | ~ ssList(X6)
                              | app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f142]) ).

fof(f142,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & X0 = X2
                  & ( ( nil = X3
                      & nil = X2 )
                    | ? [X8] :
                        ( ! [X9] :
                            ( ~ ssItem(X9)
                            | ~ memberP(X3,X9)
                            | ~ leq(X8,X9)
                            | X8 = X9 )
                        & cons(X8,nil) = X2
                        & memberP(X3,X8)
                        & ssItem(X8) ) )
                  & ! [X4] :
                      ( ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( app(app(X5,cons(X4,nil)),X6) != X0
                              | ? [X7] :
                                  ( memberP(X6,X7)
                                  & lt(X4,X7)
                                  & ~ leq(X4,X7)
                                  & memberP(X5,X7)
                                  & ssItem(X7) )
                              | ~ ssList(X6) ) )
                      | ~ ssItem(X4) )
                  & nil != X0
                  & 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)
                   => ( X1 != X3
                      | X0 != X2
                      | ( ( nil != X3
                          | nil != X2 )
                        & ! [X8] :
                            ( ssItem(X8)
                           => ( ? [X9] :
                                  ( X8 != X9
                                  & memberP(X3,X9)
                                  & leq(X8,X9)
                                  & ssItem(X9) )
                              | cons(X8,nil) != X2
                              | ~ memberP(X3,X8) ) ) )
                      | ? [X4] :
                          ( ? [X5] :
                              ( ssList(X5)
                              & ? [X6] :
                                  ( app(app(X5,cons(X4,nil)),X6) = X0
                                  & ! [X7] :
                                      ( ssItem(X7)
                                     => ( ~ memberP(X6,X7)
                                        | ~ lt(X4,X7)
                                        | leq(X4,X7)
                                        | ~ memberP(X5,X7) ) )
                                  & ssList(X6) ) )
                          & ssItem(X4) )
                      | nil = X0 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f374,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f164]) ).

fof(f164,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).

fof(f749,plain,
    ! [X0] :
      ( sK16 != app(sK16,X0)
      | ~ ssList(X0) ),
    inference(backward_demodulation,[],[f671,f733]) ).

fof(f733,plain,
    app(nil,sK16) = sK16,
    inference(resolution,[],[f498,f376]) ).

fof(f498,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f156]) ).

fof(f156,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f671,plain,
    ! [X0] :
      ( app(app(nil,sK16),X0) != sK16
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f670,f395]) ).

fof(f395,plain,
    nil != sK16,
    inference(cnf_transformation,[],[f256]) ).

fof(f670,plain,
    ! [X0] :
      ( nil = sK16
      | app(app(nil,sK16),X0) != sK16
      | ~ ssList(X0) ),
    inference(superposition,[],[f666,f611]) ).

fof(f611,plain,
    ( sF59 = sK16
    | nil = sK16 ),
    inference(forward_demodulation,[],[f610,f384]) ).

fof(f384,plain,
    sK18 = sK16,
    inference(cnf_transformation,[],[f256]) ).

fof(f610,plain,
    ( nil = sK16
    | sK18 = sF59 ),
    inference(backward_demodulation,[],[f599,f384]) ).

fof(f599,plain,
    ( sK18 = sF59
    | nil = sK18 ),
    inference(definition_folding,[],[f386,f597]) ).

fof(f597,plain,
    sF59 = cons(sK20,nil),
    introduced(function_definition,[]) ).

fof(f386,plain,
    ( nil = sK18
    | sK18 = cons(sK20,nil) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f666,plain,
    ! [X0] :
      ( app(app(nil,sF59),X0) != sK16
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f664,f395]) ).

fof(f664,plain,
    ! [X0] :
      ( app(app(nil,sF59),X0) != sK16
      | ~ ssList(X0)
      | nil = sK16 ),
    inference(resolution,[],[f662,f612]) ).

fof(f612,plain,
    ( ssItem(sK20)
    | nil = sK16 ),
    inference(forward_demodulation,[],[f388,f384]) ).

fof(f388,plain,
    ( ssItem(sK20)
    | nil = sK18 ),
    inference(cnf_transformation,[],[f256]) ).

fof(f662,plain,
    ! [X0] :
      ( ~ ssItem(sK20)
      | app(app(nil,sF59),X0) != sK16
      | ~ ssList(X0) ),
    inference(duplicate_literal_removal,[],[f661]) ).

fof(f661,plain,
    ! [X0] :
      ( app(app(nil,sF59),X0) != sK16
      | ~ ssList(X0)
      | ~ ssItem(sK20)
      | app(app(nil,sF59),X0) != sK16 ),
    inference(forward_demodulation,[],[f660,f597]) ).

fof(f660,plain,
    ! [X0] :
      ( ~ ssItem(sK20)
      | sK16 != app(app(nil,cons(sK20,nil)),X0)
      | app(app(nil,sF59),X0) != sK16
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f659,f561]) ).

fof(f659,plain,
    ! [X0] :
      ( app(app(nil,sF59),X0) != sK16
      | ~ ssList(X0)
      | ~ ssItem(sK20)
      | sK16 != app(app(nil,cons(sK20,nil)),X0)
      | ~ ssList(nil) ),
    inference(duplicate_literal_removal,[],[f658]) ).

fof(f658,plain,
    ! [X0] :
      ( ~ ssItem(sK20)
      | ~ ssList(X0)
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssItem(sK20)
      | app(app(nil,sF59),X0) != sK16
      | sK16 != app(app(nil,cons(sK20,nil)),X0) ),
    inference(resolution,[],[f655,f380]) ).

fof(f380,plain,
    ! [X8,X6,X7] :
      ( ssItem(sK21(X6,X7,X8))
      | ~ ssItem(X6)
      | ~ ssList(X8)
      | ~ ssList(X7)
      | app(app(X7,cons(X6,nil)),X8) != sK16 ),
    inference(cnf_transformation,[],[f256]) ).

fof(f655,plain,
    ! [X0] :
      ( ~ ssItem(sK21(sK20,nil,X0))
      | ~ ssList(X0)
      | ~ ssItem(sK20)
      | app(app(nil,sF59),X0) != sK16 ),
    inference(subsumption_resolution,[],[f654,f561]) ).

fof(f654,plain,
    ! [X0] :
      ( ~ ssList(nil)
      | ~ ssItem(sK21(sK20,nil,X0))
      | app(app(nil,sF59),X0) != sK16
      | ~ ssList(X0)
      | ~ ssItem(sK20) ),
    inference(resolution,[],[f631,f483]) ).

fof(f483,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f198]) ).

fof(f198,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f631,plain,
    ! [X4,X5] :
      ( memberP(X4,sK21(sK20,X4,X5))
      | ~ ssList(X5)
      | ~ ssList(X4)
      | ~ ssItem(sK20)
      | sK16 != app(app(X4,sF59),X5) ),
    inference(superposition,[],[f381,f597]) ).

fof(f381,plain,
    ! [X8,X6,X7] :
      ( app(app(X7,cons(X6,nil)),X8) != sK16
      | memberP(X7,sK21(X6,X7,X8))
      | ~ ssList(X7)
      | ~ ssList(X8)
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f256]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SWC239+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.10/0.31  % Computer : n002.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Tue Aug 30 18:49:44 EDT 2022
% 0.10/0.31  % CPUTime    : 
% 0.16/0.46  % (30565)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)
% 0.16/0.47  % (30567)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)
% 0.16/0.48  % (30580)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)
% 0.16/0.48  % (30587)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)
% 0.16/0.49  % (30574)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)
% 0.16/0.50  % (30589)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.16/0.50  % (30566)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)
% 0.16/0.50  % (30578)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.16/0.50  % (30576)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)
% 0.16/0.51  % (30581)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)
% 0.16/0.52  % (30568)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)
% 0.16/0.52  % (30580)First to succeed.
% 0.16/0.52  TRYING [1]
% 0.16/0.52  TRYING [2]
% 0.16/0.52  % (30571)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)
% 0.16/0.52  % (30569)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.16/0.52  % (30577)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.16/0.53  % (30573)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.53  % (30573)Instruction limit reached!
% 0.16/0.53  % (30573)------------------------------
% 0.16/0.53  % (30573)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.53  % (30573)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.53  % (30573)Termination reason: Unknown
% 0.16/0.53  % (30573)Termination phase: Preprocessing 2
% 0.16/0.53  
% 0.16/0.53  % (30573)Memory used [KB]: 1023
% 0.16/0.53  % (30573)Time elapsed: 0.003 s
% 0.16/0.53  % (30573)Instructions burned: 3 (million)
% 0.16/0.53  % (30573)------------------------------
% 0.16/0.53  % (30573)------------------------------
% 0.16/0.53  % (30567)Instruction limit reached!
% 0.16/0.53  % (30567)------------------------------
% 0.16/0.53  % (30567)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.53  % (30567)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.53  % (30567)Termination reason: Unknown
% 0.16/0.53  % (30567)Termination phase: Saturation
% 0.16/0.53  
% 0.16/0.53  % (30567)Memory used [KB]: 1663
% 0.16/0.53  % (30567)Time elapsed: 0.143 s
% 0.16/0.53  % (30567)Instructions burned: 38 (million)
% 0.16/0.53  % (30567)------------------------------
% 0.16/0.53  % (30567)------------------------------
% 0.16/0.54  % (30586)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.16/0.54  % (30593)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.16/0.54  % (30575)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.16/0.54  % (30583)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.16/0.54  % (30574)Also succeeded, but the first one will report.
% 0.16/0.54  % (30580)Refutation found. Thanks to Tanya!
% 0.16/0.54  % SZS status Theorem for theBenchmark
% 0.16/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.54  % (30580)------------------------------
% 0.16/0.54  % (30580)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.54  % (30580)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.54  % (30580)Termination reason: Refutation
% 0.16/0.54  
% 0.16/0.54  % (30580)Memory used [KB]: 1535
% 0.16/0.54  % (30580)Time elapsed: 0.149 s
% 0.16/0.54  % (30580)Instructions burned: 28 (million)
% 0.16/0.54  % (30580)------------------------------
% 0.16/0.54  % (30580)------------------------------
% 0.16/0.54  % (30564)Success in time 0.223 s
%------------------------------------------------------------------------------