TSTP Solution File: SWC252+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC252+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 18:42:42 EDT 2022

% Result   : Theorem 0.19s 0.58s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   62 (  13 unt;   0 def)
%            Number of atoms       :  428 ( 157 equ)
%            Maximal formula atoms :   42 (   6 avg)
%            Number of connectives :  530 ( 164   ~; 155   |; 190   &)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :  128 (  70   !;  58   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f715,plain,
    $false,
    inference(trivial_inequality_removal,[],[f714]) ).

fof(f714,plain,
    nil != nil,
    inference(superposition,[],[f359,f698]) ).

fof(f698,plain,
    nil = sK6,
    inference(duplicate_literal_removal,[],[f697]) ).

fof(f697,plain,
    ( nil = sK6
    | nil = sK6 ),
    inference(resolution,[],[f696,f570]) ).

fof(f570,plain,
    ( ssItem(sK10)
    | nil = sK6 ),
    inference(definition_unfolding,[],[f364,f357]) ).

fof(f357,plain,
    sK8 = sK6,
    inference(cnf_transformation,[],[f239]) ).

fof(f239,plain,
    ( ssList(sK6)
    & ssList(sK8)
    & sK9 = sK7
    & ( ( nil = sK8
        & nil = sK9 )
      | ( sK8 = cons(sK10,nil)
        & ssItem(sK10)
        & memberP(sK9,sK10) ) )
    & nil != sK6
    & ssList(sK9)
    & sK8 = sK6
    & ! [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ( ssItem(sK11(X5,X6,X7))
                  & lt(X5,sK11(X5,X6,X7))
                  & memberP(X6,sK11(X5,X6,X7))
                  & ~ leq(X5,sK11(X5,X6,X7))
                  & memberP(X7,sK11(X5,X6,X7)) )
                | ~ ssList(X7)
                | app(app(X6,cons(X5,nil)),X7) != sK6 )
            | ~ ssList(X6) )
        | ~ ssItem(X5) )
    & ssList(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11])],[f232,f238,f237,f236,f235,f234,f233]) ).

fof(f233,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X1 = X3
                    & ( ( nil = X2
                        & nil = X3 )
                      | ? [X4] :
                          ( cons(X4,nil) = X2
                          & ssItem(X4)
                          & memberP(X3,X4) ) )
                    & nil != X0
                    & ssList(X3)
                    & X0 = X2
                    & ! [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ? [X8] :
                                    ( ssItem(X8)
                                    & lt(X5,X8)
                                    & memberP(X6,X8)
                                    & ~ leq(X5,X8)
                                    & memberP(X7,X8) )
                                | ~ ssList(X7)
                                | app(app(X6,cons(X5,nil)),X7) != X0 )
                            | ~ ssList(X6) )
                        | ~ ssItem(X5) ) ) )
            & ssList(X1) ) )
   => ( ssList(sK6)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( cons(X4,nil) = X2
                        & ssItem(X4)
                        & memberP(X3,X4) ) )
                  & nil != sK6
                  & ssList(X3)
                  & sK6 = X2
                  & ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ? [X8] :
                                  ( ssItem(X8)
                                  & lt(X5,X8)
                                  & memberP(X6,X8)
                                  & ~ leq(X5,X8)
                                  & memberP(X7,X8) )
                              | ~ ssList(X7)
                              | app(app(X6,cons(X5,nil)),X7) != sK6 )
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) ) ) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f234,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( X1 = X3
                & ( ( nil = X2
                    & nil = X3 )
                  | ? [X4] :
                      ( cons(X4,nil) = X2
                      & ssItem(X4)
                      & memberP(X3,X4) ) )
                & nil != sK6
                & ssList(X3)
                & sK6 = X2
                & ! [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ? [X8] :
                                ( ssItem(X8)
                                & lt(X5,X8)
                                & memberP(X6,X8)
                                & ~ leq(X5,X8)
                                & memberP(X7,X8) )
                            | ~ ssList(X7)
                            | app(app(X6,cons(X5,nil)),X7) != sK6 )
                        | ~ ssList(X6) )
                    | ~ ssItem(X5) ) ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK7 = X3
              & ( ( nil = X2
                  & nil = X3 )
                | ? [X4] :
                    ( cons(X4,nil) = X2
                    & ssItem(X4)
                    & memberP(X3,X4) ) )
              & nil != sK6
              & ssList(X3)
              & sK6 = X2
              & ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ? [X8] :
                              ( ssItem(X8)
                              & lt(X5,X8)
                              & memberP(X6,X8)
                              & ~ leq(X5,X8)
                              & memberP(X7,X8) )
                          | ~ ssList(X7)
                          | app(app(X6,cons(X5,nil)),X7) != sK6 )
                      | ~ ssList(X6) )
                  | ~ ssItem(X5) ) ) )
      & ssList(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f235,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK7 = X3
            & ( ( nil = X2
                & nil = X3 )
              | ? [X4] :
                  ( cons(X4,nil) = X2
                  & ssItem(X4)
                  & memberP(X3,X4) ) )
            & nil != sK6
            & ssList(X3)
            & sK6 = X2
            & ! [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ? [X8] :
                            ( ssItem(X8)
                            & lt(X5,X8)
                            & memberP(X6,X8)
                            & ~ leq(X5,X8)
                            & memberP(X7,X8) )
                        | ~ ssList(X7)
                        | app(app(X6,cons(X5,nil)),X7) != sK6 )
                    | ~ ssList(X6) )
                | ~ ssItem(X5) ) ) )
   => ( ssList(sK8)
      & ? [X3] :
          ( sK7 = X3
          & ( ( nil = sK8
              & nil = X3 )
            | ? [X4] :
                ( cons(X4,nil) = sK8
                & ssItem(X4)
                & memberP(X3,X4) ) )
          & nil != sK6
          & ssList(X3)
          & sK8 = sK6
          & ! [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ? [X8] :
                          ( ssItem(X8)
                          & lt(X5,X8)
                          & memberP(X6,X8)
                          & ~ leq(X5,X8)
                          & memberP(X7,X8) )
                      | ~ ssList(X7)
                      | app(app(X6,cons(X5,nil)),X7) != sK6 )
                  | ~ ssList(X6) )
              | ~ ssItem(X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f236,plain,
    ( ? [X3] :
        ( sK7 = X3
        & ( ( nil = sK8
            & nil = X3 )
          | ? [X4] :
              ( cons(X4,nil) = sK8
              & ssItem(X4)
              & memberP(X3,X4) ) )
        & nil != sK6
        & ssList(X3)
        & sK8 = sK6
        & ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ? [X8] :
                        ( ssItem(X8)
                        & lt(X5,X8)
                        & memberP(X6,X8)
                        & ~ leq(X5,X8)
                        & memberP(X7,X8) )
                    | ~ ssList(X7)
                    | app(app(X6,cons(X5,nil)),X7) != sK6 )
                | ~ ssList(X6) )
            | ~ ssItem(X5) ) )
   => ( sK9 = sK7
      & ( ( nil = sK8
          & nil = sK9 )
        | ? [X4] :
            ( cons(X4,nil) = sK8
            & ssItem(X4)
            & memberP(sK9,X4) ) )
      & nil != sK6
      & ssList(sK9)
      & sK8 = sK6
      & ! [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ? [X8] :
                      ( ssItem(X8)
                      & lt(X5,X8)
                      & memberP(X6,X8)
                      & ~ leq(X5,X8)
                      & memberP(X7,X8) )
                  | ~ ssList(X7)
                  | app(app(X6,cons(X5,nil)),X7) != sK6 )
              | ~ ssList(X6) )
          | ~ ssItem(X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f237,plain,
    ( ? [X4] :
        ( cons(X4,nil) = sK8
        & ssItem(X4)
        & memberP(sK9,X4) )
   => ( sK8 = cons(sK10,nil)
      & ssItem(sK10)
      & memberP(sK9,sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f238,plain,
    ! [X5,X6,X7] :
      ( ? [X8] :
          ( ssItem(X8)
          & lt(X5,X8)
          & memberP(X6,X8)
          & ~ leq(X5,X8)
          & memberP(X7,X8) )
     => ( ssItem(sK11(X5,X6,X7))
        & lt(X5,sK11(X5,X6,X7))
        & memberP(X6,sK11(X5,X6,X7))
        & ~ leq(X5,sK11(X5,X6,X7))
        & memberP(X7,sK11(X5,X6,X7)) ) ),
    introduced(choice_axiom,[]) ).

fof(f232,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( cons(X4,nil) = X2
                        & ssItem(X4)
                        & memberP(X3,X4) ) )
                  & nil != X0
                  & ssList(X3)
                  & X0 = X2
                  & ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ? [X8] :
                                  ( ssItem(X8)
                                  & lt(X5,X8)
                                  & memberP(X6,X8)
                                  & ~ leq(X5,X8)
                                  & memberP(X7,X8) )
                              | ~ ssList(X7)
                              | app(app(X6,cons(X5,nil)),X7) != X0 )
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) ) ) )
          & ssList(X1) ) ),
    inference(rectify,[],[f202]) ).

fof(f202,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X8] :
                        ( cons(X8,nil) = X2
                        & ssItem(X8)
                        & memberP(X3,X8) ) )
                  & nil != X0
                  & ssList(X3)
                  & X0 = X2
                  & ! [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ? [X7] :
                                  ( ssItem(X7)
                                  & lt(X4,X7)
                                  & memberP(X5,X7)
                                  & ~ leq(X4,X7)
                                  & memberP(X6,X7) )
                              | ~ ssList(X6)
                              | app(app(X5,cons(X4,nil)),X6) != X0 )
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) ) ) )
          & ssList(X1) ) ),
    inference(flattening,[],[f201]) ).

fof(f201,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ~ ssList(X6)
                              | ? [X7] :
                                  ( memberP(X5,X7)
                                  & lt(X4,X7)
                                  & ~ leq(X4,X7)
                                  & memberP(X6,X7)
                                  & ssItem(X7) )
                              | app(app(X5,cons(X4,nil)),X6) != X0 )
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & X1 = X3
                  & X0 = X2
                  & nil != X0
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X8] :
                        ( memberP(X3,X8)
                        & cons(X8,nil) = X2
                        & ssItem(X8) ) )
                  & 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)
                   => ( ? [X4] :
                          ( ? [X5] :
                              ( ? [X6] :
                                  ( ssList(X6)
                                  & ! [X7] :
                                      ( ssItem(X7)
                                     => ( ~ memberP(X5,X7)
                                        | ~ lt(X4,X7)
                                        | leq(X4,X7)
                                        | ~ memberP(X6,X7) ) )
                                  & app(app(X5,cons(X4,nil)),X6) = X0 )
                              & ssList(X5) )
                          & ssItem(X4) )
                      | X1 != X3
                      | X0 != X2
                      | nil = X0
                      | ( ( nil != X3
                          | nil != X2 )
                        & ! [X8] :
                            ( ssItem(X8)
                           => ( ~ memberP(X3,X8)
                              | cons(X8,nil) != X2 ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f364,plain,
    ( nil = sK8
    | ssItem(sK10) ),
    inference(cnf_transformation,[],[f239]) ).

fof(f696,plain,
    ( ~ ssItem(sK10)
    | nil = sK6 ),
    inference(resolution,[],[f691,f508]) ).

fof(f508,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f209]) ).

fof(f209,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

fof(f691,plain,
    ( memberP(nil,sK10)
    | nil = sK6 ),
    inference(backward_demodulation,[],[f571,f690]) ).

fof(f690,plain,
    nil = sK7,
    inference(duplicate_literal_removal,[],[f688]) ).

fof(f688,plain,
    ( nil = sK7
    | nil = sK7 ),
    inference(resolution,[],[f687,f573]) ).

fof(f573,plain,
    ( ssItem(sK10)
    | nil = sK7 ),
    inference(definition_unfolding,[],[f361,f366]) ).

fof(f366,plain,
    sK9 = sK7,
    inference(cnf_transformation,[],[f239]) ).

fof(f361,plain,
    ( nil = sK9
    | ssItem(sK10) ),
    inference(cnf_transformation,[],[f239]) ).

fof(f687,plain,
    ( ~ ssItem(sK10)
    | nil = sK7 ),
    inference(resolution,[],[f686,f400]) ).

fof(f400,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f686,plain,
    ( ~ ssList(nil)
    | nil = sK7
    | ~ ssItem(sK10) ),
    inference(trivial_inequality_removal,[],[f685]) ).

fof(f685,plain,
    ( ~ ssList(nil)
    | nil = sK7
    | sK6 != sK6
    | ~ ssItem(sK10) ),
    inference(forward_demodulation,[],[f684,f652]) ).

fof(f652,plain,
    app(sK6,nil) = sK6,
    inference(resolution,[],[f412,f568]) ).

fof(f568,plain,
    ssList(sK6),
    inference(definition_unfolding,[],[f367,f357]) ).

fof(f367,plain,
    ssList(sK8),
    inference(cnf_transformation,[],[f239]) ).

fof(f412,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(ennf_transformation,[],[f84]) ).

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

fof(f684,plain,
    ( ~ ssItem(sK10)
    | ~ ssList(nil)
    | nil = sK7
    | app(sK6,nil) != sK6 ),
    inference(forward_demodulation,[],[f680,f633]) ).

fof(f633,plain,
    app(nil,sK6) = sK6,
    inference(resolution,[],[f408,f568]) ).

fof(f408,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,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/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f680,plain,
    ( app(app(nil,sK6),nil) != sK6
    | nil = sK7
    | ~ ssList(nil)
    | ~ ssItem(sK10) ),
    inference(duplicate_literal_removal,[],[f678]) ).

fof(f678,plain,
    ( nil = sK7
    | nil = sK7
    | ~ ssItem(sK10)
    | app(app(nil,sK6),nil) != sK6
    | ~ ssList(nil) ),
    inference(superposition,[],[f675,f572]) ).

fof(f572,plain,
    ( cons(sK10,nil) = sK6
    | nil = sK7 ),
    inference(definition_unfolding,[],[f362,f366,f357]) ).

fof(f362,plain,
    ( nil = sK9
    | sK8 = cons(sK10,nil) ),
    inference(cnf_transformation,[],[f239]) ).

fof(f675,plain,
    ( app(app(nil,cons(sK10,nil)),nil) != sK6
    | nil = sK7
    | ~ ssList(nil)
    | ~ ssItem(sK10) ),
    inference(duplicate_literal_removal,[],[f674]) ).

fof(f674,plain,
    ( ~ ssItem(sK10)
    | nil = sK7
    | ~ ssList(nil)
    | ~ ssList(nil)
    | ~ ssItem(sK10)
    | ~ ssList(nil)
    | app(app(nil,cons(sK10,nil)),nil) != sK6 ),
    inference(resolution,[],[f671,f356]) ).

fof(f356,plain,
    ! [X6,X7,X5] :
      ( ssItem(sK11(X5,X6,X7))
      | ~ ssItem(X5)
      | ~ ssList(X6)
      | app(app(X6,cons(X5,nil)),X7) != sK6
      | ~ ssList(X7) ),
    inference(cnf_transformation,[],[f239]) ).

fof(f671,plain,
    ( ~ ssItem(sK11(sK10,nil,nil))
    | ~ ssList(nil)
    | nil = sK7
    | ~ ssItem(sK10) ),
    inference(trivial_inequality_removal,[],[f670]) ).

fof(f670,plain,
    ( ~ ssItem(sK11(sK10,nil,nil))
    | sK6 != sK6
    | ~ ssItem(sK10)
    | ~ ssList(nil)
    | nil = sK7 ),
    inference(duplicate_literal_removal,[],[f669]) ).

fof(f669,plain,
    ( ~ ssList(nil)
    | nil = sK7
    | ~ ssItem(sK10)
    | sK6 != sK6
    | ~ ssList(nil)
    | ~ ssItem(sK11(sK10,nil,nil)) ),
    inference(superposition,[],[f649,f652]) ).

fof(f649,plain,
    ! [X0] :
      ( app(sK6,X0) != sK6
      | ~ ssList(X0)
      | ~ ssItem(sK10)
      | ~ ssItem(sK11(sK10,nil,X0))
      | ~ ssList(nil)
      | nil = sK7 ),
    inference(backward_demodulation,[],[f630,f633]) ).

fof(f630,plain,
    ! [X0] :
      ( ~ ssItem(sK10)
      | nil = sK7
      | ~ ssItem(sK11(sK10,nil,X0))
      | app(app(nil,sK6),X0) != sK6
      | ~ ssList(nil)
      | ~ ssList(X0) ),
    inference(superposition,[],[f629,f572]) ).

fof(f629,plain,
    ! [X0,X1] :
      ( app(app(nil,cons(X0,nil)),X1) != sK6
      | ~ ssItem(X0)
      | ~ ssList(nil)
      | ~ ssList(X1)
      | ~ ssItem(sK11(X0,nil,X1)) ),
    inference(resolution,[],[f354,f508]) ).

fof(f354,plain,
    ! [X6,X7,X5] :
      ( memberP(X6,sK11(X5,X6,X7))
      | app(app(X6,cons(X5,nil)),X7) != sK6
      | ~ ssList(X7)
      | ~ ssItem(X5)
      | ~ ssList(X6) ),
    inference(cnf_transformation,[],[f239]) ).

fof(f571,plain,
    ( memberP(sK7,sK10)
    | nil = sK6 ),
    inference(definition_unfolding,[],[f363,f357,f366]) ).

fof(f363,plain,
    ( nil = sK8
    | memberP(sK9,sK10) ),
    inference(cnf_transformation,[],[f239]) ).

fof(f359,plain,
    nil != sK6,
    inference(cnf_transformation,[],[f239]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWC252+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 18:03:20 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.46  % (15924)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)
% 0.19/0.47  % (15916)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.51  % (15897)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)
% 0.19/0.52  % (15902)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52  % (15912)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.52  % (15899)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (15917)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)
% 0.19/0.52  % (15896)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)
% 0.19/0.53  % (15898)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)
% 0.19/0.53  % (15909)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)
% 0.19/0.53  % (15903)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.53  % (15904)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)
% 0.19/0.53  % (15903)Instruction limit reached!
% 0.19/0.53  % (15903)------------------------------
% 0.19/0.53  % (15903)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (15903)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (15903)Termination reason: Unknown
% 0.19/0.53  % (15903)Termination phase: Naming
% 0.19/0.53  
% 0.19/0.53  % (15903)Memory used [KB]: 1023
% 0.19/0.53  % (15903)Time elapsed: 0.002 s
% 0.19/0.53  % (15903)Instructions burned: 3 (million)
% 0.19/0.53  % (15903)------------------------------
% 0.19/0.53  % (15903)------------------------------
% 0.19/0.53  % (15902)Instruction limit reached!
% 0.19/0.53  % (15902)------------------------------
% 0.19/0.53  % (15902)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (15902)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (15902)Termination reason: Unknown
% 0.19/0.53  % (15902)Termination phase: Function definition elimination
% 0.19/0.53  
% 0.19/0.53  % (15902)Memory used [KB]: 1279
% 0.19/0.53  % (15902)Time elapsed: 0.008 s
% 0.19/0.53  % (15902)Instructions burned: 8 (million)
% 0.19/0.53  % (15902)------------------------------
% 0.19/0.53  % (15902)------------------------------
% 0.19/0.53  % (15900)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)
% 0.19/0.53  % (15901)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)
% 0.19/0.53  % (15914)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)
% 0.19/0.53  % (15905)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53  % (15913)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.54  % (15919)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.54  % (15920)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.54  % (15907)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.54  % (15895)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)
% 0.19/0.54  % (15906)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)
% 0.19/0.54  % (15921)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)
% 0.19/0.54  % (15922)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)
% 0.19/0.54  % (15911)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)
% 0.19/0.55  % (15918)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)
% 0.19/0.55  % (15910)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)
% 0.19/0.56  % (15923)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.56  % (15908)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.56  % (15904)First to succeed.
% 0.19/0.56  % (15915)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)
% 0.19/0.56  TRYING [1]
% 0.19/0.57  % (15897)Instruction limit reached!
% 0.19/0.57  % (15897)------------------------------
% 0.19/0.57  % (15897)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.58  % (15896)Refutation not found, incomplete strategy% (15896)------------------------------
% 0.19/0.58  % (15896)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.58  TRYING [1]
% 0.19/0.58  % (15904)Refutation found. Thanks to Tanya!
% 0.19/0.58  % SZS status Theorem for theBenchmark
% 0.19/0.58  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.58  % (15904)------------------------------
% 0.19/0.58  % (15904)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.58  % (15904)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.58  % (15904)Termination reason: Refutation
% 0.19/0.58  
% 0.19/0.58  % (15904)Memory used [KB]: 1535
% 0.19/0.58  % (15904)Time elapsed: 0.166 s
% 0.19/0.58  % (15904)Instructions burned: 23 (million)
% 0.19/0.58  % (15904)------------------------------
% 0.19/0.58  % (15904)------------------------------
% 0.19/0.58  % (15894)Success in time 0.235 s
%------------------------------------------------------------------------------