TSTP Solution File: SWC040+1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC040+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -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 : Thu Aug 31 20:55:51 EDT 2023

% Result   : Theorem 0.17s 0.40s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   21 (   8 unt;   0 def)
%            Number of atoms       :  209 ( 123 equ)
%            Maximal formula atoms :   30 (   9 avg)
%            Number of connectives :  238 (  50   ~;  36   |; 134   &)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   60 (;  12   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f741,plain,
    $false,
    inference(subsumption_resolution,[],[f612,f714]) ).

fof(f714,plain,
    sK20 = sK21,
    inference(trivial_inequality_removal,[],[f611]) ).

fof(f611,plain,
    ( sK21 != sK21
    | sK20 = sK21 ),
    inference(definition_unfolding,[],[f384,f606,f606]) ).

fof(f606,plain,
    nil = sK21,
    inference(definition_unfolding,[],[f380,f381]) ).

fof(f381,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f256]) ).

fof(f256,plain,
    ( ( ~ neq(sK21,nil)
      | ( sK21 = app(sK23,cons(sK22,nil))
        & sK20 = app(cons(sK22,nil),sK23)
        & ssList(sK23)
        & ssItem(sK22) ) )
    & ( nil != sK21
      | nil = sK20 )
    & nil != sK18
    & sK18 = sK20
    & sK19 = sK21
    & nil = sK19
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22,sK23])],[f99,f255,f254,f253,f252,f251,f250]) ).

fof(f250,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ neq(X3,nil)
                      | ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X3
                              & app(cons(X4,nil),X5) = X2
                              & ssList(X5) )
                          & ssItem(X4) ) )
                    & ( nil != X3
                      | nil = X2 )
                    & nil != X0
                    & X0 = X2
                    & X1 = X3
                    & nil = X1
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ? [X5] :
                            ( app(X5,cons(X4,nil)) = X3
                            & app(cons(X4,nil),X5) = X2
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & nil != sK18
                  & sK18 = X2
                  & X1 = X3
                  & nil = X1
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f251,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ neq(X3,nil)
                  | ? [X4] :
                      ( ? [X5] :
                          ( app(X5,cons(X4,nil)) = X3
                          & app(cons(X4,nil),X5) = X2
                          & ssList(X5) )
                      & ssItem(X4) ) )
                & ( nil != X3
                  | nil = X2 )
                & nil != sK18
                & sK18 = X2
                & X1 = X3
                & nil = X1
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ neq(X3,nil)
                | ? [X4] :
                    ( ? [X5] :
                        ( app(X5,cons(X4,nil)) = X3
                        & app(cons(X4,nil),X5) = X2
                        & ssList(X5) )
                    & ssItem(X4) ) )
              & ( nil != X3
                | nil = X2 )
              & nil != sK18
              & sK18 = X2
              & sK19 = X3
              & nil = sK19
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ neq(X3,nil)
              | ? [X4] :
                  ( ? [X5] :
                      ( app(X5,cons(X4,nil)) = X3
                      & app(cons(X4,nil),X5) = X2
                      & ssList(X5) )
                  & ssItem(X4) ) )
            & ( nil != X3
              | nil = X2 )
            & nil != sK18
            & sK18 = X2
            & sK19 = X3
            & nil = sK19
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ neq(X3,nil)
            | ? [X4] :
                ( ? [X5] :
                    ( app(X5,cons(X4,nil)) = X3
                    & app(cons(X4,nil),X5) = sK20
                    & ssList(X5) )
                & ssItem(X4) ) )
          & ( nil != X3
            | nil = sK20 )
          & nil != sK18
          & sK18 = sK20
          & sK19 = X3
          & nil = sK19
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X3] :
        ( ( ~ neq(X3,nil)
          | ? [X4] :
              ( ? [X5] :
                  ( app(X5,cons(X4,nil)) = X3
                  & app(cons(X4,nil),X5) = sK20
                  & ssList(X5) )
              & ssItem(X4) ) )
        & ( nil != X3
          | nil = sK20 )
        & nil != sK18
        & sK18 = sK20
        & sK19 = X3
        & nil = sK19
        & ssList(X3) )
   => ( ( ~ neq(sK21,nil)
        | ? [X4] :
            ( ? [X5] :
                ( app(X5,cons(X4,nil)) = sK21
                & app(cons(X4,nil),X5) = sK20
                & ssList(X5) )
            & ssItem(X4) ) )
      & ( nil != sK21
        | nil = sK20 )
      & nil != sK18
      & sK18 = sK20
      & sK19 = sK21
      & nil = sK19
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f254,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( app(X5,cons(X4,nil)) = sK21
            & app(cons(X4,nil),X5) = sK20
            & ssList(X5) )
        & ssItem(X4) )
   => ( ? [X5] :
          ( sK21 = app(X5,cons(sK22,nil))
          & sK20 = app(cons(sK22,nil),X5)
          & ssList(X5) )
      & ssItem(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f255,plain,
    ( ? [X5] :
        ( sK21 = app(X5,cons(sK22,nil))
        & sK20 = app(cons(sK22,nil),X5)
        & ssList(X5) )
   => ( sK21 = app(sK23,cons(sK22,nil))
      & sK20 = app(cons(sK22,nil),sK23)
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ? [X5] :
                            ( app(X5,cons(X4,nil)) = X3
                            & app(cons(X4,nil),X5) = X2
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & nil = X1
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ? [X5] :
                            ( app(X5,cons(X4,nil)) = X3
                            & app(cons(X4,nil),X5) = X2
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & nil = X1
                  & 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)
                   => ( ( neq(X3,nil)
                        & ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( ssList(X5)
                               => ( app(X5,cons(X4,nil)) != X3
                                  | app(cons(X4,nil),X5) != X2 ) ) ) )
                      | ( nil = X3
                        & nil != X2 )
                      | nil = X0
                      | X0 != X2
                      | X1 != X3
                      | nil != X1 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( neq(X3,nil)
                      & ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( app(X5,cons(X4,nil)) != X3
                                | app(cons(X4,nil),X5) != X2 ) ) ) )
                    | ( nil = X3
                      & nil != X2 )
                    | nil = X0
                    | X0 != X2
                    | X1 != X3
                    | nil != X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.DWl0O3mo8s/Vampire---4.8_32707',co1) ).

fof(f380,plain,
    nil = sK19,
    inference(cnf_transformation,[],[f256]) ).

fof(f384,plain,
    ( nil != sK21
    | nil = sK20 ),
    inference(cnf_transformation,[],[f256]) ).

fof(f612,plain,
    sK20 != sK21,
    inference(definition_unfolding,[],[f383,f606,f382]) ).

fof(f382,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f256]) ).

fof(f383,plain,
    nil != sK18,
    inference(cnf_transformation,[],[f256]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11  % Problem    : SWC040+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.12  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.33  % Computer : n002.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Mon Aug 28 15:46:34 EDT 2023
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  This is a FOF_THM_RFO_SEQ problem
% 0.11/0.33  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.DWl0O3mo8s/Vampire---4.8_32707
% 0.11/0.34  % (362)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.39  % (365)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.17/0.39  % (369)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.17/0.39  % (368)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.17/0.39  % (363)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.17/0.39  % (367)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.17/0.39  % (366)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.17/0.39  % (364)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.17/0.40  % (366)First to succeed.
% 0.17/0.40  % (369)Also succeeded, but the first one will report.
% 0.17/0.40  % (368)Also succeeded, but the first one will report.
% 0.17/0.40  % (366)Refutation found. Thanks to Tanya!
% 0.17/0.40  % SZS status Theorem for Vampire---4
% 0.17/0.40  % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.40  % (366)------------------------------
% 0.17/0.40  % (366)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.17/0.40  % (366)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.17/0.40  % (366)Termination reason: Refutation
% 0.17/0.40  
% 0.17/0.40  % (366)Memory used [KB]: 5884
% 0.17/0.40  % (366)Time elapsed: 0.006 s
% 0.17/0.40  % (366)------------------------------
% 0.17/0.40  % (366)------------------------------
% 0.17/0.40  % (362)Success in time 0.062 s
% 0.17/0.40  % Vampire---4.8 exiting
%------------------------------------------------------------------------------