TSTP Solution File: SWC217+1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC217+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 : n032.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 20:57:32 EDT 2023

% Result   : Theorem 0.16s 0.36s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   48 (  11 unt;   0 def)
%            Number of atoms       :  260 (  85 equ)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives :  302 (  90   ~;  70   |; 118   &)
%                                         (   5 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   4 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   59 (;  24   !;  35   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f799,plain,
    $false,
    inference(avatar_sat_refutation,[],[f586,f591,f605,f711]) ).

fof(f711,plain,
    ( ~ spl52_3
    | ~ spl52_4 ),
    inference(avatar_contradiction_clause,[],[f710]) ).

fof(f710,plain,
    ( $false
    | ~ spl52_3
    | ~ spl52_4 ),
    inference(subsumption_resolution,[],[f709,f357]) ).

fof(f357,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/tmp/tmp.KpLhAusM50/Vampire---4.8_26188',ax17) ).

fof(f709,plain,
    ( ~ ssList(nil)
    | ~ spl52_3
    | ~ spl52_4 ),
    inference(subsumption_resolution,[],[f708,f590]) ).

fof(f590,plain,
    ( ssItem(sK4)
    | ~ spl52_4 ),
    inference(avatar_component_clause,[],[f588]) ).

fof(f588,plain,
    ( spl52_4
  <=> ssItem(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_4])]) ).

fof(f708,plain,
    ( ~ ssItem(sK4)
    | ~ ssList(nil)
    | ~ spl52_3 ),
    inference(subsumption_resolution,[],[f639,f612]) ).

fof(f612,plain,
    nil = sK0,
    inference(subsumption_resolution,[],[f611,f602]) ).

fof(f602,plain,
    ssList(sK0),
    inference(forward_demodulation,[],[f339,f342]) ).

fof(f342,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f228]) ).

fof(f228,plain,
    ( ( ~ neq(sK3,nil)
      | ( memberP(sK3,sK4)
        & sK2 = cons(sK4,nil)
        & ssItem(sK4) ) )
    & ( nil != sK3
      | nil = sK2 )
    & ~ neq(sK0,nil)
    & neq(sK1,nil)
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f99,f227,f226,f225,f224,f223]) ).

fof(f223,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ neq(X3,nil)
                      | ? [X4] :
                          ( memberP(X3,X4)
                          & cons(X4,nil) = X2
                          & ssItem(X4) ) )
                    & ( nil != X3
                      | nil = X2 )
                    & ~ neq(X0,nil)
                    & neq(X1,nil)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & ~ neq(sK0,nil)
                  & neq(X1,nil)
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f224,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ neq(X3,nil)
                  | ? [X4] :
                      ( memberP(X3,X4)
                      & cons(X4,nil) = X2
                      & ssItem(X4) ) )
                & ( nil != X3
                  | nil = X2 )
                & ~ neq(sK0,nil)
                & neq(X1,nil)
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ neq(X3,nil)
                | ? [X4] :
                    ( memberP(X3,X4)
                    & cons(X4,nil) = X2
                    & ssItem(X4) ) )
              & ( nil != X3
                | nil = X2 )
              & ~ neq(sK0,nil)
              & neq(sK1,nil)
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ neq(X3,nil)
              | ? [X4] :
                  ( memberP(X3,X4)
                  & cons(X4,nil) = X2
                  & ssItem(X4) ) )
            & ( nil != X3
              | nil = X2 )
            & ~ neq(sK0,nil)
            & neq(sK1,nil)
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ neq(X3,nil)
            | ? [X4] :
                ( memberP(X3,X4)
                & cons(X4,nil) = sK2
                & ssItem(X4) ) )
          & ( nil != X3
            | nil = sK2 )
          & ~ neq(sK0,nil)
          & neq(sK1,nil)
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f226,plain,
    ( ? [X3] :
        ( ( ~ neq(X3,nil)
          | ? [X4] :
              ( memberP(X3,X4)
              & cons(X4,nil) = sK2
              & ssItem(X4) ) )
        & ( nil != X3
          | nil = sK2 )
        & ~ neq(sK0,nil)
        & neq(sK1,nil)
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( ~ neq(sK3,nil)
        | ? [X4] :
            ( memberP(sK3,X4)
            & cons(X4,nil) = sK2
            & ssItem(X4) ) )
      & ( nil != sK3
        | nil = sK2 )
      & ~ neq(sK0,nil)
      & neq(sK1,nil)
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f227,plain,
    ( ? [X4] :
        ( memberP(sK3,X4)
        & cons(X4,nil) = sK2
        & ssItem(X4) )
   => ( memberP(sK3,sK4)
      & sK2 = cons(sK4,nil)
      & ssItem(sK4) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & ~ neq(X0,nil)
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & 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)
                           => ( ~ memberP(X3,X4)
                              | cons(X4,nil) != X2 ) ) )
                      | ( nil = X3
                        & nil != X2 )
                      | neq(X0,nil)
                      | ~ neq(X1,nil)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    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)
                         => ( ~ memberP(X3,X4)
                            | cons(X4,nil) != X2 ) ) )
                    | ( nil = X3
                      & nil != X2 )
                    | neq(X0,nil)
                    | ~ neq(X1,nil)
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.KpLhAusM50/Vampire---4.8_26188',co1) ).

fof(f339,plain,
    ssList(sK2),
    inference(cnf_transformation,[],[f228]) ).

fof(f611,plain,
    ( nil = sK0
    | ~ ssList(sK0) ),
    inference(subsumption_resolution,[],[f609,f357]) ).

fof(f609,plain,
    ( nil = sK0
    | ~ ssList(nil)
    | ~ ssList(sK0) ),
    inference(resolution,[],[f344,f510]) ).

fof(f510,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f318]) ).

fof(f318,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f198]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(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/tmp/tmp.KpLhAusM50/Vampire---4.8_26188',ax15) ).

fof(f344,plain,
    ~ neq(sK0,nil),
    inference(cnf_transformation,[],[f228]) ).

fof(f639,plain,
    ( nil != sK0
    | ~ ssItem(sK4)
    | ~ ssList(nil)
    | ~ spl52_3 ),
    inference(superposition,[],[f494,f606]) ).

fof(f606,plain,
    ( sK0 = cons(sK4,nil)
    | ~ spl52_3 ),
    inference(forward_demodulation,[],[f585,f342]) ).

fof(f585,plain,
    ( sK2 = cons(sK4,nil)
    | ~ spl52_3 ),
    inference(avatar_component_clause,[],[f583]) ).

fof(f583,plain,
    ( spl52_3
  <=> sK2 = cons(sK4,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_3])]) ).

fof(f494,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f180,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) != X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) != X0 ) ),
    file('/export/starexec/sandbox/tmp/tmp.KpLhAusM50/Vampire---4.8_26188',ax18) ).

fof(f605,plain,
    spl52_2,
    inference(avatar_contradiction_clause,[],[f604]) ).

fof(f604,plain,
    ( $false
    | spl52_2 ),
    inference(subsumption_resolution,[],[f603,f343]) ).

fof(f343,plain,
    neq(sK1,nil),
    inference(cnf_transformation,[],[f228]) ).

fof(f603,plain,
    ( ~ neq(sK1,nil)
    | spl52_2 ),
    inference(forward_demodulation,[],[f580,f341]) ).

fof(f341,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f228]) ).

fof(f580,plain,
    ( ~ neq(sK3,nil)
    | spl52_2 ),
    inference(avatar_component_clause,[],[f578]) ).

fof(f578,plain,
    ( spl52_2
  <=> neq(sK3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl52_2])]) ).

fof(f591,plain,
    ( spl52_4
    | ~ spl52_2 ),
    inference(avatar_split_clause,[],[f346,f578,f588]) ).

fof(f346,plain,
    ( ~ neq(sK3,nil)
    | ssItem(sK4) ),
    inference(cnf_transformation,[],[f228]) ).

fof(f586,plain,
    ( spl52_3
    | ~ spl52_2 ),
    inference(avatar_split_clause,[],[f347,f578,f583]) ).

fof(f347,plain,
    ( ~ neq(sK3,nil)
    | sK2 = cons(sK4,nil) ),
    inference(cnf_transformation,[],[f228]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SWC217+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.31  % Computer : n032.cluster.edu
% 0.13/0.31  % Model    : x86_64 x86_64
% 0.13/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31  % Memory   : 8042.1875MB
% 0.13/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31  % CPULimit   : 300
% 0.13/0.31  % WCLimit    : 300
% 0.13/0.31  % DateTime   : Mon Aug 28 15:09:30 EDT 2023
% 0.13/0.31  % CPUTime    : 
% 0.13/0.31  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.31  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.KpLhAusM50/Vampire---4.8_26188
% 0.16/0.31  % (26295)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.35  % (26302)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.16/0.35  % (26298)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)
% 0.16/0.35  % (26300)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)
% 0.16/0.36  % (26302)First to succeed.
% 0.16/0.36  % (26302)Refutation found. Thanks to Tanya!
% 0.16/0.36  % SZS status Theorem for Vampire---4
% 0.16/0.36  % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.36  % (26302)------------------------------
% 0.16/0.36  % (26302)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.16/0.36  % (26302)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.16/0.36  % (26302)Termination reason: Refutation
% 0.16/0.36  
% 0.16/0.36  % (26302)Memory used [KB]: 6012
% 0.16/0.36  % (26302)Time elapsed: 0.008 s
% 0.16/0.36  % (26302)------------------------------
% 0.16/0.36  % (26302)------------------------------
% 0.16/0.36  % (26295)Success in time 0.044 s
% 0.16/0.36  % Vampire---4.8 exiting
%------------------------------------------------------------------------------