TSTP Solution File: NUM561+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : 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 : Thu Aug 31 12:11:24 EDT 2023

% Result   : Theorem 0.22s 0.44s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   39 (  13 unt;   0 def)
%            Number of atoms       :  163 (  39 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  203 (  79   ~;  76   |;  36   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   2 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-3 aty)
%            Number of variables   :   77 (;  61   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f430,plain,
    $false,
    inference(avatar_sat_refutation,[],[f423,f429]) ).

fof(f429,plain,
    ~ spl16_1,
    inference(avatar_contradiction_clause,[],[f428]) ).

fof(f428,plain,
    ( $false
    | ~ spl16_1 ),
    inference(subsumption_resolution,[],[f427,f414]) ).

fof(f414,plain,
    ( aSet0(szDzozmdt0(xF))
    | ~ spl16_1 ),
    inference(avatar_component_clause,[],[f413]) ).

fof(f413,plain,
    ( spl16_1
  <=> aSet0(szDzozmdt0(xF)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).

fof(f427,plain,
    ~ aSet0(szDzozmdt0(xF)),
    inference(resolution,[],[f426,f258]) ).

fof(f258,plain,
    ! [X0] :
      ( aSubsetOf0(X0,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0] :
      ( aSubsetOf0(X0,X0)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( aSet0(X0)
     => aSubsetOf0(X0,X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',mSubRefl) ).

fof(f426,plain,
    ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF)),
    inference(subsumption_resolution,[],[f425,f241]) ).

fof(f241,plain,
    aFunction0(xF),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,axiom,
    aFunction0(xF),
    file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',m__2911) ).

fof(f425,plain,
    ( ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
    | ~ aFunction0(xF) ),
    inference(subsumption_resolution,[],[f424,f242]) ).

fof(f242,plain,
    aElementOf0(xx,szDzozmdt0(xF)),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,axiom,
    aElementOf0(xx,szDzozmdt0(xF)),
    file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',m__2911_02) ).

fof(f424,plain,
    ( ~ aElementOf0(xx,szDzozmdt0(xF))
    | ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
    | ~ aFunction0(xF) ),
    inference(resolution,[],[f240,f368]) ).

fof(f368,plain,
    ! [X0,X1,X7] :
      ( aElementOf0(sdtlpdtrp0(X0,X7),sdtlcdtrc0(X0,X1))
      | ~ aElementOf0(X7,X1)
      | ~ aSubsetOf0(X1,szDzozmdt0(X0))
      | ~ aFunction0(X0) ),
    inference(equality_resolution,[],[f367]) ).

fof(f367,plain,
    ! [X2,X0,X1,X7] :
      ( aElementOf0(sdtlpdtrp0(X0,X7),X2)
      | ~ aElementOf0(X7,X1)
      | sdtlcdtrc0(X0,X1) != X2
      | ~ aSubsetOf0(X1,szDzozmdt0(X0))
      | ~ aFunction0(X0) ),
    inference(equality_resolution,[],[f253]) ).

fof(f253,plain,
    ! [X2,X0,X1,X6,X7] :
      ( aElementOf0(X6,X2)
      | sdtlpdtrp0(X0,X7) != X6
      | ~ aElementOf0(X7,X1)
      | sdtlcdtrc0(X0,X1) != X2
      | ~ aSubsetOf0(X1,szDzozmdt0(X0))
      | ~ aFunction0(X0) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f180,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( sdtlcdtrc0(X0,X1) = X2
                | ( ( ! [X4] :
                        ( sdtlpdtrp0(X0,X4) != sK0(X0,X1,X2)
                        | ~ aElementOf0(X4,X1) )
                    | ~ aElementOf0(sK0(X0,X1,X2),X2) )
                  & ( ( sK0(X0,X1,X2) = sdtlpdtrp0(X0,sK1(X0,X1,X2))
                      & aElementOf0(sK1(X0,X1,X2),X1) )
                    | aElementOf0(sK0(X0,X1,X2),X2) ) )
                | ~ aSet0(X2) )
              & ( ( ! [X6] :
                      ( ( aElementOf0(X6,X2)
                        | ! [X7] :
                            ( sdtlpdtrp0(X0,X7) != X6
                            | ~ aElementOf0(X7,X1) ) )
                      & ( ( sdtlpdtrp0(X0,sK2(X0,X1,X6)) = X6
                          & aElementOf0(sK2(X0,X1,X6),X1) )
                        | ~ aElementOf0(X6,X2) ) )
                  & aSet0(X2) )
                | sdtlcdtrc0(X0,X1) != X2 ) )
          | ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
      | ~ aFunction0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f176,f179,f178,f177]) ).

fof(f177,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4] :
                ( sdtlpdtrp0(X0,X4) != X3
                | ~ aElementOf0(X4,X1) )
            | ~ aElementOf0(X3,X2) )
          & ( ? [X5] :
                ( sdtlpdtrp0(X0,X5) = X3
                & aElementOf0(X5,X1) )
            | aElementOf0(X3,X2) ) )
     => ( ( ! [X4] :
              ( sdtlpdtrp0(X0,X4) != sK0(X0,X1,X2)
              | ~ aElementOf0(X4,X1) )
          | ~ aElementOf0(sK0(X0,X1,X2),X2) )
        & ( ? [X5] :
              ( sdtlpdtrp0(X0,X5) = sK0(X0,X1,X2)
              & aElementOf0(X5,X1) )
          | aElementOf0(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f178,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( sdtlpdtrp0(X0,X5) = sK0(X0,X1,X2)
          & aElementOf0(X5,X1) )
     => ( sK0(X0,X1,X2) = sdtlpdtrp0(X0,sK1(X0,X1,X2))
        & aElementOf0(sK1(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f179,plain,
    ! [X0,X1,X6] :
      ( ? [X8] :
          ( sdtlpdtrp0(X0,X8) = X6
          & aElementOf0(X8,X1) )
     => ( sdtlpdtrp0(X0,sK2(X0,X1,X6)) = X6
        & aElementOf0(sK2(X0,X1,X6),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f176,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( sdtlcdtrc0(X0,X1) = X2
                | ? [X3] :
                    ( ( ! [X4] :
                          ( sdtlpdtrp0(X0,X4) != X3
                          | ~ aElementOf0(X4,X1) )
                      | ~ aElementOf0(X3,X2) )
                    & ( ? [X5] :
                          ( sdtlpdtrp0(X0,X5) = X3
                          & aElementOf0(X5,X1) )
                      | aElementOf0(X3,X2) ) )
                | ~ aSet0(X2) )
              & ( ( ! [X6] :
                      ( ( aElementOf0(X6,X2)
                        | ! [X7] :
                            ( sdtlpdtrp0(X0,X7) != X6
                            | ~ aElementOf0(X7,X1) ) )
                      & ( ? [X8] :
                            ( sdtlpdtrp0(X0,X8) = X6
                            & aElementOf0(X8,X1) )
                        | ~ aElementOf0(X6,X2) ) )
                  & aSet0(X2) )
                | sdtlcdtrc0(X0,X1) != X2 ) )
          | ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
      | ~ aFunction0(X0) ),
    inference(rectify,[],[f175]) ).

fof(f175,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( sdtlcdtrc0(X0,X1) = X2
                | ? [X3] :
                    ( ( ! [X4] :
                          ( sdtlpdtrp0(X0,X4) != X3
                          | ~ aElementOf0(X4,X1) )
                      | ~ aElementOf0(X3,X2) )
                    & ( ? [X4] :
                          ( sdtlpdtrp0(X0,X4) = X3
                          & aElementOf0(X4,X1) )
                      | aElementOf0(X3,X2) ) )
                | ~ aSet0(X2) )
              & ( ( ! [X3] :
                      ( ( aElementOf0(X3,X2)
                        | ! [X4] :
                            ( sdtlpdtrp0(X0,X4) != X3
                            | ~ aElementOf0(X4,X1) ) )
                      & ( ? [X4] :
                            ( sdtlpdtrp0(X0,X4) = X3
                            & aElementOf0(X4,X1) )
                        | ~ aElementOf0(X3,X2) ) )
                  & aSet0(X2) )
                | sdtlcdtrc0(X0,X1) != X2 ) )
          | ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
      | ~ aFunction0(X0) ),
    inference(flattening,[],[f174]) ).

fof(f174,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( sdtlcdtrc0(X0,X1) = X2
                | ? [X3] :
                    ( ( ! [X4] :
                          ( sdtlpdtrp0(X0,X4) != X3
                          | ~ aElementOf0(X4,X1) )
                      | ~ aElementOf0(X3,X2) )
                    & ( ? [X4] :
                          ( sdtlpdtrp0(X0,X4) = X3
                          & aElementOf0(X4,X1) )
                      | aElementOf0(X3,X2) ) )
                | ~ aSet0(X2) )
              & ( ( ! [X3] :
                      ( ( aElementOf0(X3,X2)
                        | ! [X4] :
                            ( sdtlpdtrp0(X0,X4) != X3
                            | ~ aElementOf0(X4,X1) ) )
                      & ( ? [X4] :
                            ( sdtlpdtrp0(X0,X4) = X3
                            & aElementOf0(X4,X1) )
                        | ~ aElementOf0(X3,X2) ) )
                  & aSet0(X2) )
                | sdtlcdtrc0(X0,X1) != X2 ) )
          | ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
      | ~ aFunction0(X0) ),
    inference(nnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( sdtlcdtrc0(X0,X1) = X2
            <=> ( ! [X3] :
                    ( aElementOf0(X3,X2)
                  <=> ? [X4] :
                        ( sdtlpdtrp0(X0,X4) = X3
                        & aElementOf0(X4,X1) ) )
                & aSet0(X2) ) )
          | ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
      | ~ aFunction0(X0) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f68,axiom,
    ! [X0] :
      ( aFunction0(X0)
     => ! [X1] :
          ( aSubsetOf0(X1,szDzozmdt0(X0))
         => ! [X2] :
              ( sdtlcdtrc0(X0,X1) = X2
            <=> ( ! [X3] :
                    ( aElementOf0(X3,X2)
                  <=> ? [X4] :
                        ( sdtlpdtrp0(X0,X4) = X3
                        & aElementOf0(X4,X1) ) )
                & aSet0(X2) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',mDefSImg) ).

fof(f240,plain,
    ~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
    inference(flattening,[],[f72]) ).

fof(f72,negated_conjecture,
    ~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
    inference(negated_conjecture,[],[f71]) ).

fof(f71,conjecture,
    aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
    file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',m__) ).

fof(f423,plain,
    spl16_1,
    inference(avatar_contradiction_clause,[],[f422]) ).

fof(f422,plain,
    ( $false
    | spl16_1 ),
    inference(subsumption_resolution,[],[f421,f241]) ).

fof(f421,plain,
    ( ~ aFunction0(xF)
    | spl16_1 ),
    inference(resolution,[],[f415,f248]) ).

fof(f248,plain,
    ! [X0] :
      ( aSet0(szDzozmdt0(X0))
      | ~ aFunction0(X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0] :
      ( aSet0(szDzozmdt0(X0))
      | ~ aFunction0(X0) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f64,axiom,
    ! [X0] :
      ( aFunction0(X0)
     => aSet0(szDzozmdt0(X0)) ),
    file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',mDomSet) ).

fof(f415,plain,
    ( ~ aSet0(szDzozmdt0(xF))
    | spl16_1 ),
    inference(avatar_component_clause,[],[f413]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15  % Problem    : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.16  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.37  % Computer : n017.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Fri Aug 25 09:33:55 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061
% 0.15/0.37  % (13196)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.41  % (13202)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)
% 0.22/0.43  % (13198)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.22/0.43  % (13197)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)
% 0.22/0.43  % (13199)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)
% 0.22/0.43  % (13201)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)
% 0.22/0.43  % (13203)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.22/0.43  % (13200)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.22/0.44  % (13203)First to succeed.
% 0.22/0.44  % (13203)Refutation found. Thanks to Tanya!
% 0.22/0.44  % SZS status Theorem for Vampire---4
% 0.22/0.44  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.44  % (13203)------------------------------
% 0.22/0.44  % (13203)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.44  % (13203)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.44  % (13203)Termination reason: Refutation
% 0.22/0.44  
% 0.22/0.44  % (13203)Memory used [KB]: 5756
% 0.22/0.44  % (13203)Time elapsed: 0.007 s
% 0.22/0.44  % (13203)------------------------------
% 0.22/0.44  % (13203)------------------------------
% 0.22/0.44  % (13196)Success in time 0.067 s
% 0.22/0.44  % Vampire---4.8 exiting
%------------------------------------------------------------------------------