TSTP Solution File: NUM410+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n011.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 12:07:56 EDT 2023

% Result   : Theorem 0.22s 0.43s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   26 (  10 unt;   0 def)
%            Number of atoms       :   87 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   94 (  33   ~;  26   |;  22   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   24 (;  21   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f218,plain,
    $false,
    inference(subsumption_resolution,[],[f216,f129]) ).

fof(f129,plain,
    ~ transfinite_sequence_of(sK0,relation_rng(sK0)),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ( ~ transfinite_sequence_of(sK0,relation_rng(sK0))
    & ordinal(relation_dom(sK0))
    & function(sK0)
    & relation(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f59,f89]) ).

fof(f89,plain,
    ( ? [X0] :
        ( ~ transfinite_sequence_of(X0,relation_rng(X0))
        & ordinal(relation_dom(X0))
        & function(X0)
        & relation(X0) )
   => ( ~ transfinite_sequence_of(sK0,relation_rng(sK0))
      & ordinal(relation_dom(sK0))
      & function(sK0)
      & relation(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ? [X0] :
      ( ~ transfinite_sequence_of(X0,relation_rng(X0))
      & ordinal(relation_dom(X0))
      & function(X0)
      & relation(X0) ),
    inference(flattening,[],[f58]) ).

fof(f58,plain,
    ? [X0] :
      ( ~ transfinite_sequence_of(X0,relation_rng(X0))
      & ordinal(relation_dom(X0))
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ( ordinal(relation_dom(X0))
         => transfinite_sequence_of(X0,relation_rng(X0)) ) ),
    inference(negated_conjecture,[],[f40]) ).

fof(f40,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( ordinal(relation_dom(X0))
       => transfinite_sequence_of(X0,relation_rng(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131',t46_ordinal1) ).

fof(f216,plain,
    transfinite_sequence_of(sK0,relation_rng(sK0)),
    inference(unit_resulting_resolution,[],[f126,f127,f162,f213,f170]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( transfinite_sequence_of(X1,X0)
      | ~ subset(relation_rng(X1),X0)
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ( ( transfinite_sequence_of(X1,X0)
          | ~ subset(relation_rng(X1),X0) )
        & ( subset(relation_rng(X1),X0)
          | ~ transfinite_sequence_of(X1,X0) ) )
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) )
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) )
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( transfinite_sequence(X1)
        & function(X1)
        & relation(X1) )
     => ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131',d8_ordinal1) ).

fof(f213,plain,
    transfinite_sequence(sK0),
    inference(unit_resulting_resolution,[],[f126,f127,f128,f157]) ).

fof(f157,plain,
    ! [X0] :
      ( transfinite_sequence(X0)
      | ~ ordinal(relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ( ( transfinite_sequence(X0)
          | ~ ordinal(relation_dom(X0)) )
        & ( ordinal(relation_dom(X0))
          | ~ transfinite_sequence(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ( transfinite_sequence(X0)
      <=> ordinal(relation_dom(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( ( transfinite_sequence(X0)
      <=> ordinal(relation_dom(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( transfinite_sequence(X0)
      <=> ordinal(relation_dom(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131',d7_ordinal1) ).

fof(f128,plain,
    ordinal(relation_dom(sK0)),
    inference(cnf_transformation,[],[f90]) ).

fof(f162,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131',reflexivity_r1_tarski) ).

fof(f127,plain,
    function(sK0),
    inference(cnf_transformation,[],[f90]) ).

fof(f126,plain,
    relation(sK0),
    inference(cnf_transformation,[],[f90]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri Aug 25 09:32:08 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.azHYmW3pUt/Vampire---4.8_12131
% 0.15/0.36  % (12259)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (12276)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.22/0.42  % (12268)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.22/0.42  % (12272)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.22/0.42  % (12274)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.42  % (12267)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.22/0.42  % (12263)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.22/0.42  % (12277)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.22/0.43  % (12272)First to succeed.
% 0.22/0.43  % (12268)Also succeeded, but the first one will report.
% 0.22/0.43  % (12272)Refutation found. Thanks to Tanya!
% 0.22/0.43  % SZS status Theorem for Vampire---4
% 0.22/0.43  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.43  % (12272)------------------------------
% 0.22/0.43  % (12272)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43  % (12272)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43  % (12272)Termination reason: Refutation
% 0.22/0.43  
% 0.22/0.43  % (12272)Memory used [KB]: 5500
% 0.22/0.43  % (12272)Time elapsed: 0.005 s
% 0.22/0.43  % (12272)------------------------------
% 0.22/0.43  % (12272)------------------------------
% 0.22/0.43  % (12259)Success in time 0.064 s
% 0.22/0.43  % Vampire---4.8 exiting
%------------------------------------------------------------------------------