TSTP Solution File: SEU118+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU118+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 : n023.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 : Sat Sep  2 00:06:35 EDT 2023

% Result   : Theorem 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   46 (   8 unt;   0 def)
%            Number of atoms       :  179 (   8 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  220 (  87   ~;  75   |;  40   &)
%                                         (   8 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   75 (;  65   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f260,plain,
    $false,
    inference(resolution,[],[f259,f93]) ).

fof(f93,plain,
    element(sK3,powerset(sK2)),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ( ~ element(sK3,finite_subsets(sK2))
    & finite(sK2)
    & element(sK3,powerset(sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f37,f63]) ).

fof(f63,plain,
    ( ? [X0,X1] :
        ( ~ element(X1,finite_subsets(X0))
        & finite(X0)
        & element(X1,powerset(X0)) )
   => ( ~ element(sK3,finite_subsets(sK2))
      & finite(sK2)
      & element(sK3,powerset(sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ? [X0,X1] :
      ( ~ element(X1,finite_subsets(X0))
      & finite(X0)
      & element(X1,powerset(X0)) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ? [X0,X1] :
      ( ~ element(X1,finite_subsets(X0))
      & finite(X0)
      & element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,negated_conjecture,
    ~ ! [X0,X1] :
        ( element(X1,powerset(X0))
       => ( finite(X0)
         => element(X1,finite_subsets(X0)) ) ),
    inference(negated_conjecture,[],[f27]) ).

fof(f27,conjecture,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => ( finite(X0)
       => element(X1,finite_subsets(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJWVOPRoJT/Vampire---4.8_19730',t34_finsub_1) ).

fof(f259,plain,
    ~ element(sK3,powerset(sK2)),
    inference(duplicate_literal_removal,[],[f255]) ).

fof(f255,plain,
    ( ~ element(sK3,powerset(sK2))
    | ~ element(sK3,powerset(sK2)) ),
    inference(resolution,[],[f221,f94]) ).

fof(f94,plain,
    finite(sK2),
    inference(cnf_transformation,[],[f64]) ).

fof(f221,plain,
    ! [X0] :
      ( ~ finite(X0)
      | ~ element(sK3,powerset(X0))
      | ~ element(sK3,powerset(sK2)) ),
    inference(resolution,[],[f219,f119]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( finite(X1)
      | ~ element(X1,powerset(X0))
      | ~ finite(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( finite(X1)
          | ~ element(X1,powerset(X0)) )
      | ~ finite(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( finite(X0)
     => ! [X1] :
          ( element(X1,powerset(X0))
         => finite(X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJWVOPRoJT/Vampire---4.8_19730',cc2_finset_1) ).

fof(f219,plain,
    ( ~ finite(sK3)
    | ~ element(sK3,powerset(sK2)) ),
    inference(resolution,[],[f218,f98]) ).

fof(f98,plain,
    ! [X0] : preboolean(finite_subsets(X0)),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] : preboolean(finite_subsets(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.LJWVOPRoJT/Vampire---4.8_19730',dt_k5_finsub_1) ).

fof(f218,plain,
    ( ~ preboolean(finite_subsets(sK2))
    | ~ finite(sK3)
    | ~ element(sK3,powerset(sK2)) ),
    inference(resolution,[],[f216,f149]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJWVOPRoJT/Vampire---4.8_19730',t3_subset) ).

fof(f216,plain,
    ( ~ subset(sK3,sK2)
    | ~ finite(sK3)
    | ~ preboolean(finite_subsets(sK2)) ),
    inference(resolution,[],[f215,f143]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( sP1(X1,X0)
      | ~ preboolean(X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( sP1(X1,X0)
      | ~ preboolean(X1) ),
    inference(definition_folding,[],[f47,f61,f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ( finite(X2)
            & subset(X2,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f61,plain,
    ! [X1,X0] :
      ( ( finite_subsets(X0) = X1
      <=> sP0(X0,X1) )
      | ~ sP1(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ( finite_subsets(X0) = X1
      <=> ! [X2] :
            ( in(X2,X1)
          <=> ( finite(X2)
              & subset(X2,X0) ) ) )
      | ~ preboolean(X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( preboolean(X1)
     => ( finite_subsets(X0) = X1
      <=> ! [X2] :
            ( in(X2,X1)
          <=> ( finite(X2)
              & subset(X2,X0) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJWVOPRoJT/Vampire---4.8_19730',d5_finsub_1) ).

fof(f215,plain,
    ( ~ sP1(finite_subsets(sK2),sK2)
    | ~ finite(sK3)
    | ~ subset(sK3,sK2) ),
    inference(resolution,[],[f212,f200]) ).

fof(f200,plain,
    ! [X0] :
      ( sP0(X0,finite_subsets(X0))
      | ~ sP1(finite_subsets(X0),X0) ),
    inference(equality_resolution,[],[f135]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( finite_subsets(X1) != X0
      | sP0(X1,X0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ( ( finite_subsets(X1) = X0
          | ~ sP0(X1,X0) )
        & ( sP0(X1,X0)
          | finite_subsets(X1) != X0 ) )
      | ~ sP1(X0,X1) ),
    inference(rectify,[],[f77]) ).

fof(f77,plain,
    ! [X1,X0] :
      ( ( ( finite_subsets(X0) = X1
          | ~ sP0(X0,X1) )
        & ( sP0(X0,X1)
          | finite_subsets(X0) != X1 ) )
      | ~ sP1(X1,X0) ),
    inference(nnf_transformation,[],[f61]) ).

fof(f212,plain,
    ! [X18] :
      ( ~ sP0(X18,finite_subsets(sK2))
      | ~ subset(sK3,X18)
      | ~ finite(sK3) ),
    inference(resolution,[],[f139,f182]) ).

fof(f182,plain,
    ~ in(sK3,finite_subsets(sK2)),
    inference(resolution,[],[f145,f95]) ).

fof(f95,plain,
    ~ element(sK3,finite_subsets(sK2)),
    inference(cnf_transformation,[],[f64]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.LJWVOPRoJT/Vampire---4.8_19730',t1_subset) ).

fof(f139,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ finite(X3)
      | ~ subset(X3,X0)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ~ finite(sK10(X0,X1))
            | ~ subset(sK10(X0,X1),X0)
            | ~ in(sK10(X0,X1),X1) )
          & ( ( finite(sK10(X0,X1))
              & subset(sK10(X0,X1),X0) )
            | in(sK10(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ finite(X3)
              | ~ subset(X3,X0) )
            & ( ( finite(X3)
                & subset(X3,X0) )
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f81,f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ finite(X2)
            | ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( ( finite(X2)
              & subset(X2,X0) )
            | in(X2,X1) ) )
     => ( ( ~ finite(sK10(X0,X1))
          | ~ subset(sK10(X0,X1),X0)
          | ~ in(sK10(X0,X1),X1) )
        & ( ( finite(sK10(X0,X1))
            & subset(sK10(X0,X1),X0) )
          | in(sK10(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ~ finite(X2)
              | ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( ( finite(X2)
                & subset(X2,X0) )
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ finite(X3)
              | ~ subset(X3,X0) )
            & ( ( finite(X3)
                & subset(X3,X0) )
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ~ finite(X2)
              | ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( ( finite(X2)
                & subset(X2,X0) )
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ finite(X2)
              | ~ subset(X2,X0) )
            & ( ( finite(X2)
                & subset(X2,X0) )
              | ~ in(X2,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ~ finite(X2)
              | ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( ( finite(X2)
                & subset(X2,X0) )
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ finite(X2)
              | ~ subset(X2,X0) )
            & ( ( finite(X2)
                & subset(X2,X0) )
              | ~ in(X2,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f60]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SEU118+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 30 14:10:24 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.14/0.40  % (19916)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.41  % (19924)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.14/0.41  % (19919)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.14/0.41  % (19920)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.14/0.41  % (19922)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.14/0.41  % (19921)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.14/0.41  % (19923)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.14/0.41  % (19925)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.20/0.41  TRYING [1]
% 0.20/0.41  TRYING [2]
% 0.20/0.41  % (19924)First to succeed.
% 0.20/0.41  TRYING [3]
% 0.20/0.41  % (19924)Refutation found. Thanks to Tanya!
% 0.20/0.41  % SZS status Theorem for Vampire---4
% 0.20/0.41  % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.41  % (19924)------------------------------
% 0.20/0.41  % (19924)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.41  % (19924)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.41  % (19924)Termination reason: Refutation
% 0.20/0.41  
% 0.20/0.41  % (19924)Memory used [KB]: 1023
% 0.20/0.41  % (19924)Time elapsed: 0.005 s
% 0.20/0.41  % (19924)------------------------------
% 0.20/0.41  % (19924)------------------------------
% 0.20/0.41  % (19916)Success in time 0.062 s
% 0.20/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------