TSTP Solution File: SEU174+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU174+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n009.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 : Sun May  5 09:20:44 EDT 2024

% Result   : Theorem 0.60s 0.77s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   53 (   9 unt;   0 def)
%            Number of atoms       :  194 (  42 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  242 ( 101   ~;  88   |;  36   &)
%                                         (   6 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   94 (  81   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f766,plain,
    $false,
    inference(avatar_sat_refutation,[],[f689,f765]) ).

fof(f765,plain,
    ~ spl31_8,
    inference(avatar_contradiction_clause,[],[f764]) ).

fof(f764,plain,
    ( $false
    | ~ spl31_8 ),
    inference(subsumption_resolution,[],[f750,f371]) ).

fof(f371,plain,
    empty_set != sK4,
    inference(cnf_transformation,[],[f230]) ).

fof(f230,plain,
    ( empty_set = complements_of_subsets(sK3,sK4)
    & empty_set != sK4
    & element(sK4,powerset(powerset(sK3))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f163,f229]) ).

fof(f229,plain,
    ( ? [X0,X1] :
        ( empty_set = complements_of_subsets(X0,X1)
        & empty_set != X1
        & element(X1,powerset(powerset(X0))) )
   => ( empty_set = complements_of_subsets(sK3,sK4)
      & empty_set != sK4
      & element(sK4,powerset(powerset(sK3))) ) ),
    introduced(choice_axiom,[]) ).

fof(f163,plain,
    ? [X0,X1] :
      ( empty_set = complements_of_subsets(X0,X1)
      & empty_set != X1
      & element(X1,powerset(powerset(X0))) ),
    inference(flattening,[],[f162]) ).

fof(f162,plain,
    ? [X0,X1] :
      ( empty_set = complements_of_subsets(X0,X1)
      & empty_set != X1
      & element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f99]) ).

fof(f99,negated_conjecture,
    ~ ! [X0,X1] :
        ( element(X1,powerset(powerset(X0)))
       => ~ ( empty_set = complements_of_subsets(X0,X1)
            & empty_set != X1 ) ),
    inference(negated_conjecture,[],[f98]) ).

fof(f98,conjecture,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => ~ ( empty_set = complements_of_subsets(X0,X1)
          & empty_set != X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.BNiWGVFe2F/Vampire---4.8_16739',t46_setfam_1) ).

fof(f750,plain,
    ( empty_set = sK4
    | ~ spl31_8 ),
    inference(resolution,[],[f748,f398]) ).

fof(f398,plain,
    ! [X0] :
      ( in(sK7(X0),X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f242]) ).

fof(f242,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK7(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f240,f241]) ).

fof(f241,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK7(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f240,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f239]) ).

fof(f239,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.BNiWGVFe2F/Vampire---4.8_16739',d1_xboole_0) ).

fof(f748,plain,
    ( ! [X0] : ~ in(X0,sK4)
    | ~ spl31_8 ),
    inference(subsumption_resolution,[],[f747,f619]) ).

fof(f619,plain,
    ! [X0] :
      ( element(X0,powerset(sK3))
      | ~ in(X0,sK4) ),
    inference(resolution,[],[f370,f431]) ).

fof(f431,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X2))
      | element(X0,X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f186]) ).

fof(f186,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f185]) ).

fof(f185,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f103]) ).

fof(f103,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox/tmp/tmp.BNiWGVFe2F/Vampire---4.8_16739',t4_subset) ).

fof(f370,plain,
    element(sK4,powerset(powerset(sK3))),
    inference(cnf_transformation,[],[f230]) ).

fof(f747,plain,
    ( ! [X0] :
        ( ~ in(X0,sK4)
        | ~ element(X0,powerset(sK3)) )
    | ~ spl31_8 ),
    inference(subsumption_resolution,[],[f746,f685]) ).

fof(f685,plain,
    ( element(empty_set,powerset(powerset(sK3)))
    | ~ spl31_8 ),
    inference(avatar_component_clause,[],[f684]) ).

fof(f684,plain,
    ( spl31_8
  <=> element(empty_set,powerset(powerset(sK3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl31_8])]) ).

fof(f746,plain,
    ! [X0] :
      ( ~ in(X0,sK4)
      | ~ element(X0,powerset(sK3))
      | ~ element(empty_set,powerset(powerset(sK3))) ),
    inference(subsumption_resolution,[],[f745,f570]) ).

fof(f570,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f397]) ).

fof(f397,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f242]) ).

fof(f745,plain,
    ! [X0] :
      ( ~ in(X0,sK4)
      | ~ element(X0,powerset(sK3))
      | in(subset_complement(sK3,X0),empty_set)
      | ~ element(empty_set,powerset(powerset(sK3))) ),
    inference(subsumption_resolution,[],[f741,f370]) ).

fof(f741,plain,
    ! [X0] :
      ( ~ element(sK4,powerset(powerset(sK3)))
      | ~ in(X0,sK4)
      | ~ element(X0,powerset(sK3))
      | in(subset_complement(sK3,X0),empty_set)
      | ~ element(empty_set,powerset(powerset(sK3))) ),
    inference(superposition,[],[f598,f690]) ).

fof(f690,plain,
    sK4 = complements_of_subsets(sK3,empty_set),
    inference(subsumption_resolution,[],[f677,f370]) ).

fof(f677,plain,
    ( sK4 = complements_of_subsets(sK3,empty_set)
    | ~ element(sK4,powerset(powerset(sK3))) ),
    inference(superposition,[],[f479,f372]) ).

fof(f372,plain,
    empty_set = complements_of_subsets(sK3,sK4),
    inference(cnf_transformation,[],[f230]) ).

fof(f479,plain,
    ! [X0,X1] :
      ( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(cnf_transformation,[],[f193]) ).

fof(f193,plain,
    ! [X0,X1] :
      ( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
    file('/export/starexec/sandbox/tmp/tmp.BNiWGVFe2F/Vampire---4.8_16739',involutiveness_k7_setfam_1) ).

fof(f598,plain,
    ! [X0,X1,X4] :
      ( ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
      | ~ in(X4,complements_of_subsets(X0,X1))
      | ~ element(X4,powerset(X0))
      | in(subset_complement(X0,X4),X1)
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(equality_resolution,[],[f481]) ).

fof(f481,plain,
    ! [X2,X0,X1,X4] :
      ( in(subset_complement(X0,X4),X1)
      | ~ in(X4,X2)
      | ~ element(X4,powerset(X0))
      | complements_of_subsets(X0,X1) != X2
      | ~ element(X2,powerset(powerset(X0)))
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(cnf_transformation,[],[f300]) ).

fof(f300,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( complements_of_subsets(X0,X1) = X2
              | ( ( ~ in(subset_complement(X0,sK26(X0,X1,X2)),X1)
                  | ~ in(sK26(X0,X1,X2),X2) )
                & ( in(subset_complement(X0,sK26(X0,X1,X2)),X1)
                  | in(sK26(X0,X1,X2),X2) )
                & element(sK26(X0,X1,X2),powerset(X0)) ) )
            & ( ! [X4] :
                  ( ( ( in(X4,X2)
                      | ~ in(subset_complement(X0,X4),X1) )
                    & ( in(subset_complement(X0,X4),X1)
                      | ~ in(X4,X2) ) )
                  | ~ element(X4,powerset(X0)) )
              | complements_of_subsets(X0,X1) != X2 ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f298,f299]) ).

fof(f299,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(subset_complement(X0,X3),X1)
            | ~ in(X3,X2) )
          & ( in(subset_complement(X0,X3),X1)
            | in(X3,X2) )
          & element(X3,powerset(X0)) )
     => ( ( ~ in(subset_complement(X0,sK26(X0,X1,X2)),X1)
          | ~ in(sK26(X0,X1,X2),X2) )
        & ( in(subset_complement(X0,sK26(X0,X1,X2)),X1)
          | in(sK26(X0,X1,X2),X2) )
        & element(sK26(X0,X1,X2),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f298,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( complements_of_subsets(X0,X1) = X2
              | ? [X3] :
                  ( ( ~ in(subset_complement(X0,X3),X1)
                    | ~ in(X3,X2) )
                  & ( in(subset_complement(X0,X3),X1)
                    | in(X3,X2) )
                  & element(X3,powerset(X0)) ) )
            & ( ! [X4] :
                  ( ( ( in(X4,X2)
                      | ~ in(subset_complement(X0,X4),X1) )
                    & ( in(subset_complement(X0,X4),X1)
                      | ~ in(X4,X2) ) )
                  | ~ element(X4,powerset(X0)) )
              | complements_of_subsets(X0,X1) != X2 ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(rectify,[],[f297]) ).

fof(f297,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( complements_of_subsets(X0,X1) = X2
              | ? [X3] :
                  ( ( ~ in(subset_complement(X0,X3),X1)
                    | ~ in(X3,X2) )
                  & ( in(subset_complement(X0,X3),X1)
                    | in(X3,X2) )
                  & element(X3,powerset(X0)) ) )
            & ( ! [X3] :
                  ( ( ( in(X3,X2)
                      | ~ in(subset_complement(X0,X3),X1) )
                    & ( in(subset_complement(X0,X3),X1)
                      | ~ in(X3,X2) ) )
                  | ~ element(X3,powerset(X0)) )
              | complements_of_subsets(X0,X1) != X2 ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(flattening,[],[f296]) ).

fof(f296,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( complements_of_subsets(X0,X1) = X2
              | ? [X3] :
                  ( ( ~ in(subset_complement(X0,X3),X1)
                    | ~ in(X3,X2) )
                  & ( in(subset_complement(X0,X3),X1)
                    | in(X3,X2) )
                  & element(X3,powerset(X0)) ) )
            & ( ! [X3] :
                  ( ( ( in(X3,X2)
                      | ~ in(subset_complement(X0,X3),X1) )
                    & ( in(subset_complement(X0,X3),X1)
                      | ~ in(X3,X2) ) )
                  | ~ element(X3,powerset(X0)) )
              | complements_of_subsets(X0,X1) != X2 ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(nnf_transformation,[],[f195]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( complements_of_subsets(X0,X1) = X2
          <=> ! [X3] :
                ( ( in(X3,X2)
                <=> in(subset_complement(X0,X3),X1) )
                | ~ element(X3,powerset(X0)) ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => ! [X2] :
          ( element(X2,powerset(powerset(X0)))
         => ( complements_of_subsets(X0,X1) = X2
          <=> ! [X3] :
                ( element(X3,powerset(X0))
               => ( in(X3,X2)
                <=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.BNiWGVFe2F/Vampire---4.8_16739',d8_setfam_1) ).

fof(f689,plain,
    spl31_8,
    inference(avatar_split_clause,[],[f688,f684]) ).

fof(f688,plain,
    element(empty_set,powerset(powerset(sK3))),
    inference(subsumption_resolution,[],[f676,f370]) ).

fof(f676,plain,
    ( element(empty_set,powerset(powerset(sK3)))
    | ~ element(sK4,powerset(powerset(sK3))) ),
    inference(superposition,[],[f480,f372]) ).

fof(f480,plain,
    ! [X0,X1] :
      ( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f194,plain,
    ! [X0,X1] :
      ( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
    file('/export/starexec/sandbox/tmp/tmp.BNiWGVFe2F/Vampire---4.8_16739',dt_k7_setfam_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU174+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36  % Computer : n009.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 11:27:25 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.BNiWGVFe2F/Vampire---4.8_16739
% 0.58/0.75  % (17010)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.58/0.75  % (17012)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.58/0.75  % (17011)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.58/0.75  % (17009)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.58/0.75  % (17015)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.58/0.75  % (17014)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.58/0.75  % (17008)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.58/0.76  % (17013)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.58/0.77  % (17013)First to succeed.
% 0.58/0.77  % (17013)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16994"
% 0.60/0.77  % (17013)Refutation found. Thanks to Tanya!
% 0.60/0.77  % SZS status Theorem for Vampire---4
% 0.60/0.77  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.77  % (17013)------------------------------
% 0.60/0.77  % (17013)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77  % (17013)Termination reason: Refutation
% 0.60/0.77  
% 0.60/0.77  % (17013)Memory used [KB]: 1378
% 0.60/0.77  % (17013)Time elapsed: 0.018 s
% 0.60/0.77  % (17013)Instructions burned: 21 (million)
% 0.60/0.77  % (16994)Success in time 0.406 s
% 0.60/0.77  % Vampire---4.8 exiting
%------------------------------------------------------------------------------