TSTP Solution File: SEU321+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n027.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 17:58:01 EDT 2023

% Result   : Theorem 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   54 (  14 unt;   0 def)
%            Number of atoms       :  195 (  19 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  220 (  79   ~;  70   |;  52   &)
%                                         (   2 <=>;  15  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   59 (;  38   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f854,plain,
    $false,
    inference(subsumption_resolution,[],[f797,f123]) ).

fof(f123,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    ( v5_membered(empty_set)
    & v4_membered(empty_set)
    & v3_membered(empty_set)
    & v2_membered(empty_set)
    & v1_membered(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',fc6_membered) ).

fof(f797,plain,
    ~ empty(empty_set),
    inference(backward_demodulation,[],[f200,f792]) ).

fof(f792,plain,
    empty_set = sF11,
    inference(subsumption_resolution,[],[f791,f742]) ).

fof(f742,plain,
    ( in(sK4,sK3)
    | empty_set = sF11 ),
    inference(forward_literal_rewriting,[],[f741,f186]) ).

fof(f186,plain,
    ( ~ in(sK4,sF12)
    | in(sK4,sK3) ),
    inference(definition_folding,[],[f122,f185,f184]) ).

fof(f184,plain,
    the_carrier(sK2) = sF11,
    introduced(function_definition,[]) ).

fof(f185,plain,
    subset_complement(sF11,sK3) = sF12,
    introduced(function_definition,[]) ).

fof(f122,plain,
    ( in(sK4,sK3)
    | ~ in(sK4,subset_complement(the_carrier(sK2),sK3)) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ( ( in(sK4,sK3)
      | ~ in(sK4,subset_complement(the_carrier(sK2),sK3)) )
    & ( ~ in(sK4,sK3)
      | in(sK4,subset_complement(the_carrier(sK2),sK3)) )
    & element(sK4,the_carrier(sK2))
    & element(sK3,powerset(the_carrier(sK2)))
    & one_sorted_str(sK2)
    & ~ empty_carrier(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f99,f102,f101,f100]) ).

fof(f100,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ( in(X2,X1)
                  | ~ in(X2,subset_complement(the_carrier(X0),X1)) )
                & ( ~ in(X2,X1)
                  | in(X2,subset_complement(the_carrier(X0),X1)) )
                & element(X2,the_carrier(X0)) )
            & element(X1,powerset(the_carrier(X0))) )
        & one_sorted_str(X0)
        & ~ empty_carrier(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,X1)
                | ~ in(X2,subset_complement(the_carrier(sK2),X1)) )
              & ( ~ in(X2,X1)
                | in(X2,subset_complement(the_carrier(sK2),X1)) )
              & element(X2,the_carrier(sK2)) )
          & element(X1,powerset(the_carrier(sK2))) )
      & one_sorted_str(sK2)
      & ~ empty_carrier(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ( in(X2,X1)
              | ~ in(X2,subset_complement(the_carrier(sK2),X1)) )
            & ( ~ in(X2,X1)
              | in(X2,subset_complement(the_carrier(sK2),X1)) )
            & element(X2,the_carrier(sK2)) )
        & element(X1,powerset(the_carrier(sK2))) )
   => ( ? [X2] :
          ( ( in(X2,sK3)
            | ~ in(X2,subset_complement(the_carrier(sK2),sK3)) )
          & ( ~ in(X2,sK3)
            | in(X2,subset_complement(the_carrier(sK2),sK3)) )
          & element(X2,the_carrier(sK2)) )
      & element(sK3,powerset(the_carrier(sK2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ( ? [X2] :
        ( ( in(X2,sK3)
          | ~ in(X2,subset_complement(the_carrier(sK2),sK3)) )
        & ( ~ in(X2,sK3)
          | in(X2,subset_complement(the_carrier(sK2),sK3)) )
        & element(X2,the_carrier(sK2)) )
   => ( ( in(sK4,sK3)
        | ~ in(sK4,subset_complement(the_carrier(sK2),sK3)) )
      & ( ~ in(sK4,sK3)
        | in(sK4,subset_complement(the_carrier(sK2),sK3)) )
      & element(sK4,the_carrier(sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,X1)
                | ~ in(X2,subset_complement(the_carrier(X0),X1)) )
              & ( ~ in(X2,X1)
                | in(X2,subset_complement(the_carrier(X0),X1)) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,X1)
                | ~ in(X2,subset_complement(the_carrier(X0),X1)) )
              & ( ~ in(X2,X1)
                | in(X2,subset_complement(the_carrier(X0),X1)) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f62,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,subset_complement(the_carrier(X0),X1))
              <~> ~ in(X2,X1) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,subset_complement(the_carrier(X0),X1))
              <~> ~ in(X2,X1) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,negated_conjecture,
    ~ ! [X0] :
        ( ( one_sorted_str(X0)
          & ~ empty_carrier(X0) )
       => ! [X1] :
            ( element(X1,powerset(the_carrier(X0)))
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => ( in(X2,subset_complement(the_carrier(X0),X1))
                <=> ~ in(X2,X1) ) ) ) ),
    inference(negated_conjecture,[],[f40]) ).

fof(f40,conjecture,
    ! [X0] :
      ( ( one_sorted_str(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( in(X2,subset_complement(the_carrier(X0),X1))
              <=> ~ in(X2,X1) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',l40_tops_1) ).

fof(f741,plain,
    ( in(sK4,sF12)
    | empty_set = sF11 ),
    inference(subsumption_resolution,[],[f740,f187]) ).

fof(f187,plain,
    ( ~ in(sK4,sK3)
    | in(sK4,sF12) ),
    inference(definition_folding,[],[f121,f185,f184]) ).

fof(f121,plain,
    ( ~ in(sK4,sK3)
    | in(sK4,subset_complement(the_carrier(sK2),sK3)) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f740,plain,
    ( in(sK4,sF12)
    | in(sK4,sK3)
    | empty_set = sF11 ),
    inference(forward_demodulation,[],[f733,f185]) ).

fof(f733,plain,
    ( in(sK4,sK3)
    | in(sK4,subset_complement(sF11,sK3))
    | empty_set = sF11 ),
    inference(resolution,[],[f588,f190]) ).

fof(f190,plain,
    element(sK3,sF13),
    inference(definition_folding,[],[f119,f189,f184]) ).

fof(f189,plain,
    powerset(sF11) = sF13,
    introduced(function_definition,[]) ).

fof(f119,plain,
    element(sK3,powerset(the_carrier(sK2))),
    inference(cnf_transformation,[],[f103]) ).

fof(f588,plain,
    ! [X0] :
      ( ~ element(X0,sF13)
      | in(sK4,X0)
      | in(sK4,subset_complement(sF11,X0))
      | empty_set = sF11 ),
    inference(resolution,[],[f408,f188]) ).

fof(f188,plain,
    element(sK4,sF11),
    inference(definition_folding,[],[f120,f184]) ).

fof(f120,plain,
    element(sK4,the_carrier(sK2)),
    inference(cnf_transformation,[],[f103]) ).

fof(f408,plain,
    ! [X0,X1] :
      ( ~ element(X1,sF11)
      | in(X1,X0)
      | ~ element(X0,sF13)
      | in(X1,subset_complement(sF11,X0))
      | empty_set = sF11 ),
    inference(superposition,[],[f156,f189]) ).

fof(f156,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X0))
      | in(X2,X1)
      | ~ element(X2,X0)
      | in(X2,subset_complement(X0,X1))
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( in(X2,subset_complement(X0,X1))
              | in(X2,X1)
              | ~ element(X2,X0) )
          | ~ element(X1,powerset(X0)) )
      | empty_set = X0 ),
    inference(flattening,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( in(X2,subset_complement(X0,X1))
              | in(X2,X1)
              | ~ element(X2,X0) )
          | ~ element(X1,powerset(X0)) )
      | empty_set = X0 ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( empty_set != X0
     => ! [X1] :
          ( element(X1,powerset(X0))
         => ! [X2] :
              ( element(X2,X0)
             => ( ~ in(X2,X1)
               => in(X2,subset_complement(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',t50_subset_1) ).

fof(f791,plain,
    ( ~ in(sK4,sK3)
    | empty_set = sF11 ),
    inference(forward_literal_rewriting,[],[f790,f187]) ).

fof(f790,plain,
    ( ~ in(sK4,sF12)
    | empty_set = sF11 ),
    inference(subsumption_resolution,[],[f789,f190]) ).

fof(f789,plain,
    ( ~ element(sK3,sF13)
    | ~ in(sK4,sF12)
    | empty_set = sF11 ),
    inference(forward_demodulation,[],[f788,f189]) ).

fof(f788,plain,
    ( ~ in(sK4,sF12)
    | empty_set = sF11
    | ~ element(sK3,powerset(sF11)) ),
    inference(superposition,[],[f746,f185]) ).

fof(f746,plain,
    ! [X0] :
      ( ~ in(sK4,subset_complement(X0,sK3))
      | empty_set = sF11
      | ~ element(sK3,powerset(X0)) ),
    inference(resolution,[],[f742,f170]) ).

fof(f170,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(flattening,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,axiom,
    ! [X0,X1,X2] :
      ( element(X2,powerset(X0))
     => ~ ( in(X1,X2)
          & in(X1,subset_complement(X0,X2)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',t54_subset_1) ).

fof(f200,plain,
    ~ empty(sF11),
    inference(subsumption_resolution,[],[f199,f117]) ).

fof(f117,plain,
    ~ empty_carrier(sK2),
    inference(cnf_transformation,[],[f103]) ).

fof(f199,plain,
    ( ~ empty(sF11)
    | empty_carrier(sK2) ),
    inference(subsumption_resolution,[],[f198,f118]) ).

fof(f118,plain,
    one_sorted_str(sK2),
    inference(cnf_transformation,[],[f103]) ).

fof(f198,plain,
    ( ~ empty(sF11)
    | ~ one_sorted_str(sK2)
    | empty_carrier(sK2) ),
    inference(superposition,[],[f157,f184]) ).

fof(f157,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0] :
      ( ( one_sorted_str(X0)
        & ~ empty_carrier(X0) )
     => ~ empty(the_carrier(X0)) ),
    file('/export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173',fc1_struct_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Aug 23 22:00:17 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.33  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.HWUNZrYnLZ/Vampire---4.8_13173
% 0.12/0.33  % (13426)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.38  % (13436)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.19/0.39  % (13431)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.19/0.39  % (13430)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.19/0.39  % (13435)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.19/0.39  % (13432)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.19/0.39  % (13433)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.19/0.40  % (13434)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_424 on Vampire---4 for (424ds/0Mi)
% 0.19/0.41  % (13436)First to succeed.
% 0.19/0.41  % (13435)Also succeeded, but the first one will report.
% 0.19/0.41  % (13436)Refutation found. Thanks to Tanya!
% 0.19/0.41  % SZS status Theorem for Vampire---4
% 0.19/0.41  % SZS output start Proof for Vampire---4
% See solution above
% 0.19/0.41  % (13436)------------------------------
% 0.19/0.41  % (13436)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.19/0.41  % (13436)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.19/0.41  % (13436)Termination reason: Refutation
% 0.19/0.41  
% 0.19/0.41  % (13436)Memory used [KB]: 1663
% 0.19/0.41  % (13436)Time elapsed: 0.026 s
% 0.19/0.41  % (13436)------------------------------
% 0.19/0.41  % (13436)------------------------------
% 0.19/0.41  % (13426)Success in time 0.076 s
% 0.19/0.41  % Vampire---4.8 exiting
%------------------------------------------------------------------------------