TSTP Solution File: SEU147+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU147+2 : 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 : n028.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 00:06:49 EDT 2023

% Result   : Theorem 15.13s 2.62s
% Output   : Refutation 15.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   66 (  22 unt;   0 def)
%            Number of atoms       :  219 (  49 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  247 (  94   ~;  90   |;  44   &)
%                                         (  15 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   1 con; 0-2 aty)
%            Number of variables   :  126 (; 117   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f128418,plain,
    $false,
    inference(subsumption_resolution,[],[f128347,f15580]) ).

fof(f15580,plain,
    ~ in(sK14(powerset(empty_set),singleton(empty_set)),singleton(empty_set)),
    inference(unit_resulting_resolution,[],[f15453,f266]) ).

fof(f266,plain,
    ! [X0,X1] :
      ( ~ in(sK14(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK14(X0,X1),X1)
          & in(sK14(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f147,f148]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK14(X0,X1),X1)
        & in(sK14(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f146]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d3_tarski) ).

fof(f15453,plain,
    ~ subset(powerset(empty_set),singleton(empty_set)),
    inference(unit_resulting_resolution,[],[f196,f14865,f258]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f141]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d10_xboole_0) ).

fof(f14865,plain,
    ! [X0] : subset(singleton(empty_set),powerset(X0)),
    inference(unit_resulting_resolution,[],[f14787,f221]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | subset(singleton(X0),X1) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ( subset(singleton(X0),X1)
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ~ subset(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',l2_zfmisc_1) ).

fof(f14787,plain,
    ! [X0] : in(empty_set,powerset(X0)),
    inference(unit_resulting_resolution,[],[f197,f713,f268]) ).

fof(f268,plain,
    ! [X3,X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ subset(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ~ subset(sK15(X0,X1),X0)
            | ~ in(sK15(X0,X1),X1) )
          & ( subset(sK15(X0,X1),X0)
            | in(sK15(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f151,f152]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK15(X0,X1),X0)
          | ~ in(sK15(X0,X1),X1) )
        & ( subset(sK15(X0,X1),X0)
          | in(sK15(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f150]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ subset(X2,X0) )
            & ( subset(X2,X0)
              | ~ in(X2,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f713,plain,
    ! [X0] : sP0(X0,powerset(X0)),
    inference(forward_demodulation,[],[f711,f238]) ).

fof(f238,plain,
    ! [X0] : set_difference(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f55]) ).

fof(f55,axiom,
    ! [X0] : set_difference(X0,empty_set) = X0,
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',t3_boole) ).

fof(f711,plain,
    ! [X0] : sP0(X0,set_difference(powerset(X0),empty_set)),
    inference(unit_resulting_resolution,[],[f238,f271]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( powerset(X0) != X1
      | sP0(X0,X1) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f9,f108]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d1_zfmisc_1) ).

fof(f197,plain,
    ! [X0] : subset(empty_set,X0),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,axiom,
    ! [X0] : subset(empty_set,X0),
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',t2_xboole_1) ).

fof(f196,plain,
    powerset(empty_set) != singleton(empty_set),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    powerset(empty_set) != singleton(empty_set),
    inference(flattening,[],[f45]) ).

fof(f45,negated_conjecture,
    powerset(empty_set) != singleton(empty_set),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    powerset(empty_set) = singleton(empty_set),
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',t1_zfmisc_1) ).

fof(f128347,plain,
    in(sK14(powerset(empty_set),singleton(empty_set)),singleton(empty_set)),
    inference(unit_resulting_resolution,[],[f128027,f22358]) ).

fof(f22358,plain,
    ! [X0,X1] :
      ( X0 != X1
      | in(X1,singleton(X0)) ),
    inference(resolution,[],[f274,f731]) ).

fof(f731,plain,
    ! [X0] : sP1(X0,singleton(X0)),
    inference(forward_demodulation,[],[f729,f238]) ).

fof(f729,plain,
    ! [X0] : sP1(X0,set_difference(singleton(X0),empty_set)),
    inference(unit_resulting_resolution,[],[f238,f277]) ).

fof(f277,plain,
    ! [X0,X1] :
      ( singleton(X0) != X1
      | sP1(X0,X1) ),
    inference(cnf_transformation,[],[f159]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ~ sP1(X0,X1) )
      & ( sP1(X0,X1)
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> sP1(X0,X1) ),
    inference(definition_folding,[],[f7,f110]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d1_tarski) ).

fof(f274,plain,
    ! [X3,X0,X1] :
      ( ~ sP1(X0,X1)
      | X0 != X3
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f158]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ( ( sK16(X0,X1) != X0
            | ~ in(sK16(X0,X1),X1) )
          & ( sK16(X0,X1) = X0
            | in(sK16(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | ~ sP1(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f156,f157]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK16(X0,X1) != X0
          | ~ in(sK16(X0,X1),X1) )
        & ( sK16(X0,X1) = X0
          | in(sK16(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f155]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | ~ sP1(X0,X1) ) ),
    inference(nnf_transformation,[],[f110]) ).

fof(f128027,plain,
    empty_set = sK14(powerset(empty_set),singleton(empty_set)),
    inference(unit_resulting_resolution,[],[f348,f127734,f261]) ).

fof(f261,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | X0 = X1
      | proper_subset(X0,X1) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( ( proper_subset(X0,X1)
        | X0 = X1
        | ~ subset(X0,X1) )
      & ( ( X0 != X1
          & subset(X0,X1) )
        | ~ proper_subset(X0,X1) ) ),
    inference(flattening,[],[f143]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ( proper_subset(X0,X1)
        | X0 = X1
        | ~ subset(X0,X1) )
      & ( ( X0 != X1
          & subset(X0,X1) )
        | ~ proper_subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( proper_subset(X0,X1)
    <=> ( X0 != X1
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',d8_xboole_0) ).

fof(f127734,plain,
    subset(sK14(powerset(empty_set),singleton(empty_set)),empty_set),
    inference(unit_resulting_resolution,[],[f713,f15579,f267]) ).

fof(f267,plain,
    ! [X3,X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ in(X3,X1)
      | subset(X3,X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f15579,plain,
    in(sK14(powerset(empty_set),singleton(empty_set)),powerset(empty_set)),
    inference(unit_resulting_resolution,[],[f15453,f265]) ).

fof(f265,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK14(X0,X1),X0) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f348,plain,
    ! [X0] : ~ proper_subset(X0,empty_set),
    inference(unit_resulting_resolution,[],[f197,f226]) ).

fof(f226,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ~ proper_subset(X1,X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ~ proper_subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f63]) ).

fof(f63,axiom,
    ! [X0,X1] :
      ~ ( proper_subset(X1,X0)
        & subset(X0,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.T9R0Q4WTN7/Vampire---4.8_7327',t60_xboole_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.32  % Computer : n028.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Wed Aug 30 14:25:27 EDT 2023
% 0.12/0.32  % CPUTime    : 
% 0.17/0.38  % (7454)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38  % (7462)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.17/0.38  % (7468)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.17/0.38  % (7466)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)
% 0.17/0.38  % (7473)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)
% 0.17/0.38  % (7479)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)
% 0.17/0.38  % (7476)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)
% 0.17/0.38  TRYING [1]
% 0.17/0.38  TRYING [2]
% 0.17/0.39  TRYING [3]
% 0.17/0.39  % (7458)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.17/0.40  TRYING [4]
% 0.17/0.42  TRYING [1]
% 0.17/0.43  TRYING [2]
% 0.17/0.44  TRYING [5]
% 0.17/0.46  TRYING [3]
% 0.17/0.54  TRYING [6]
% 0.17/0.66  TRYING [4]
% 0.17/0.75  TRYING [7]
% 4.41/1.01  TRYING [5]
% 5.29/1.20  TRYING [8]
% 7.69/1.49  TRYING [1]
% 7.69/1.49  TRYING [2]
% 7.69/1.50  TRYING [3]
% 7.98/1.51  TRYING [4]
% 8.25/1.54  TRYING [5]
% 8.92/1.64  TRYING [6]
% 10.33/1.91  TRYING [7]
% 10.33/1.99  TRYING [6]
% 12.37/2.14  TRYING [9]
% 15.13/2.52  TRYING [8]
% 15.13/2.61  % (7479)First to succeed.
% 15.13/2.62  % (7479)Refutation found. Thanks to Tanya!
% 15.13/2.62  % SZS status Theorem for Vampire---4
% 15.13/2.62  % SZS output start Proof for Vampire---4
% See solution above
% 15.13/2.62  % (7479)------------------------------
% 15.13/2.62  % (7479)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 15.13/2.62  % (7479)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 15.13/2.62  % (7479)Termination reason: Refutation
% 15.13/2.62  
% 15.13/2.62  % (7479)Memory used [KB]: 56033
% 15.13/2.62  % (7479)Time elapsed: 2.227 s
% 15.13/2.62  % (7479)------------------------------
% 15.13/2.62  % (7479)------------------------------
% 15.13/2.62  % (7454)Success in time 2.269 s
% 15.13/2.62  % Vampire---4.8 exiting
%------------------------------------------------------------------------------