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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---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 : n001.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 17:56:02 EDT 2023

% Result   : Theorem 0.23s 0.48s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   63 (  20 unt;   0 def)
%            Number of atoms       :  201 (  61 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  227 (  89   ~;  89   |;  36   &)
%                                         (   8 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :  106 (;  97   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1995,plain,
    $false,
    inference(subsumption_resolution,[],[f1980,f336]) ).

fof(f336,plain,
    in(empty_set,sF14),
    inference(superposition,[],[f309,f326]) ).

fof(f326,plain,
    unordered_pair(empty_set,empty_set) = sF14,
    introduced(function_definition,[]) ).

fof(f309,plain,
    ! [X3] : in(X3,unordered_pair(X3,X3)),
    inference(equality_resolution,[],[f308]) ).

fof(f308,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | unordered_pair(X3,X3) != X1 ),
    inference(equality_resolution,[],[f293]) ).

fof(f293,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | unordered_pair(X0,X0) != X1 ),
    inference(definition_unfolding,[],[f241,f170]) ).

fof(f170,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',t69_enumset1) ).

fof(f241,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK6(X0,X1) != X0
            | ~ in(sK6(X0,X1),X1) )
          & ( sK6(X0,X1) = X0
            | in(sK6(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f140,f141]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK6(X0,X1) != X0
          | ~ in(sK6(X0,X1),X1) )
        & ( sK6(X0,X1) = X0
          | in(sK6(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f139]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',d1_tarski) ).

fof(f1980,plain,
    ~ in(empty_set,sF14),
    inference(resolution,[],[f1978,f955]) ).

fof(f955,plain,
    ~ subset(sF13,sF14),
    inference(subsumption_resolution,[],[f954,f327]) ).

fof(f327,plain,
    sF13 != sF14,
    inference(definition_folding,[],[f272,f326,f325]) ).

fof(f325,plain,
    powerset(empty_set) = sF13,
    introduced(function_definition,[]) ).

fof(f272,plain,
    powerset(empty_set) != unordered_pair(empty_set,empty_set),
    inference(definition_unfolding,[],[f167,f170]) ).

fof(f167,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/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',t1_zfmisc_1) ).

fof(f954,plain,
    ( sF13 = sF14
    | ~ subset(sF13,sF14) ),
    inference(resolution,[],[f229,f534]) ).

fof(f534,plain,
    subset(sF14,sF13),
    inference(forward_demodulation,[],[f532,f326]) ).

fof(f532,plain,
    subset(unordered_pair(empty_set,empty_set),sF13),
    inference(resolution,[],[f281,f398]) ).

fof(f398,plain,
    in(empty_set,sF13),
    inference(resolution,[],[f394,f168]) ).

fof(f168,plain,
    ! [X0] : subset(empty_set,X0),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,axiom,
    ! [X0] : subset(empty_set,X0),
    file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',t2_xboole_1) ).

fof(f394,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | in(X0,sF13) ),
    inference(superposition,[],[f306,f325]) ).

fof(f306,plain,
    ! [X3,X0] :
      ( in(X3,powerset(X0))
      | ~ subset(X3,X0) ),
    inference(equality_resolution,[],[f237]) ).

fof(f237,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ subset(X3,X0)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ( ( ~ subset(sK5(X0,X1),X0)
            | ~ in(sK5(X0,X1),X1) )
          & ( subset(sK5(X0,X1),X0)
            | in(sK5(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f136,f137]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK5(X0,X1),X0)
          | ~ in(sK5(X0,X1),X1) )
        & ( subset(sK5(X0,X1),X0)
          | in(sK5(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( ( powerset(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) ) )
        | powerset(X0) != X1 ) ),
    inference(rectify,[],[f135]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( ( powerset(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) ) )
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',d1_zfmisc_1) ).

fof(f281,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | subset(unordered_pair(X0,X0),X1) ),
    inference(definition_unfolding,[],[f192,f170]) ).

fof(f192,plain,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,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/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',l2_zfmisc_1) ).

fof(f229,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f128]) ).

fof(f128,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/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',d10_xboole_0) ).

fof(f1978,plain,
    ! [X1] :
      ( subset(sF13,X1)
      | ~ in(empty_set,X1) ),
    inference(duplicate_literal_removal,[],[f1975]) ).

fof(f1975,plain,
    ! [X1] :
      ( ~ in(empty_set,X1)
      | subset(sF13,X1)
      | subset(sF13,X1) ),
    inference(superposition,[],[f235,f589]) ).

fof(f589,plain,
    ! [X7] :
      ( empty_set = sK4(sF13,X7)
      | subset(sF13,X7) ),
    inference(resolution,[],[f234,f396]) ).

fof(f396,plain,
    ! [X0] :
      ( ~ in(X0,sF13)
      | empty_set = X0 ),
    inference(forward_demodulation,[],[f395,f325]) ).

fof(f395,plain,
    ! [X0] :
      ( ~ in(X0,powerset(empty_set))
      | empty_set = X0 ),
    inference(resolution,[],[f307,f171]) ).

fof(f171,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ subset(X0,empty_set) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f57,axiom,
    ! [X0] :
      ( subset(X0,empty_set)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',t3_xboole_1) ).

fof(f307,plain,
    ! [X3,X0] :
      ( subset(X3,X0)
      | ~ in(X3,powerset(X0)) ),
    inference(equality_resolution,[],[f236]) ).

fof(f236,plain,
    ! [X3,X0,X1] :
      ( subset(X3,X0)
      | ~ in(X3,X1)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f234,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK4(X0,X1),X1)
          & in(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f132,f133]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK4(X0,X1),X1)
        & in(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,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,[],[f131]) ).

fof(f131,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,[],[f108]) ).

fof(f108,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/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303',d3_tarski) ).

fof(f235,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f134]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.16  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36  % Computer : n001.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   : Wed Aug 23 21:24:40 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303
% 0.16/0.37  % (31418)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43  % (31424)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.23/0.43  % (31421)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)
% 0.23/0.43  % (31422)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)
% 0.23/0.43  % (31419)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)
% 0.23/0.43  % (31420)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)
% 0.23/0.43  % (31425)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)
% 0.23/0.44  % (31423)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)
% 0.23/0.48  % (31424)First to succeed.
% 0.23/0.48  % (31424)Refutation found. Thanks to Tanya!
% 0.23/0.48  % SZS status Theorem for Vampire---4
% 0.23/0.48  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.48  % (31424)------------------------------
% 0.23/0.48  % (31424)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.48  % (31424)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.48  % (31424)Termination reason: Refutation
% 0.23/0.48  
% 0.23/0.48  % (31424)Memory used [KB]: 6268
% 0.23/0.48  % (31424)Time elapsed: 0.048 s
% 0.23/0.48  % (31424)------------------------------
% 0.23/0.48  % (31424)------------------------------
% 0.23/0.48  % (31418)Success in time 0.109 s
% 0.23/0.48  31421 Aborted by signal SIGHUP on /export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303
% 0.23/0.48  % (31421)------------------------------
% 0.23/0.48  % (31421)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.48  31420 Aborted by signal SIGHUP on /export/starexec/sandbox2/tmp/tmp.MPa953ff2Z/Vampire---4.8_31303
% 0.23/0.48  % (31420)------------------------------
% 0.23/0.48  % (31420)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.48  % (31421)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.48  % (31420)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.48  % (31420)Termination reason: Unknown
% 0.23/0.48  % (31420)Termination phase: Saturation
% 0.23/0.48  % (31421)Termination reason: Unknown
% 0.23/0.48  
% 0.23/0.48  % (31421)Termination phase: Saturation
% 0.23/0.48  
% 0.23/0.48  % (31420)Memory used [KB]: 1023
% 0.23/0.48  % (31421)Memory used [KB]: 1151
% 0.23/0.48  % (31420)Time elapsed: 0.051 s
% 0.23/0.48  % (31421)Time elapsed: 0.050 s
% 0.23/0.48  % (31420)------------------------------
% 0.23/0.48  % (31420)------------------------------
% 0.23/0.48  % (31421)------------------------------
% 0.23/0.48  % (31421)------------------------------
% 0.23/0.48  % Vampire---4.8 exiting
%------------------------------------------------------------------------------