TSTP Solution File: SEU127+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU127+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 : n020.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 17:55:52 EDT 2023

% Result   : Theorem 0.25s 0.46s
% Output   : Refutation 0.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   32 (  13 unt;   0 def)
%            Number of atoms       :  128 (  13 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  154 (  58   ~;  55   |;  33   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   79 (;  68   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f602,plain,
    $false,
    inference(subsumption_resolution,[],[f596,f151]) ).

fof(f151,plain,
    ~ subset(sF10,sK0),
    inference(definition_folding,[],[f90,f150]) ).

fof(f150,plain,
    set_intersection2(sK0,sK1) = sF10,
    introduced(function_definition,[]) ).

fof(f90,plain,
    ~ subset(set_intersection2(sK0,sK1),sK0),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ~ subset(set_intersection2(sK0,sK1),sK0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f42,f59]) ).

fof(f59,plain,
    ( ? [X0,X1] : ~ subset(set_intersection2(X0,X1),X0)
   => ~ subset(set_intersection2(sK0,sK1),sK0) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ? [X0,X1] : ~ subset(set_intersection2(X0,X1),X0),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,negated_conjecture,
    ~ ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    inference(negated_conjecture,[],[f23]) ).

fof(f23,conjecture,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    file('/export/starexec/sandbox2/tmp/tmp.ONo6lhbZeE/Vampire---4.8_5956',t17_xboole_1) ).

fof(f596,plain,
    subset(sF10,sK0),
    inference(superposition,[],[f565,f150]) ).

fof(f565,plain,
    ! [X2,X3] : subset(set_intersection2(X3,X2),X3),
    inference(superposition,[],[f535,f111]) ).

fof(f111,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox2/tmp/tmp.ONo6lhbZeE/Vampire---4.8_5956',commutativity_k3_xboole_0) ).

fof(f535,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X1),
    inference(duplicate_literal_removal,[],[f525]) ).

fof(f525,plain,
    ! [X0,X1] :
      ( subset(set_intersection2(X0,X1),X1)
      | subset(set_intersection2(X0,X1),X1) ),
    inference(resolution,[],[f219,f123]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( in(sK5(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK5(X0,X1),X1)
          & in(sK5(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f73,f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK5(X0,X1),X1)
        & in(sK5(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,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,[],[f72]) ).

fof(f72,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,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.ONo6lhbZeE/Vampire---4.8_5956',d3_tarski) ).

fof(f219,plain,
    ! [X10,X11,X12] :
      ( ~ in(sK5(X10,X11),set_intersection2(X12,X11))
      | subset(X10,X11) ),
    inference(resolution,[],[f145,f124]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ~ in(sK5(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f145,plain,
    ! [X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,set_intersection2(X0,X1)) ),
    inference(equality_resolution,[],[f128]) ).

fof(f128,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ( ( ~ in(sK6(X0,X1,X2),X1)
            | ~ in(sK6(X0,X1,X2),X0)
            | ~ in(sK6(X0,X1,X2),X2) )
          & ( ( in(sK6(X0,X1,X2),X1)
              & in(sK6(X0,X1,X2),X0) )
            | in(sK6(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f78,f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK6(X0,X1,X2),X1)
          | ~ in(sK6(X0,X1,X2),X0)
          | ~ in(sK6(X0,X1,X2),X2) )
        & ( ( in(sK6(X0,X1,X2),X1)
            & in(sK6(X0,X1,X2),X0) )
          | in(sK6(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(rectify,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.ONo6lhbZeE/Vampire---4.8_5956',d3_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : SEU127+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.17  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.17/0.38  % Computer : n020.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit   : 300
% 0.17/0.38  % WCLimit    : 300
% 0.17/0.38  % DateTime   : Wed Aug 23 16:45:16 EDT 2023
% 0.17/0.38  % CPUTime    : 
% 0.17/0.38  This is a FOF_THM_RFO_SEQ problem
% 0.17/0.38  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.ONo6lhbZeE/Vampire---4.8_5956
% 0.17/0.38  % (6064)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.44  % (6077)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.25/0.44  % (6074)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)
% 0.25/0.44  % (6071)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)
% 0.25/0.44  % (6066)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)
% 0.25/0.44  % (6065)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)
% 0.25/0.44  % (6068)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)
% 0.25/0.44  % (6079)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)
% 0.25/0.46  % (6077)First to succeed.
% 0.25/0.46  % (6074)Also succeeded, but the first one will report.
% 0.25/0.46  % (6077)Refutation found. Thanks to Tanya!
% 0.25/0.46  % SZS status Theorem for Vampire---4
% 0.25/0.46  % SZS output start Proof for Vampire---4
% See solution above
% 0.25/0.46  % (6077)------------------------------
% 0.25/0.46  % (6077)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.25/0.46  % (6077)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.25/0.46  % (6077)Termination reason: Refutation
% 0.25/0.46  
% 0.25/0.46  % (6077)Memory used [KB]: 5756
% 0.25/0.46  % (6077)Time elapsed: 0.020 s
% 0.25/0.46  % (6077)------------------------------
% 0.25/0.46  % (6077)------------------------------
% 0.25/0.46  % (6064)Success in time 0.075 s
% 0.25/0.46  % Vampire---4.8 exiting
%------------------------------------------------------------------------------