TSTP Solution File: SET014+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n026.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 15:34:07 EDT 2023

% Result   : Theorem 0.23s 0.44s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (   7 unt;   0 def)
%            Number of atoms       :   93 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   94 (  33   ~;  29   |;  24   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   58 (;  46   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f133,plain,
    $false,
    inference(resolution,[],[f130,f25]) ).

fof(f25,plain,
    ~ subset(union(sK0,sK2),sK1),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ( ~ subset(union(sK0,sK2),sK1)
    & subset(sK2,sK1)
    & subset(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11]) ).

fof(f11,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(union(X0,X2),X1)
        & subset(X2,X1)
        & subset(X0,X1) )
   => ( ~ subset(union(sK0,sK2),sK1)
      & subset(sK2,sK1)
      & subset(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ? [X0,X1,X2] :
      ( ~ subset(union(X0,X2),X1)
      & subset(X2,X1)
      & subset(X0,X1) ),
    inference(flattening,[],[f8]) ).

fof(f8,plain,
    ? [X0,X1,X2] :
      ( ~ subset(union(X0,X2),X1)
      & subset(X2,X1)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( subset(X2,X1)
          & subset(X0,X1) )
       => subset(union(X0,X2),X1) ),
    inference(negated_conjecture,[],[f6]) ).

fof(f6,conjecture,
    ! [X0,X1,X2] :
      ( ( subset(X2,X1)
        & subset(X0,X1) )
     => subset(union(X0,X2),X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.vdDlzrosGF/Vampire---4.8_24848',prove_union_subset) ).

fof(f130,plain,
    subset(union(sK0,sK2),sK1),
    inference(resolution,[],[f128,f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ~ member(sK4(X0,sK1),sK0)
      | subset(X0,sK1) ),
    inference(resolution,[],[f47,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ member(sK4(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK4(X0,X1),X1)
          & member(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f18,f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK4(X0,X1),X1)
        & member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.vdDlzrosGF/Vampire---4.8_24848',subset_defn) ).

fof(f47,plain,
    ! [X0] :
      ( member(X0,sK1)
      | ~ member(X0,sK0) ),
    inference(resolution,[],[f32,f23]) ).

fof(f23,plain,
    subset(sK0,sK1),
    inference(cnf_transformation,[],[f12]) ).

fof(f32,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ member(X3,X0)
      | member(X3,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f128,plain,
    member(sK4(union(sK0,sK2),sK1),sK0),
    inference(resolution,[],[f125,f25]) ).

fof(f125,plain,
    ( subset(union(sK0,sK2),sK1)
    | member(sK4(union(sK0,sK2),sK1),sK0) ),
    inference(resolution,[],[f55,f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ member(sK4(X0,sK1),sK2)
      | subset(X0,sK1) ),
    inference(resolution,[],[f48,f34]) ).

fof(f48,plain,
    ! [X1] :
      ( member(X1,sK1)
      | ~ member(X1,sK2) ),
    inference(resolution,[],[f32,f24]) ).

fof(f24,plain,
    subset(sK2,sK1),
    inference(cnf_transformation,[],[f12]) ).

fof(f55,plain,
    ( member(sK4(union(sK0,sK2),sK1),sK2)
    | member(sK4(union(sK0,sK2),sK1),sK0) ),
    inference(resolution,[],[f35,f40]) ).

fof(f40,plain,
    member(sK4(union(sK0,sK2),sK1),union(sK0,sK2)),
    inference(resolution,[],[f33,f25]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.vdDlzrosGF/Vampire---4.8_24848',union_defn) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET014+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36  % Computer : n026.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   : Sat Aug 26 12:41:33 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.vdDlzrosGF/Vampire---4.8_24848
% 0.16/0.37  % (24956)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43  % (24964)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_501 on Vampire---4 for (501ds/0Mi)
% 0.23/0.43  % (24957)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_1169 on Vampire---4 for (1169ds/0Mi)
% 0.23/0.43  % (24961)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.23/0.43  % (24958)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.23/0.43  % (24962)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.23/0.43  % (24960)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.23/0.43  % (24961)First to succeed.
% 0.23/0.44  % (24961)Refutation found. Thanks to Tanya!
% 0.23/0.44  % SZS status Theorem for Vampire---4
% 0.23/0.44  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.44  % (24961)------------------------------
% 0.23/0.44  % (24961)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.44  % (24961)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.44  % (24961)Termination reason: Refutation
% 0.23/0.44  
% 0.23/0.44  % (24961)Memory used [KB]: 1023
% 0.23/0.44  % (24961)Time elapsed: 0.007 s
% 0.23/0.44  % (24961)------------------------------
% 0.23/0.44  % (24961)------------------------------
% 0.23/0.44  % (24956)Success in time 0.064 s
% 0.23/0.44  % Vampire---4.8 exiting
%------------------------------------------------------------------------------