TSTP Solution File: SEU148+3 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% 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 : n008.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 17:56:03 EDT 2023

% Result   : Theorem 0.21s 0.42s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   30 (   8 unt;   0 def)
%            Number of atoms       :   97 (  60 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  109 (  42   ~;  41   |;  19   &)
%                                         (   3 <=>;   4  =>;   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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   46 (;  39   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f77,plain,
    $false,
    inference(trivial_inequality_removal,[],[f73]) ).

fof(f73,plain,
    sK0 != sK0,
    inference(backward_demodulation,[],[f27,f70]) ).

fof(f70,plain,
    sK0 = sK1,
    inference(trivial_inequality_removal,[],[f69]) ).

fof(f69,plain,
    ( empty_set != empty_set
    | sK0 = sK1 ),
    inference(superposition,[],[f29,f59]) ).

fof(f59,plain,
    ( empty_set = singleton(sK0)
    | sK0 = sK1 ),
    inference(resolution,[],[f57,f43]) ).

fof(f43,plain,
    ! [X3,X0] :
      ( ~ in(X3,singleton(X0))
      | X0 = X3 ),
    inference(equality_resolution,[],[f32]) ).

fof(f32,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK2(X0,X1) != X0
            | ~ in(sK2(X0,X1),X1) )
          & ( sK2(X0,X1) = X0
            | in(sK2(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK2(X0,X1) != X0
          | ~ in(sK2(X0,X1),X1) )
        & ( sK2(X0,X1) = X0
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,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,[],[f16]) ).

fof(f16,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,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.5daFV2TPrc/Vampire---4.8_1172',d1_tarski) ).

fof(f57,plain,
    ( in(sK1,singleton(sK0))
    | empty_set = singleton(sK0) ),
    inference(superposition,[],[f42,f51]) ).

fof(f51,plain,
    ( singleton(sK0) = singleton(sK1)
    | empty_set = singleton(sK0) ),
    inference(resolution,[],[f36,f26]) ).

fof(f26,plain,
    subset(singleton(sK0),singleton(sK1)),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( sK0 != sK1
    & subset(singleton(sK0),singleton(sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f14]) ).

fof(f14,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & subset(singleton(X0),singleton(X1)) )
   => ( sK0 != sK1
      & subset(singleton(sK0),singleton(sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ? [X0,X1] :
      ( X0 != X1
      & subset(singleton(X0),singleton(X1)) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(singleton(X0),singleton(X1))
       => X0 = X1 ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1] :
      ( subset(singleton(X0),singleton(X1))
     => X0 = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.5daFV2TPrc/Vampire---4.8_1172',t6_zfmisc_1) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ subset(X0,singleton(X1))
      | empty_set = X0
      | singleton(X1) = X0 ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( subset(X0,singleton(X1))
        | ( singleton(X1) != X0
          & empty_set != X0 ) )
      & ( singleton(X1) = X0
        | empty_set = X0
        | ~ subset(X0,singleton(X1)) ) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,singleton(X1))
        | ( singleton(X1) != X0
          & empty_set != X0 ) )
      & ( singleton(X1) = X0
        | empty_set = X0
        | ~ subset(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,singleton(X1))
    <=> ( singleton(X1) = X0
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.5daFV2TPrc/Vampire---4.8_1172',l4_zfmisc_1) ).

fof(f42,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f41]) ).

fof(f41,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f29,plain,
    ! [X0] : singleton(X0) != empty_set,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : singleton(X0) != empty_set,
    file('/export/starexec/sandbox2/tmp/tmp.5daFV2TPrc/Vampire---4.8_1172',l1_zfmisc_1) ).

fof(f27,plain,
    sK0 != sK1,
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 16:39:32 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.5daFV2TPrc/Vampire---4.8_1172
% 0.14/0.36  % (1331)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (1333)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)
% 0.21/0.42  % (1336)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)
% 0.21/0.42  % (1340)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)
% 0.21/0.42  % (1338)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)
% 0.21/0.42  % (1348)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)
% 0.21/0.42  % (1355)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.21/0.42  % (1348)Refutation not found, incomplete strategy% (1348)------------------------------
% 0.21/0.42  % (1348)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42  % (1356)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)
% 0.21/0.42  % (1348)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42  % (1348)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42  
% 0.21/0.42  % (1348)Memory used [KB]: 895
% 0.21/0.42  % (1348)Time elapsed: 0.003 s
% 0.21/0.42  % (1348)------------------------------
% 0.21/0.42  % (1348)------------------------------
% 0.21/0.42  % (1340)First to succeed.
% 0.21/0.42  % (1355)Also succeeded, but the first one will report.
% 0.21/0.42  % (1340)Refutation found. Thanks to Tanya!
% 0.21/0.42  % SZS status Theorem for Vampire---4
% 0.21/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.42  % (1340)------------------------------
% 0.21/0.42  % (1340)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42  % (1340)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42  % (1340)Termination reason: Refutation
% 0.21/0.42  
% 0.21/0.42  % (1340)Memory used [KB]: 895
% 0.21/0.42  % (1340)Time elapsed: 0.004 s
% 0.21/0.42  % (1340)------------------------------
% 0.21/0.42  % (1340)------------------------------
% 0.21/0.42  % (1331)Success in time 0.063 s
% 0.21/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------