TSTP Solution File: SEU106+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU106+1 : 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 : n013.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 17:55:44 EDT 2023

% Result   : Theorem 0.23s 0.48s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   46 (   9 unt;   0 def)
%            Number of atoms       :  170 (   6 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  211 (  87   ~;  72   |;  37   &)
%                                         (   3 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   1 con; 0-2 aty)
%            Number of variables   :   91 (;  82   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1781,plain,
    $false,
    inference(unit_resulting_resolution,[],[f123,f1780,f245]) ).

fof(f245,plain,
    ! [X4] :
      ( element(sK4(X4),X4)
      | preboolean(X4) ),
    inference(resolution,[],[f171,f147]) ).

fof(f147,plain,
    ! [X0] :
      ( in(sK4(X0),X0)
      | preboolean(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( ( preboolean(X0)
        | ( ( ~ in(set_difference(sK4(X0),sK5(X0)),X0)
            | ~ in(set_union2(sK4(X0),sK5(X0)),X0) )
          & in(sK5(X0),X0)
          & in(sK4(X0),X0) ) )
      & ( ! [X3,X4] :
            ( ( in(set_difference(X3,X4),X0)
              & in(set_union2(X3,X4),X0) )
            | ~ in(X4,X0)
            | ~ in(X3,X0) )
        | ~ preboolean(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f103,f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( ( ~ in(set_difference(X1,X2),X0)
            | ~ in(set_union2(X1,X2),X0) )
          & in(X2,X0)
          & in(X1,X0) )
     => ( ( ~ in(set_difference(sK4(X0),sK5(X0)),X0)
          | ~ in(set_union2(sK4(X0),sK5(X0)),X0) )
        & in(sK5(X0),X0)
        & in(sK4(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0] :
      ( ( preboolean(X0)
        | ? [X1,X2] :
            ( ( ~ in(set_difference(X1,X2),X0)
              | ~ in(set_union2(X1,X2),X0) )
            & in(X2,X0)
            & in(X1,X0) ) )
      & ( ! [X3,X4] :
            ( ( in(set_difference(X3,X4),X0)
              & in(set_union2(X3,X4),X0) )
            | ~ in(X4,X0)
            | ~ in(X3,X0) )
        | ~ preboolean(X0) ) ),
    inference(rectify,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ( preboolean(X0)
        | ? [X1,X2] :
            ( ( ~ in(set_difference(X1,X2),X0)
              | ~ in(set_union2(X1,X2),X0) )
            & in(X2,X0)
            & in(X1,X0) ) )
      & ( ! [X1,X2] :
            ( ( in(set_difference(X1,X2),X0)
              & in(set_union2(X1,X2),X0) )
            | ~ in(X2,X0)
            | ~ in(X1,X0) )
        | ~ preboolean(X0) ) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( preboolean(X0)
    <=> ! [X1,X2] :
          ( ( in(set_difference(X1,X2),X0)
            & in(set_union2(X1,X2),X0) )
          | ~ in(X2,X0)
          | ~ in(X1,X0) ) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( preboolean(X0)
    <=> ! [X1,X2] :
          ( ( in(set_difference(X1,X2),X0)
            & in(set_union2(X1,X2),X0) )
          | ~ in(X2,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0] :
      ( preboolean(X0)
    <=> ! [X1,X2] :
          ( ( in(X2,X0)
            & in(X1,X0) )
         => ( in(set_difference(X1,X2),X0)
            & in(set_union2(X1,X2),X0) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t10_finsub_1) ).

fof(f171,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | element(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t1_subset) ).

fof(f1780,plain,
    ~ element(sK4(sK0),sK0),
    inference(subsumption_resolution,[],[f1778,f123]) ).

fof(f1778,plain,
    ( ~ element(sK4(sK0),sK0)
    | preboolean(sK0) ),
    inference(resolution,[],[f1772,f246]) ).

fof(f246,plain,
    ! [X5] :
      ( element(sK5(X5),X5)
      | preboolean(X5) ),
    inference(resolution,[],[f171,f148]) ).

fof(f148,plain,
    ! [X0] :
      ( in(sK5(X0),X0)
      | preboolean(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f1772,plain,
    ( ~ element(sK5(sK0),sK0)
    | ~ element(sK4(sK0),sK0) ),
    inference(subsumption_resolution,[],[f1771,f122]) ).

fof(f122,plain,
    ! [X2,X1] :
      ( in(set_union2(X1,X2),sK0)
      | ~ element(X2,sK0)
      | ~ element(X1,sK0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ( ~ preboolean(sK0)
    & ! [X1] :
        ( ! [X2] :
            ( ( in(set_union2(X1,X2),sK0)
              & in(symmetric_difference(X1,X2),sK0) )
            | ~ element(X2,sK0) )
        | ~ element(X1,sK0) )
    & ~ empty(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f63,f94]) ).

fof(f94,plain,
    ( ? [X0] :
        ( ~ preboolean(X0)
        & ! [X1] :
            ( ! [X2] :
                ( ( in(set_union2(X1,X2),X0)
                  & in(symmetric_difference(X1,X2),X0) )
                | ~ element(X2,X0) )
            | ~ element(X1,X0) )
        & ~ empty(X0) )
   => ( ~ preboolean(sK0)
      & ! [X1] :
          ( ! [X2] :
              ( ( in(set_union2(X1,X2),sK0)
                & in(symmetric_difference(X1,X2),sK0) )
              | ~ element(X2,sK0) )
          | ~ element(X1,sK0) )
      & ~ empty(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ? [X0] :
      ( ~ preboolean(X0)
      & ! [X1] :
          ( ! [X2] :
              ( ( in(set_union2(X1,X2),X0)
                & in(symmetric_difference(X1,X2),X0) )
              | ~ element(X2,X0) )
          | ~ element(X1,X0) )
      & ~ empty(X0) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ? [X0] :
      ( ~ preboolean(X0)
      & ! [X1] :
          ( ! [X2] :
              ( ( in(set_union2(X1,X2),X0)
                & in(symmetric_difference(X1,X2),X0) )
              | ~ element(X2,X0) )
          | ~ element(X1,X0) )
      & ~ empty(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,negated_conjecture,
    ~ ! [X0] :
        ( ~ empty(X0)
       => ( ! [X1] :
              ( element(X1,X0)
             => ! [X2] :
                  ( element(X2,X0)
                 => ( in(set_union2(X1,X2),X0)
                    & in(symmetric_difference(X1,X2),X0) ) ) )
         => preboolean(X0) ) ),
    inference(negated_conjecture,[],[f34]) ).

fof(f34,conjecture,
    ! [X0] :
      ( ~ empty(X0)
     => ( ! [X1] :
            ( element(X1,X0)
           => ! [X2] :
                ( element(X2,X0)
               => ( in(set_union2(X1,X2),X0)
                  & in(symmetric_difference(X1,X2),X0) ) ) )
       => preboolean(X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t17_finsub_1) ).

fof(f1771,plain,
    ( ~ in(set_union2(sK4(sK0),sK5(sK0)),sK0)
    | ~ element(sK4(sK0),sK0)
    | ~ element(sK5(sK0),sK0) ),
    inference(subsumption_resolution,[],[f1762,f123]) ).

fof(f1762,plain,
    ( preboolean(sK0)
    | ~ in(set_union2(sK4(sK0),sK5(sK0)),sK0)
    | ~ element(sK4(sK0),sK0)
    | ~ element(sK5(sK0),sK0) ),
    inference(resolution,[],[f149,f871]) ).

fof(f871,plain,
    ! [X4,X5] :
      ( in(set_difference(X5,X4),sK0)
      | ~ element(X5,sK0)
      | ~ element(X4,sK0) ),
    inference(duplicate_literal_removal,[],[f853]) ).

fof(f853,plain,
    ! [X4,X5] :
      ( ~ element(X4,sK0)
      | ~ element(X5,sK0)
      | in(set_difference(X5,X4),sK0)
      | ~ element(X5,sK0) ),
    inference(resolution,[],[f839,f516]) ).

fof(f516,plain,
    ! [X6,X7] :
      ( ~ element(set_intersection2(X7,X6),sK0)
      | in(set_difference(X6,X7),sK0)
      | ~ element(X6,sK0) ),
    inference(superposition,[],[f492,f159]) ).

fof(f159,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',commutativity_k3_xboole_0) ).

fof(f492,plain,
    ! [X0,X1] :
      ( ~ element(set_intersection2(X0,X1),sK0)
      | in(set_difference(X0,X1),sK0)
      | ~ element(X0,sK0) ),
    inference(superposition,[],[f121,f162]) ).

fof(f162,plain,
    ! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
    file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t100_xboole_1) ).

fof(f121,plain,
    ! [X2,X1] :
      ( in(symmetric_difference(X1,X2),sK0)
      | ~ element(X2,sK0)
      | ~ element(X1,sK0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f839,plain,
    ! [X0,X1] :
      ( element(set_intersection2(X1,X0),sK0)
      | ~ element(X1,sK0)
      | ~ element(X0,sK0) ),
    inference(resolution,[],[f735,f171]) ).

fof(f735,plain,
    ! [X0,X1] :
      ( in(set_intersection2(X0,X1),sK0)
      | ~ element(X1,sK0)
      | ~ element(X0,sK0) ),
    inference(subsumption_resolution,[],[f725,f243]) ).

fof(f243,plain,
    ! [X2,X3] :
      ( element(set_union2(X2,X3),sK0)
      | ~ element(X3,sK0)
      | ~ element(X2,sK0) ),
    inference(resolution,[],[f171,f122]) ).

fof(f725,plain,
    ! [X0,X1] :
      ( ~ element(set_union2(X0,X1),sK0)
      | in(set_intersection2(X0,X1),sK0)
      | ~ element(X1,sK0)
      | ~ element(X0,sK0) ),
    inference(resolution,[],[f703,f242]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( element(symmetric_difference(X0,X1),sK0)
      | ~ element(X1,sK0)
      | ~ element(X0,sK0) ),
    inference(resolution,[],[f171,f121]) ).

fof(f703,plain,
    ! [X0,X1] :
      ( ~ element(symmetric_difference(X0,X1),sK0)
      | ~ element(set_union2(X0,X1),sK0)
      | in(set_intersection2(X0,X1),sK0) ),
    inference(superposition,[],[f121,f163]) ).

fof(f163,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
    file('/export/starexec/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960',t95_xboole_1) ).

fof(f149,plain,
    ! [X0] :
      ( ~ in(set_difference(sK4(X0),sK5(X0)),X0)
      | preboolean(X0)
      | ~ in(set_union2(sK4(X0),sK5(X0)),X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f123,plain,
    ~ preboolean(sK0),
    inference(cnf_transformation,[],[f95]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU106+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37  % Computer : n013.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Thu Aug 24 01:01:47 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/sandbox/tmp/tmp.qpuYB6MTa8/Vampire---4.8_18960
% 0.16/0.37  % (19267)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43  % (19274)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)
% 0.23/0.43  % (19272)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)
% 0.23/0.43  % (19273)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  % (19268)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)
% 0.23/0.44  % (19271)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)
% 0.23/0.44  % (19270)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)
% 0.23/0.48  % (19269)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)
% 0.23/0.48  % (19272)First to succeed.
% 0.23/0.48  % (19272)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  % (19272)------------------------------
% 0.23/0.48  % (19272)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.48  % (19272)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.48  % (19272)Termination reason: Refutation
% 0.23/0.48  
% 0.23/0.48  % (19272)Memory used [KB]: 1535
% 0.23/0.48  % (19272)Time elapsed: 0.048 s
% 0.23/0.48  % (19272)------------------------------
% 0.23/0.48  % (19272)------------------------------
% 0.23/0.48  % (19267)Success in time 0.109 s
% 0.23/0.49  % Vampire---4.8 exiting
%------------------------------------------------------------------------------