TSTP Solution File: GEO117+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : GEO117+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n015.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 : Wed Aug 30 23:31:00 EDT 2023

% Result   : Theorem 0.23s 0.45s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   33 (  10 unt;   0 def)
%            Number of atoms       :  181 (  11 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  225 (  77   ~;  70   |;  66   &)
%                                         (   8 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-4 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-4 aty)
%            Number of variables   :  129 (; 111   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f291,plain,
    $false,
    inference(subsumption_resolution,[],[f281,f150]) ).

fof(f150,plain,
    ordered_by(sK0,sK1,sK1),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ordered_by(sK0,sK1,sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f57,f82]) ).

fof(f82,plain,
    ( ? [X0,X1] : ordered_by(X0,X1,X1)
   => ordered_by(sK0,sK1,sK1) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ? [X0,X1] : ordered_by(X0,X1,X1),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,plain,
    ~ ! [X0,X1] : ~ ordered_by(X0,X1,X1),
    inference(rectify,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X8,X2] : ~ ordered_by(X8,X2,X2),
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X8,X2] : ~ ordered_by(X8,X2,X2),
    file('/export/starexec/sandbox2/tmp/tmp.doJcAH4ql5/Vampire---4.8_17153',theorem_4_4) ).

fof(f281,plain,
    ~ ordered_by(sK0,sK1,sK1),
    inference(resolution,[],[f279,f150]) ).

fof(f279,plain,
    ! [X2,X0,X1] :
      ( ~ ordered_by(X0,X1,X2)
      | ~ ordered_by(X0,X2,X1) ),
    inference(resolution,[],[f277,f221]) ).

fof(f221,plain,
    ! [X2,X3,X0,X1] :
      ( between_o(X0,X1,X2,X3)
      | ~ ordered_by(X0,X2,X1)
      | ~ ordered_by(X0,X3,X2) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_o(X0,X1,X2,X3)
        | ( ( ~ ordered_by(X0,X2,X1)
            | ~ ordered_by(X0,X3,X2) )
          & ( ~ ordered_by(X0,X2,X3)
            | ~ ordered_by(X0,X1,X2) ) ) )
      & ( ( ordered_by(X0,X2,X1)
          & ordered_by(X0,X3,X2) )
        | ( ordered_by(X0,X2,X3)
          & ordered_by(X0,X1,X2) )
        | ~ between_o(X0,X1,X2,X3) ) ),
    inference(flattening,[],[f143]) ).

fof(f143,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_o(X0,X1,X2,X3)
        | ( ( ~ ordered_by(X0,X2,X1)
            | ~ ordered_by(X0,X3,X2) )
          & ( ~ ordered_by(X0,X2,X3)
            | ~ ordered_by(X0,X1,X2) ) ) )
      & ( ( ordered_by(X0,X2,X1)
          & ordered_by(X0,X3,X2) )
        | ( ordered_by(X0,X2,X3)
          & ordered_by(X0,X1,X2) )
        | ~ between_o(X0,X1,X2,X3) ) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X2,X3] :
      ( between_o(X0,X1,X2,X3)
    <=> ( ( ordered_by(X0,X2,X1)
          & ordered_by(X0,X3,X2) )
        | ( ordered_by(X0,X2,X3)
          & ordered_by(X0,X1,X2) ) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X8,X2,X4,X6] :
      ( between_o(X8,X2,X4,X6)
    <=> ( ( ordered_by(X8,X4,X2)
          & ordered_by(X8,X6,X4) )
        | ( ordered_by(X8,X4,X6)
          & ordered_by(X8,X2,X4) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.doJcAH4ql5/Vampire---4.8_17153',between_o_defn) ).

fof(f277,plain,
    ! [X2,X0,X1] : ~ between_o(X0,X1,X2,X1),
    inference(resolution,[],[f224,f233]) ).

fof(f233,plain,
    ! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
    inference(equality_resolution,[],[f210]) ).

fof(f210,plain,
    ! [X2,X3,X0,X1] :
      ( X1 != X3
      | ~ between_c(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_c(X0,X1,X2,X3)
        | ! [X4] :
            ( ~ inner_point(X2,X4)
            | ~ end_point(X3,X4)
            | ~ end_point(X1,X4)
            | ~ part_of(X4,X0) )
        | X1 = X3 )
      & ( ( inner_point(X2,sK21(X0,X1,X2,X3))
          & end_point(X3,sK21(X0,X1,X2,X3))
          & end_point(X1,sK21(X0,X1,X2,X3))
          & part_of(sK21(X0,X1,X2,X3),X0)
          & X1 != X3 )
        | ~ between_c(X0,X1,X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f140,f141]) ).

fof(f141,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X5] :
          ( inner_point(X2,X5)
          & end_point(X3,X5)
          & end_point(X1,X5)
          & part_of(X5,X0) )
     => ( inner_point(X2,sK21(X0,X1,X2,X3))
        & end_point(X3,sK21(X0,X1,X2,X3))
        & end_point(X1,sK21(X0,X1,X2,X3))
        & part_of(sK21(X0,X1,X2,X3),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f140,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_c(X0,X1,X2,X3)
        | ! [X4] :
            ( ~ inner_point(X2,X4)
            | ~ end_point(X3,X4)
            | ~ end_point(X1,X4)
            | ~ part_of(X4,X0) )
        | X1 = X3 )
      & ( ( ? [X5] :
              ( inner_point(X2,X5)
              & end_point(X3,X5)
              & end_point(X1,X5)
              & part_of(X5,X0) )
          & X1 != X3 )
        | ~ between_c(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f139]) ).

fof(f139,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_c(X0,X1,X2,X3)
        | ! [X4] :
            ( ~ inner_point(X2,X4)
            | ~ end_point(X3,X4)
            | ~ end_point(X1,X4)
            | ~ part_of(X4,X0) )
        | X1 = X3 )
      & ( ( ? [X4] :
              ( inner_point(X2,X4)
              & end_point(X3,X4)
              & end_point(X1,X4)
              & part_of(X4,X0) )
          & X1 != X3 )
        | ~ between_c(X0,X1,X2,X3) ) ),
    inference(flattening,[],[f138]) ).

fof(f138,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_c(X0,X1,X2,X3)
        | ! [X4] :
            ( ~ inner_point(X2,X4)
            | ~ end_point(X3,X4)
            | ~ end_point(X1,X4)
            | ~ part_of(X4,X0) )
        | X1 = X3 )
      & ( ( ? [X4] :
              ( inner_point(X2,X4)
              & end_point(X3,X4)
              & end_point(X1,X4)
              & part_of(X4,X0) )
          & X1 != X3 )
        | ~ between_c(X0,X1,X2,X3) ) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3] :
      ( between_c(X0,X1,X2,X3)
    <=> ( ? [X4] :
            ( inner_point(X2,X4)
            & end_point(X3,X4)
            & end_point(X1,X4)
            & part_of(X4,X0) )
        & X1 != X3 ) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X2,X4,X6] :
      ( between_c(X0,X2,X4,X6)
    <=> ( ? [X7] :
            ( inner_point(X4,X7)
            & end_point(X6,X7)
            & end_point(X2,X7)
            & part_of(X7,X0) )
        & X2 != X6 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.doJcAH4ql5/Vampire---4.8_17153',between_c_defn) ).

fof(f224,plain,
    ! [X2,X3,X0,X1] :
      ( between_c(sK23(X0,X1,X2,X3),X0,X1,X2)
      | ~ between_o(X3,X0,X1,X2) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_o(X3,X0,X1,X2)
        | ! [X4] :
            ( ~ between_c(X4,X0,X1,X2)
            | ( ( ~ incident_c(sK22(X3,X4),X4)
                | ~ incident_o(sK22(X3,X4),X3) )
              & ( incident_c(sK22(X3,X4),X4)
                | incident_o(sK22(X3,X4),X3) ) ) ) )
      & ( ( between_c(sK23(X0,X1,X2,X3),X0,X1,X2)
          & ! [X7] :
              ( ( incident_o(X7,X3)
                | ~ incident_c(X7,sK23(X0,X1,X2,X3)) )
              & ( incident_c(X7,sK23(X0,X1,X2,X3))
                | ~ incident_o(X7,X3) ) ) )
        | ~ between_o(X3,X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f146,f148,f147]) ).

fof(f147,plain,
    ! [X3,X4] :
      ( ? [X5] :
          ( ( ~ incident_c(X5,X4)
            | ~ incident_o(X5,X3) )
          & ( incident_c(X5,X4)
            | incident_o(X5,X3) ) )
     => ( ( ~ incident_c(sK22(X3,X4),X4)
          | ~ incident_o(sK22(X3,X4),X3) )
        & ( incident_c(sK22(X3,X4),X4)
          | incident_o(sK22(X3,X4),X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f148,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X6] :
          ( between_c(X6,X0,X1,X2)
          & ! [X7] :
              ( ( incident_o(X7,X3)
                | ~ incident_c(X7,X6) )
              & ( incident_c(X7,X6)
                | ~ incident_o(X7,X3) ) ) )
     => ( between_c(sK23(X0,X1,X2,X3),X0,X1,X2)
        & ! [X7] :
            ( ( incident_o(X7,X3)
              | ~ incident_c(X7,sK23(X0,X1,X2,X3)) )
            & ( incident_c(X7,sK23(X0,X1,X2,X3))
              | ~ incident_o(X7,X3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_o(X3,X0,X1,X2)
        | ! [X4] :
            ( ~ between_c(X4,X0,X1,X2)
            | ? [X5] :
                ( ( ~ incident_c(X5,X4)
                  | ~ incident_o(X5,X3) )
                & ( incident_c(X5,X4)
                  | incident_o(X5,X3) ) ) ) )
      & ( ? [X6] :
            ( between_c(X6,X0,X1,X2)
            & ! [X7] :
                ( ( incident_o(X7,X3)
                  | ~ incident_c(X7,X6) )
                & ( incident_c(X7,X6)
                  | ~ incident_o(X7,X3) ) ) )
        | ~ between_o(X3,X0,X1,X2) ) ),
    inference(rectify,[],[f145]) ).

fof(f145,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_o(X3,X0,X1,X2)
        | ! [X4] :
            ( ~ between_c(X4,X0,X1,X2)
            | ? [X5] :
                ( ( ~ incident_c(X5,X4)
                  | ~ incident_o(X5,X3) )
                & ( incident_c(X5,X4)
                  | incident_o(X5,X3) ) ) ) )
      & ( ? [X4] :
            ( between_c(X4,X0,X1,X2)
            & ! [X5] :
                ( ( incident_o(X5,X3)
                  | ~ incident_c(X5,X4) )
                & ( incident_c(X5,X4)
                  | ~ incident_o(X5,X3) ) ) )
        | ~ between_o(X3,X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1,X2,X3] :
      ( between_o(X3,X0,X1,X2)
    <=> ? [X4] :
          ( between_c(X4,X0,X1,X2)
          & ! [X5] :
              ( incident_o(X5,X3)
            <=> incident_c(X5,X4) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X2,X4,X6,X8] :
      ( between_o(X8,X2,X4,X6)
    <=> ? [X0] :
          ( between_c(X0,X2,X4,X6)
          & ! [X2] :
              ( incident_o(X2,X8)
            <=> incident_c(X2,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.doJcAH4ql5/Vampire---4.8_17153',o3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : GEO117+1 : TPTP v8.1.2. Released v2.4.0.
% 0.15/0.16  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37  % Computer : n015.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   : Tue Aug 29 23:41:27 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.22/0.38  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.doJcAH4ql5/Vampire---4.8_17153
% 0.22/0.38  % (17627)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (17630)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)
% 0.23/0.44  % (17633)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)
% 0.23/0.44  % (17631)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)
% 0.23/0.44  % (17629)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  % (17635)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  % (17632)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  % (17634)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.23/0.45  % (17632)Refutation not found, incomplete strategy% (17632)------------------------------
% 0.23/0.45  % (17632)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.45  % (17632)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.45  % (17632)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.45  
% 0.23/0.45  % (17634)First to succeed.
% 0.23/0.45  % (17632)Memory used [KB]: 10234
% 0.23/0.45  % (17632)Time elapsed: 0.009 s
% 0.23/0.45  % (17632)------------------------------
% 0.23/0.45  % (17632)------------------------------
% 0.23/0.45  % (17634)Refutation found. Thanks to Tanya!
% 0.23/0.45  % SZS status Theorem for Vampire---4
% 0.23/0.45  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.45  % (17634)------------------------------
% 0.23/0.45  % (17634)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.45  % (17634)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.45  % (17634)Termination reason: Refutation
% 0.23/0.45  
% 0.23/0.45  % (17634)Memory used [KB]: 5628
% 0.23/0.45  % (17634)Time elapsed: 0.009 s
% 0.23/0.45  % (17634)------------------------------
% 0.23/0.45  % (17634)------------------------------
% 0.23/0.45  % (17627)Success in time 0.068 s
% 0.23/0.45  % Vampire---4.8 exiting
%------------------------------------------------------------------------------