TSTP Solution File: NUM501+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% 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 : n012.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 12:10:13 EDT 2023

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   59 (  17 unt;   0 def)
%            Number of atoms       :  230 (  59 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  278 ( 107   ~;  91   |;  68   &)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :   80 (;  65   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4223,plain,
    $false,
    inference(subsumption_resolution,[],[f4222,f184]) ).

fof(f184,plain,
    aNaturalNumber0(xk),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,axiom,
    ( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & aNaturalNumber0(xk) ),
    file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',m__2306) ).

fof(f4222,plain,
    ~ aNaturalNumber0(xk),
    inference(subsumption_resolution,[],[f4221,f198]) ).

fof(f198,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ( aNaturalNumber0(xp)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',m__1837) ).

fof(f4221,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xk) ),
    inference(subsumption_resolution,[],[f4189,f1275]) ).

fof(f1275,plain,
    ~ doDivides0(xk,sF18),
    inference(subsumption_resolution,[],[f1268,f184]) ).

fof(f1268,plain,
    ( ~ doDivides0(xk,sF18)
    | ~ aNaturalNumber0(xk) ),
    inference(resolution,[],[f1240,f190]) ).

fof(f190,plain,
    doDivides0(xr,xk),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( xr = X0
        | sz10 = X0
        | ( ~ doDivides0(X0,xr)
          & ! [X1] :
              ( sdtasdt0(X0,X1) != xr
              | ~ aNaturalNumber0(X1) ) )
        | ~ aNaturalNumber0(X0) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & xk = sdtasdt0(xr,sK6)
    & aNaturalNumber0(sK6)
    & aNaturalNumber0(xr) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f59,f139]) ).

fof(f139,plain,
    ( ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
   => ( xk = sdtasdt0(xr,sK6)
      & aNaturalNumber0(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( xr = X0
        | sz10 = X0
        | ( ~ doDivides0(X0,xr)
          & ! [X1] :
              ( sdtasdt0(X0,X1) != xr
              | ~ aNaturalNumber0(X1) ) )
        | ~ aNaturalNumber0(X0) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
    & aNaturalNumber0(xr) ),
    inference(flattening,[],[f58]) ).

fof(f58,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( xr = X0
        | sz10 = X0
        | ( ~ doDivides0(X0,xr)
          & ! [X1] :
              ( sdtasdt0(X0,X1) != xr
              | ~ aNaturalNumber0(X1) ) )
        | ~ aNaturalNumber0(X0) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
    & aNaturalNumber0(xr) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( ( ( doDivides0(X0,xr)
            | ? [X1] :
                ( sdtasdt0(X0,X1) = xr
                & aNaturalNumber0(X1) ) )
          & aNaturalNumber0(X0) )
       => ( xr = X0
          | sz10 = X0 ) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
    & aNaturalNumber0(xr) ),
    inference(rectify,[],[f48]) ).

fof(f48,axiom,
    ( isPrime0(xr)
    & ! [X0] :
        ( ( ( doDivides0(X0,xr)
            | ? [X1] :
                ( sdtasdt0(X0,X1) = xr
                & aNaturalNumber0(X1) ) )
          & aNaturalNumber0(X0) )
       => ( xr = X0
          | sz10 = X0 ) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X0] :
        ( xk = sdtasdt0(xr,X0)
        & aNaturalNumber0(X0) )
    & aNaturalNumber0(xr) ),
    file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',m__2342) ).

fof(f1240,plain,
    ! [X0] :
      ( ~ doDivides0(xr,X0)
      | ~ doDivides0(X0,sF18)
      | ~ aNaturalNumber0(X0) ),
    inference(subsumption_resolution,[],[f1239,f187]) ).

fof(f187,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[],[f140]) ).

fof(f1239,plain,
    ! [X0] :
      ( ~ doDivides0(X0,sF18)
      | ~ doDivides0(xr,X0)
      | ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(xr) ),
    inference(subsumption_resolution,[],[f1232,f371]) ).

fof(f371,plain,
    aNaturalNumber0(sF18),
    inference(subsumption_resolution,[],[f370,f196]) ).

fof(f196,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f39]) ).

fof(f370,plain,
    ( aNaturalNumber0(sF18)
    | ~ aNaturalNumber0(xn) ),
    inference(subsumption_resolution,[],[f362,f197]) ).

fof(f197,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f39]) ).

fof(f362,plain,
    ( aNaturalNumber0(sF18)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[],[f268,f323]) ).

fof(f323,plain,
    sdtasdt0(xn,xm) = sF18,
    introduced(function_definition,[]) ).

fof(f268,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',mSortsB_02) ).

fof(f1232,plain,
    ! [X0] :
      ( ~ doDivides0(X0,sF18)
      | ~ doDivides0(xr,X0)
      | ~ aNaturalNumber0(sF18)
      | ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(xr) ),
    inference(resolution,[],[f305,f324]) ).

fof(f324,plain,
    ~ doDivides0(xr,sF18),
    inference(definition_folding,[],[f183,f323]) ).

fof(f183,plain,
    ~ doDivides0(xr,sdtasdt0(xn,xm)),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ( ~ doDivides0(xr,sdtasdt0(xn,xm))
    & ! [X0] :
        ( sdtasdt0(xn,xm) != sdtasdt0(xr,X0)
        | ~ aNaturalNumber0(X0) ) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,negated_conjecture,
    ~ ( doDivides0(xr,sdtasdt0(xn,xm))
      | ? [X0] :
          ( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
          & aNaturalNumber0(X0) ) ),
    inference(negated_conjecture,[],[f49]) ).

fof(f49,conjecture,
    ( doDivides0(xr,sdtasdt0(xn,xm))
    | ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
        & aNaturalNumber0(X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',m__) ).

fof(f305,plain,
    ! [X2,X0,X1] :
      ( doDivides0(X0,X2)
      | ~ doDivides0(X1,X2)
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( doDivides0(X0,X2)
      | ~ doDivides0(X1,X2)
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1,X2] :
      ( doDivides0(X0,X2)
      | ~ doDivides0(X1,X2)
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( doDivides0(X1,X2)
          & doDivides0(X0,X1) )
       => doDivides0(X0,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',mDivTrans) ).

fof(f4189,plain,
    ( doDivides0(xk,sF18)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xk) ),
    inference(superposition,[],[f333,f4169]) ).

fof(f4169,plain,
    sF18 = sdtasdt0(xk,xp),
    inference(forward_demodulation,[],[f4151,f328]) ).

fof(f328,plain,
    sdtasdt0(xp,xk) = sF18,
    inference(forward_demodulation,[],[f185,f323]) ).

fof(f185,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(cnf_transformation,[],[f45]) ).

fof(f4151,plain,
    sdtasdt0(xp,xk) = sdtasdt0(xk,xp),
    inference(resolution,[],[f452,f184]) ).

fof(f452,plain,
    ! [X10] :
      ( ~ aNaturalNumber0(X10)
      | sdtasdt0(X10,xp) = sdtasdt0(xp,X10) ),
    inference(resolution,[],[f270,f198]) ).

fof(f270,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',mMulComm) ).

fof(f333,plain,
    ! [X2,X0] :
      ( doDivides0(X0,sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X0) ),
    inference(subsumption_resolution,[],[f321,f268]) ).

fof(f321,plain,
    ! [X2,X0] :
      ( doDivides0(X0,sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f293]) ).

fof(f293,plain,
    ! [X2,X0,X1] :
      ( doDivides0(X0,X1)
      | sdtasdt0(X0,X2) != X1
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f177]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ( sdtasdt0(X0,sK16(X0,X1)) = X1
            & aNaturalNumber0(sK16(X0,X1)) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f175,f176]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtasdt0(X0,X3) = X1
          & aNaturalNumber0(X3) )
     => ( sdtasdt0(X0,sK16(X0,X1)) = X1
        & aNaturalNumber0(sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X3] :
              ( sdtasdt0(X0,X3) = X1
              & aNaturalNumber0(X3) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f174]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X2] :
              ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582',mDefDiv) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Aug 25 17:43:26 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.35  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.MXu6MQPhDx/Vampire---4.8_12582
% 0.13/0.35  % (12713)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41  % (12716)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.21/0.41  % (12718)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.41  % (12717)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.21/0.41  % (12719)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.21/0.41  % (12720)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.21/0.41  % (12714)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.21/0.41  % (12715)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.21/0.53  % (12717)First to succeed.
% 0.21/0.53  % (12717)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for Vampire---4
% 0.21/0.53  % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.53  % (12717)------------------------------
% 0.21/0.53  % (12717)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.53  % (12717)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.53  % (12717)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (12717)Memory used [KB]: 7931
% 0.21/0.53  % (12717)Time elapsed: 0.123 s
% 0.21/0.53  % (12717)------------------------------
% 0.21/0.53  % (12717)------------------------------
% 0.21/0.53  % (12713)Success in time 0.183 s
% 0.21/0.53  % Vampire---4.8 exiting
%------------------------------------------------------------------------------