TSTP Solution File: NUM469+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM469+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n029.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 31 17:59:49 EDT 2022

% Result   : Theorem 1.36s 0.54s
% Output   : Refutation 1.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   69 (  10 unt;   0 def)
%            Number of atoms       :  173 (  49 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  165 (  61   ~;  56   |;  36   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   26 (  18   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f328,plain,
    $false,
    inference(avatar_sat_refutation,[],[f156,f171,f176,f224,f323,f327]) ).

fof(f327,plain,
    ( ~ spl3_1
    | ~ spl3_6
    | spl3_9 ),
    inference(avatar_contradiction_clause,[],[f326]) ).

fof(f326,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_6
    | spl3_9 ),
    inference(subsumption_resolution,[],[f325,f151]) ).

fof(f151,plain,
    ( aNaturalNumber0(sdtsldt0(xn,xl))
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f149]) ).

fof(f149,plain,
    ( spl3_1
  <=> aNaturalNumber0(sdtsldt0(xn,xl)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f325,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xn,xl))
    | ~ spl3_6
    | spl3_9 ),
    inference(subsumption_resolution,[],[f324,f175]) ).

fof(f175,plain,
    ( aNaturalNumber0(sdtsldt0(xm,xl))
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f173]) ).

fof(f173,plain,
    ( spl3_6
  <=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f324,plain,
    ( ~ aNaturalNumber0(sdtsldt0(xm,xl))
    | ~ aNaturalNumber0(sdtsldt0(xn,xl))
    | spl3_9 ),
    inference(resolution,[],[f317,f118]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X1,X0))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | aNaturalNumber0(sdtpldt0(X1,X0)) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X1,X0] :
      ( aNaturalNumber0(sdtpldt0(X1,X0))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X1,X0] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtpldt0(X1,X0)) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( ( aNaturalNumber0(X0)
        & aNaturalNumber0(X1) )
     => aNaturalNumber0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

fof(f317,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | spl3_9 ),
    inference(avatar_component_clause,[],[f315]) ).

fof(f315,plain,
    ( spl3_9
  <=> aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f323,plain,
    ( ~ spl3_9
    | ~ spl3_5 ),
    inference(avatar_split_clause,[],[f312,f168,f315]) ).

fof(f168,plain,
    ( spl3_5
  <=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f312,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | ~ spl3_5 ),
    inference(trivial_inequality_removal,[],[f310]) ).

fof(f310,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
    | ~ spl3_5 ),
    inference(superposition,[],[f133,f170]) ).

fof(f170,plain,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f168]) ).

fof(f133,plain,
    ! [X0] :
      ( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ( ~ doDivides0(xl,sdtpldt0(xm,xn))
    & ! [X0] :
        ( ~ aNaturalNumber0(X0)
        | sdtasdt0(xl,X0) != sdtpldt0(xm,xn) ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ( doDivides0(xl,sdtpldt0(xm,xn))
      | ? [X0] :
          ( aNaturalNumber0(X0)
          & sdtasdt0(xl,X0) = sdtpldt0(xm,xn) ) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ( doDivides0(xl,sdtpldt0(xm,xn))
    | ? [X0] :
        ( aNaturalNumber0(X0)
        & sdtasdt0(xl,X0) = sdtpldt0(xm,xn) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f224,plain,
    ~ spl3_2,
    inference(avatar_contradiction_clause,[],[f223]) ).

fof(f223,plain,
    ( $false
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f222,f204]) ).

fof(f204,plain,
    ( doDivides0(sz00,sz00)
    | ~ spl3_2 ),
    inference(backward_demodulation,[],[f178,f190]) ).

fof(f190,plain,
    ( sz00 = xn
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f184,f112]) ).

fof(f112,plain,
    aNaturalNumber0(sK2),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ( doDivides0(xl,xm)
    & doDivides0(xl,xn)
    & xm = sdtasdt0(xl,sK1)
    & aNaturalNumber0(sK1)
    & xn = sdtasdt0(xl,sK2)
    & aNaturalNumber0(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f38,f89,f88]) ).

fof(f88,plain,
    ( ? [X0] :
        ( xm = sdtasdt0(xl,X0)
        & aNaturalNumber0(X0) )
   => ( xm = sdtasdt0(xl,sK1)
      & aNaturalNumber0(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ( ? [X1] :
        ( xn = sdtasdt0(xl,X1)
        & aNaturalNumber0(X1) )
   => ( xn = sdtasdt0(xl,sK2)
      & aNaturalNumber0(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ( doDivides0(xl,xm)
    & doDivides0(xl,xn)
    & ? [X0] :
        ( xm = sdtasdt0(xl,X0)
        & aNaturalNumber0(X0) )
    & ? [X1] :
        ( xn = sdtasdt0(xl,X1)
        & aNaturalNumber0(X1) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,axiom,
    ( ? [X0] :
        ( xm = sdtasdt0(xl,X0)
        & aNaturalNumber0(X0) )
    & doDivides0(xl,xm)
    & doDivides0(xl,xn)
    & ? [X0] :
        ( xn = sdtasdt0(xl,X0)
        & aNaturalNumber0(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240_04) ).

fof(f184,plain,
    ( ~ aNaturalNumber0(sK2)
    | sz00 = xn
    | ~ spl3_2 ),
    inference(superposition,[],[f132,f182]) ).

fof(f182,plain,
    ( xn = sdtasdt0(sz00,sK2)
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f113,f155]) ).

fof(f155,plain,
    ( sz00 = xl
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f153]) ).

fof(f153,plain,
    ( spl3_2
  <=> sz00 = xl ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f113,plain,
    xn = sdtasdt0(xl,sK2),
    inference(cnf_transformation,[],[f90]) ).

fof(f132,plain,
    ! [X0] :
      ( sz00 = sdtasdt0(sz00,X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).

fof(f178,plain,
    ( doDivides0(sz00,xn)
    | ~ spl3_2 ),
    inference(backward_demodulation,[],[f116,f155]) ).

fof(f116,plain,
    doDivides0(xl,xn),
    inference(cnf_transformation,[],[f90]) ).

fof(f222,plain,
    ( ~ doDivides0(sz00,sz00)
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f220,f143]) ).

fof(f143,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(f220,plain,
    ( ~ aNaturalNumber0(sz00)
    | ~ doDivides0(sz00,sz00)
    | ~ spl3_2 ),
    inference(superposition,[],[f212,f135]) ).

fof(f135,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).

fof(f212,plain,
    ( ~ doDivides0(sz00,sdtpldt0(sz00,sz00))
    | ~ spl3_2 ),
    inference(backward_demodulation,[],[f206,f191]) ).

fof(f191,plain,
    ( sz00 = xm
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f185,f114]) ).

fof(f114,plain,
    aNaturalNumber0(sK1),
    inference(cnf_transformation,[],[f90]) ).

fof(f185,plain,
    ( sz00 = xm
    | ~ aNaturalNumber0(sK1)
    | ~ spl3_2 ),
    inference(superposition,[],[f132,f183]) ).

fof(f183,plain,
    ( xm = sdtasdt0(sz00,sK1)
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f115,f155]) ).

fof(f115,plain,
    xm = sdtasdt0(xl,sK1),
    inference(cnf_transformation,[],[f90]) ).

fof(f206,plain,
    ( ~ doDivides0(sz00,sdtpldt0(xm,sz00))
    | ~ spl3_2 ),
    inference(backward_demodulation,[],[f181,f190]) ).

fof(f181,plain,
    ( ~ doDivides0(sz00,sdtpldt0(xm,xn))
    | ~ spl3_2 ),
    inference(backward_demodulation,[],[f134,f155]) ).

fof(f134,plain,
    ~ doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnf_transformation,[],[f80]) ).

fof(f176,plain,
    ( spl3_2
    | spl3_6 ),
    inference(avatar_split_clause,[],[f102,f173,f153]) ).

fof(f102,plain,
    ( aNaturalNumber0(sdtsldt0(xm,xl))
    | sz00 = xl ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
      & xn = sdtasdt0(xl,sdtsldt0(xn,xl))
      & xm = sdtasdt0(xl,sdtsldt0(xm,xl))
      & aNaturalNumber0(sdtsldt0(xm,xl))
      & aNaturalNumber0(sdtsldt0(xn,xl)) )
    | sz00 = xl ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ( sz00 != xl
   => ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
      & xn = sdtasdt0(xl,sdtsldt0(xn,xl))
      & xm = sdtasdt0(xl,sdtsldt0(xm,xl))
      & aNaturalNumber0(sdtsldt0(xm,xl))
      & aNaturalNumber0(sdtsldt0(xn,xl)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1298) ).

fof(f171,plain,
    ( spl3_2
    | spl3_5 ),
    inference(avatar_split_clause,[],[f105,f168,f153]) ).

fof(f105,plain,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
    | sz00 = xl ),
    inference(cnf_transformation,[],[f75]) ).

fof(f156,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f101,f153,f149]) ).

fof(f101,plain,
    ( sz00 = xl
    | aNaturalNumber0(sdtsldt0(xn,xl)) ),
    inference(cnf_transformation,[],[f75]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM469+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n029.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
% 0.13/0.35  % DateTime   : Tue Aug 30 06:47:27 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.51  % (22052)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52  % (22043)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.52  % (22062)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.20/0.52  % (22059)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.52  % (22043)First to succeed.
% 0.20/0.52  % (22060)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.53  % (22052)Instruction limit reached!
% 0.20/0.53  % (22052)------------------------------
% 0.20/0.53  % (22052)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (22052)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (22052)Termination reason: Unknown
% 0.20/0.53  % (22052)Termination phase: Saturation
% 0.20/0.53  
% 0.20/0.53  % (22052)Memory used [KB]: 6140
% 0.20/0.53  % (22052)Time elapsed: 0.068 s
% 0.20/0.53  % (22052)Instructions burned: 8 (million)
% 0.20/0.53  % (22052)------------------------------
% 0.20/0.53  % (22052)------------------------------
% 1.36/0.53  % (22059)Also succeeded, but the first one will report.
% 1.36/0.53  % (22039)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.36/0.53  % (22041)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.36/0.54  % (22043)Refutation found. Thanks to Tanya!
% 1.36/0.54  % SZS status Theorem for theBenchmark
% 1.36/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 1.36/0.54  % (22043)------------------------------
% 1.36/0.54  % (22043)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54  % (22043)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.54  % (22043)Termination reason: Refutation
% 1.36/0.54  
% 1.36/0.54  % (22043)Memory used [KB]: 6140
% 1.36/0.54  % (22043)Time elapsed: 0.103 s
% 1.36/0.54  % (22043)Instructions burned: 9 (million)
% 1.36/0.54  % (22043)------------------------------
% 1.36/0.54  % (22043)------------------------------
% 1.36/0.54  % (22036)Success in time 0.179 s
%------------------------------------------------------------------------------