TSTP Solution File: KRS200+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : KRS200+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 : n007.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 17:30:01 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   47 (  11 unt;   0 def)
%            Number of atoms       :  158 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  180 (  69   ~;  41   |;  49   &)
%                                         (   7 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :  145 (  89   !;  56   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f121,plain,
    $false,
    inference(resolution,[],[f108,f97]) ).

fof(f97,plain,
    ~ model(sK12,sK10),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ( ~ model(sK12,sK10)
    & model(sK13,sK10)
    & ~ model(sK13,sK11)
    & ! [X4] :
        ( ~ model(X4,sK11)
        | model(X4,sK10) )
    & model(sK14,sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14])],[f67,f71,f70,f69,f68]) ).

fof(f68,plain,
    ( ? [X0,X1] :
        ( ? [X2] : ~ model(X2,X0)
        & ? [X3] :
            ( model(X3,X0)
            & ~ model(X3,X1) )
        & ! [X4] :
            ( ~ model(X4,X1)
            | model(X4,X0) )
        & ? [X5] : model(X5,X1) )
   => ( ? [X2] : ~ model(X2,sK10)
      & ? [X3] :
          ( model(X3,sK10)
          & ~ model(X3,sK11) )
      & ! [X4] :
          ( ~ model(X4,sK11)
          | model(X4,sK10) )
      & ? [X5] : model(X5,sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ( ? [X2] : ~ model(X2,sK10)
   => ~ model(sK12,sK10) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ( ? [X3] :
        ( model(X3,sK10)
        & ~ model(X3,sK11) )
   => ( model(sK13,sK10)
      & ~ model(sK13,sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ( ? [X5] : model(X5,sK11)
   => model(sK14,sK11) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ? [X0,X1] :
      ( ? [X2] : ~ model(X2,X0)
      & ? [X3] :
          ( model(X3,X0)
          & ~ model(X3,X1) )
      & ! [X4] :
          ( ~ model(X4,X1)
          | model(X4,X0) )
      & ? [X5] : model(X5,X1) ),
    inference(rectify,[],[f47]) ).

fof(f47,plain,
    ? [X1,X0] :
      ( ? [X5] : ~ model(X5,X1)
      & ? [X2] :
          ( model(X2,X1)
          & ~ model(X2,X0) )
      & ! [X3] :
          ( ~ model(X3,X0)
          | model(X3,X1) )
      & ? [X4] : model(X4,X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ? [X0,X1] :
      ( ! [X3] :
          ( model(X3,X0)
         => model(X3,X1) )
      & ? [X2] :
          ( model(X2,X1)
          & ~ model(X2,X0) )
      & ? [X4] : model(X4,X0)
      & ? [X5] : ~ model(X5,X1) ),
    inference(rectify,[],[f31]) ).

fof(f31,axiom,
    ? [X0,X1] :
      ( ? [X4] :
          ( ~ model(X4,X0)
          & model(X4,X1) )
      & ! [X3] :
          ( model(X3,X0)
         => model(X3,X1) )
      & ? [X2] : model(X2,X0)
      & ? [X5] : ~ model(X5,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mixed_pair) ).

fof(f108,plain,
    ! [X0,X1] : model(X0,X1),
    inference(resolution,[],[f107,f100]) ).

fof(f100,plain,
    ! [X1] : model(X1,sK16),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X1] : model(X1,sK16),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f40,f75]) ).

fof(f75,plain,
    ( ? [X0] :
      ! [X1] : model(X1,X0)
   => ! [X1] : model(X1,sK16) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ? [X0] :
    ! [X1] : model(X1,X0),
    inference(rectify,[],[f27]) ).

fof(f27,axiom,
    ? [X9] :
    ! [X8] : model(X8,X9),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tautology) ).

fof(f107,plain,
    ! [X2,X0,X1] :
      ( ~ model(X2,X0)
      | model(X2,X1) ),
    inference(subsumption_resolution,[],[f106,f88]) ).

fof(f88,plain,
    ! [X0,X1,X4] :
      ( status(X0,X1,unp)
      | ~ model(X4,X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ( model(sK7(X0),X0)
        | ! [X3] : ~ model(X3,X1)
        | ~ status(X0,X1,unp) )
      & ( status(X0,X1,unp)
        | ( ! [X4] : ~ model(X4,X0)
          & model(sK8(X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f59,f61,f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ? [X2] : model(X2,X0)
     => model(sK7(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ! [X1] :
      ( ? [X5] : model(X5,X1)
     => model(sK8(X1),X1) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( ? [X2] : model(X2,X0)
        | ! [X3] : ~ model(X3,X1)
        | ~ status(X0,X1,unp) )
      & ( status(X0,X1,unp)
        | ( ! [X4] : ~ model(X4,X0)
          & ? [X5] : model(X5,X1) ) ) ),
    inference(rectify,[],[f58]) ).

fof(f58,plain,
    ! [X1,X0] :
      ( ( ? [X2] : model(X2,X1)
        | ! [X3] : ~ model(X3,X0)
        | ~ status(X1,X0,unp) )
      & ( status(X1,X0,unp)
        | ( ! [X2] : ~ model(X2,X1)
          & ? [X3] : model(X3,X0) ) ) ),
    inference(flattening,[],[f57]) ).

fof(f57,plain,
    ! [X1,X0] :
      ( ( ? [X2] : model(X2,X1)
        | ! [X3] : ~ model(X3,X0)
        | ~ status(X1,X0,unp) )
      & ( status(X1,X0,unp)
        | ( ! [X2] : ~ model(X2,X1)
          & ? [X3] : model(X3,X0) ) ) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X1,X0] :
      ( ( ? [X2] : model(X2,X1)
        | ! [X3] : ~ model(X3,X0) )
    <=> status(X1,X0,unp) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( ~ ? [X2] : model(X2,X1)
       => ~ ? [X3] : model(X3,X0) )
    <=> status(X1,X0,unp) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( status(X0,X1,unp)
    <=> ( ~ ? [X2] : model(X2,X0)
       => ~ ? [X3] : model(X3,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unp) ).

fof(f106,plain,
    ! [X2,X0,X1] :
      ( ~ model(X2,X0)
      | model(X2,X1)
      | ~ status(X0,X1,unp) ),
    inference(resolution,[],[f105,f90]) ).

fof(f90,plain,
    ! [X3,X0,X1] :
      ( ~ status(X1,X0,thm)
      | model(X3,X0)
      | ~ model(X3,X1) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ( status(X1,X0,thm)
        | ( ~ model(sK9(X0,X1),X0)
          & model(sK9(X0,X1),X1) ) )
      & ( ! [X3] :
            ( model(X3,X0)
            | ~ model(X3,X1) )
        | ~ status(X1,X0,thm) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f64,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ model(X2,X0)
          & model(X2,X1) )
     => ( ~ model(sK9(X0,X1),X0)
        & model(sK9(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ( status(X1,X0,thm)
        | ? [X2] :
            ( ~ model(X2,X0)
            & model(X2,X1) ) )
      & ( ! [X3] :
            ( model(X3,X0)
            | ~ model(X3,X1) )
        | ~ status(X1,X0,thm) ) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ! [X1,X0] :
      ( ( status(X0,X1,thm)
        | ? [X2] :
            ( ~ model(X2,X1)
            & model(X2,X0) ) )
      & ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) ) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X1,X0] :
      ( status(X0,X1,thm)
    <=> ! [X2] :
          ( model(X2,X1)
          | ~ model(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( status(X0,X1,thm)
    <=> ! [X2] :
          ( model(X2,X0)
         => model(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

fof(f105,plain,
    ! [X0,X1] :
      ( status(X0,X1,thm)
      | ~ status(X0,X1,unp) ),
    inference(resolution,[],[f98,f101]) ).

fof(f101,plain,
    ! [X2,X3,X0,X1] :
      ( nota(X1,X0)
      | status(X3,X2,X0)
      | ~ status(X3,X2,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( nota(X1,X0)
      | ! [X2,X3] :
          ( ~ status(X3,X2,X1)
          | status(X3,X2,X0) ) ),
    inference(rectify,[],[f46]) ).

fof(f46,plain,
    ! [X1,X0] :
      ( nota(X0,X1)
      | ! [X3,X2] :
          ( ~ status(X2,X3,X0)
          | status(X2,X3,X1) ) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( status(X2,X3,X0)
          & ~ status(X2,X3,X1) )
     => nota(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( status(X2,X3,X0)
          & ~ status(X2,X3,X1) )
    <=> nota(X0,X1) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X6,X7] :
      ( nota(X6,X7)
    <=> ? [X0,X1] :
          ( status(X0,X1,X6)
          & ~ status(X0,X1,X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nota) ).

fof(f98,plain,
    ~ nota(unp,thm),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ~ nota(unp,thm),
    inference(flattening,[],[f34]) ).

fof(f34,negated_conjecture,
    ~ nota(unp,thm),
    inference(negated_conjecture,[],[f33]) ).

fof(f33,conjecture,
    nota(unp,thm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nota_unp_thm) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : KRS200+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 00:21:15 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.49  % (6176)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)
% 0.20/0.49  % (6177)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.49  % (6201)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.20/0.49  % (6177)First to succeed.
% 0.20/0.49  % (6201)Refutation not found, incomplete strategy% (6201)------------------------------
% 0.20/0.49  % (6201)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (6201)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (6201)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.49  
% 0.20/0.49  % (6201)Memory used [KB]: 6140
% 0.20/0.49  % (6201)Time elapsed: 0.103 s
% 0.20/0.49  % (6201)Instructions burned: 4 (million)
% 0.20/0.49  % (6201)------------------------------
% 0.20/0.49  % (6201)------------------------------
% 0.20/0.50  % (6177)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (6177)------------------------------
% 0.20/0.50  % (6177)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (6177)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (6177)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (6177)Memory used [KB]: 1535
% 0.20/0.50  % (6177)Time elapsed: 0.093 s
% 0.20/0.50  % (6177)Instructions burned: 2 (million)
% 0.20/0.50  % (6177)------------------------------
% 0.20/0.50  % (6177)------------------------------
% 0.20/0.50  % (6167)Success in time 0.15 s
%------------------------------------------------------------------------------