TSTP Solution File: KRS268+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KRS268+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.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 : Sun May  5 07:20:18 EDT 2024

% Result   : Theorem 0.21s 0.44s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   68 (  16 unt;   0 def)
%            Number of atoms       :  185 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  196 (  79   ~;  56   |;  39   &)
%                                         (  13 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   5 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  139 (  93   !;  46   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5177,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2342,f2345,f5136,f5143,f5176]) ).

fof(f5176,plain,
    ~ spl97_70,
    inference(avatar_contradiction_clause,[],[f5148]) ).

fof(f5148,plain,
    ( $false
    | ~ spl97_70 ),
    inference(resolution,[],[f5135,f286]) ).

fof(f286,plain,
    ! [X1] : ~ model(X1,sK44),
    inference(cnf_transformation,[],[f190]) ).

fof(f190,plain,
    ! [X1] : ~ model(X1,sK44),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f55,f189]) ).

fof(f189,plain,
    ( ? [X0] :
      ! [X1] : ~ model(X1,X0)
   => ! [X1] : ~ model(X1,sK44) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ? [X0] :
    ! [X1] : ~ model(X1,X0),
    inference(rectify,[],[f29]) ).

fof(f29,axiom,
    ? [X9] :
    ! [X8] : ~ model(X8,X9),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contradiction) ).

fof(f5135,plain,
    ( model(sK6(sK44),sK44)
    | ~ spl97_70 ),
    inference(avatar_component_clause,[],[f5133]) ).

fof(f5133,plain,
    ( spl97_70
  <=> model(sK6(sK44),sK44) ),
    introduced(avatar_definition,[new_symbols(naming,[spl97_70])]) ).

fof(f5143,plain,
    ( spl97_12
    | ~ spl97_69 ),
    inference(avatar_contradiction_clause,[],[f5142]) ).

fof(f5142,plain,
    ( $false
    | spl97_12
    | ~ spl97_69 ),
    inference(resolution,[],[f5131,f2341]) ).

fof(f2341,plain,
    ( ~ sP64(sK57)
    | spl97_12 ),
    inference(avatar_component_clause,[],[f2339]) ).

fof(f2339,plain,
    ( spl97_12
  <=> sP64(sK57) ),
    introduced(avatar_definition,[new_symbols(naming,[spl97_12])]) ).

fof(f5131,plain,
    ( ! [X0] : sP64(X0)
    | ~ spl97_69 ),
    inference(avatar_component_clause,[],[f5130]) ).

fof(f5130,plain,
    ( spl97_69
  <=> ! [X0] : sP64(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl97_69])]) ).

fof(f5136,plain,
    ( spl97_69
    | spl97_70 ),
    inference(avatar_split_clause,[],[f4879,f5133,f5130]) ).

fof(f4879,plain,
    ! [X0] :
      ( model(sK6(sK44),sK44)
      | sP64(X0) ),
    inference(resolution,[],[f4877,f309]) ).

fof(f309,plain,
    ! [X0,X1] :
      ( status(X0,X1,wca)
      | model(sK6(X0),X0)
      | sP64(X1) ),
    inference(cnf_transformation,[],[f309_D]) ).

fof(f309_D,plain,
    ! [X1] :
      ( ! [X0] :
          ( status(X0,X1,wca)
          | model(sK6(X0),X0) )
    <=> ~ sP64(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP64])]) ).

fof(f4877,plain,
    ! [X0] : ~ status(sK44,X0,wca),
    inference(resolution,[],[f2010,f1462]) ).

fof(f1462,plain,
    ! [X0] : status(sK44,X0,thm),
    inference(resolution,[],[f272,f286]) ).

fof(f272,plain,
    ! [X0,X1] :
      ( model(sK38(X0,X1),X0)
      | status(X0,X1,thm) ),
    inference(cnf_transformation,[],[f175]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) )
      & ( status(X0,X1,thm)
        | ( ~ model(sK38(X0,X1),X1)
          & model(sK38(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f173,f174]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ model(X3,X1)
          & model(X3,X0) )
     => ( ~ model(sK38(X0,X1),X1)
        & model(sK38(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) )
      & ( status(X0,X1,thm)
        | ? [X3] :
            ( ~ model(X3,X1)
            & model(X3,X0) ) ) ),
    inference(rectify,[],[f172]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) )
      & ( status(X0,X1,thm)
        | ? [X2] :
            ( ~ model(X2,X1)
            & model(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( model(X2,X1)
          | ~ model(X2,X0) )
    <=> status(X0,X1,thm) ),
    inference(ennf_transformation,[],[f5]) ).

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

fof(f2010,plain,
    ! [X0,X1] :
      ( ~ status(X0,X1,thm)
      | ~ status(X0,X1,wca) ),
    inference(resolution,[],[f281,f205]) ).

fof(f205,plain,
    ~ mighta(wca,thm),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ~ mighta(wca,thm),
    inference(flattening,[],[f34]) ).

fof(f34,negated_conjecture,
    ~ mighta(wca,thm),
    inference(negated_conjecture,[],[f33]) ).

fof(f33,conjecture,
    mighta(wca,thm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta_wca_thm) ).

fof(f281,plain,
    ! [X2,X3,X0,X1] :
      ( mighta(X0,X1)
      | ~ status(X2,X3,X1)
      | ~ status(X2,X3,X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( mighta(X0,X1)
      | ! [X2,X3] :
          ( ~ status(X2,X3,X1)
          | ~ status(X2,X3,X0) ) ),
    inference(ennf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( status(X2,X3,X1)
          & status(X2,X3,X0) )
     => mighta(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( status(X2,X3,X1)
          & status(X2,X3,X0) )
    <=> mighta(X0,X1) ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X6,X7] :
      ( ? [X0,X1] :
          ( status(X0,X1,X7)
          & status(X0,X1,X6) )
    <=> mighta(X6,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta) ).

fof(f2345,plain,
    spl97_11,
    inference(avatar_contradiction_clause,[],[f2343]) ).

fof(f2343,plain,
    ( $false
    | spl97_11 ),
    inference(resolution,[],[f2337,f424]) ).

fof(f424,plain,
    sP65(sK57),
    inference(resolution,[],[f311,f298]) ).

fof(f298,plain,
    model(sK58,sK57),
    inference(cnf_transformation,[],[f204]) ).

fof(f204,plain,
    ( model(sK58,sK57)
    & ~ model(sK55,sK57)
    & model(sK55,sK56) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56,sK57,sK58])],[f59,f203,f202]) ).

fof(f202,plain,
    ( ? [X0,X1,X2] :
        ( ? [X3] : model(X3,X2)
        & ~ model(X0,X2)
        & model(X0,X1) )
   => ( ? [X3] : model(X3,sK57)
      & ~ model(sK55,sK57)
      & model(sK55,sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f203,plain,
    ( ? [X3] : model(X3,sK57)
   => model(sK58,sK57) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ? [X0,X1,X2] :
      ( ? [X3] : model(X3,X2)
      & ~ model(X0,X2)
      & model(X0,X1) ),
    inference(rectify,[],[f32]) ).

fof(f32,axiom,
    ? [X2,X0,X1] :
      ( ? [X3] : model(X3,X1)
      & ~ model(X2,X1)
      & model(X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_thm_spt) ).

fof(f311,plain,
    ! [X1,X6] :
      ( ~ model(X6,X1)
      | sP65(X1) ),
    inference(cnf_transformation,[],[f311_D]) ).

fof(f311_D,plain,
    ! [X1] :
      ( ! [X6] : ~ model(X6,X1)
    <=> ~ sP65(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP65])]) ).

fof(f2337,plain,
    ( ~ sP65(sK57)
    | spl97_11 ),
    inference(avatar_component_clause,[],[f2335]) ).

fof(f2335,plain,
    ( spl97_11
  <=> sP65(sK57) ),
    introduced(avatar_definition,[new_symbols(naming,[spl97_11])]) ).

fof(f2342,plain,
    ( ~ spl97_11
    | ~ spl97_12 ),
    inference(avatar_split_clause,[],[f953,f2339,f2335]) ).

fof(f953,plain,
    ( ~ sP64(sK57)
    | ~ sP65(sK57) ),
    inference(resolution,[],[f312,f297]) ).

fof(f297,plain,
    ~ model(sK55,sK57),
    inference(cnf_transformation,[],[f204]) ).

fof(f312,plain,
    ! [X1,X5] :
      ( model(X5,X1)
      | ~ sP64(X1)
      | ~ sP65(X1) ),
    inference(general_splitting,[],[f310,f311_D]) ).

fof(f310,plain,
    ! [X1,X6,X5] :
      ( model(X5,X1)
      | ~ model(X6,X1)
      | ~ sP64(X1) ),
    inference(general_splitting,[],[f214,f309_D]) ).

fof(f214,plain,
    ! [X0,X1,X6,X5] :
      ( status(X0,X1,wca)
      | model(X5,X1)
      | ~ model(X6,X1)
      | model(sK6(X0),X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( ( ~ model(sK4(X1),X1)
          & model(sK5(X1),X1)
          & ! [X4] : ~ model(X4,X0) )
        | ~ status(X0,X1,wca) )
      & ( status(X0,X1,wca)
        | ! [X5] : model(X5,X1)
        | ! [X6] : ~ model(X6,X1)
        | model(sK6(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f87,f90,f89,f88]) ).

fof(f88,plain,
    ! [X1] :
      ( ? [X2] : ~ model(X2,X1)
     => ~ model(sK4(X1),X1) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X1] :
      ( ? [X3] : model(X3,X1)
     => model(sK5(X1),X1) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ! [X0] :
      ( ? [X7] : model(X7,X0)
     => model(sK6(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ( ( ? [X2] : ~ model(X2,X1)
          & ? [X3] : model(X3,X1)
          & ! [X4] : ~ model(X4,X0) )
        | ~ status(X0,X1,wca) )
      & ( status(X0,X1,wca)
        | ! [X5] : model(X5,X1)
        | ! [X6] : ~ model(X6,X1)
        | ? [X7] : model(X7,X0) ) ),
    inference(rectify,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ( ( ? [X2] : ~ model(X2,X1)
          & ? [X3] : model(X3,X1)
          & ! [X4] : ~ model(X4,X0) )
        | ~ status(X0,X1,wca) )
      & ( status(X0,X1,wca)
        | ! [X2] : model(X2,X1)
        | ! [X3] : ~ model(X3,X1)
        | ? [X4] : model(X4,X0) ) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ( ( ? [X2] : ~ model(X2,X1)
          & ? [X3] : model(X3,X1)
          & ! [X4] : ~ model(X4,X0) )
        | ~ status(X0,X1,wca) )
      & ( status(X0,X1,wca)
        | ! [X2] : model(X2,X1)
        | ! [X3] : ~ model(X3,X1)
        | ? [X4] : model(X4,X0) ) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( ? [X2] : ~ model(X2,X1)
        & ? [X3] : model(X3,X1)
        & ! [X4] : ~ model(X4,X0) )
    <=> status(X0,X1,wca) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( ? [X2] : ~ model(X2,X1)
        & ? [X3] : model(X3,X1)
        & ~ ? [X4] : model(X4,X0) )
    <=> status(X0,X1,wca) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ( ? [X4] : ~ model(X4,X1)
        & ? [X3] : model(X3,X1)
        & ~ ? [X2] : model(X2,X0) )
    <=> status(X0,X1,wca) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wca) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : KRS268+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 19:50:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (24575)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (24578)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.38  % (24576)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38  % (24579)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38  % (24577)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (24580)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38  % (24581)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38  % (24582)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [1,1,1]
% 0.14/0.39  TRYING [1,1,1]
% 0.14/0.39  TRYING [2,1,2]
% 0.14/0.39  TRYING [2,1,2]
% 0.14/0.39  TRYING [2,2,2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [2,2,2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [3,3,2]
% 0.14/0.40  TRYING [3,3,2]
% 0.14/0.40  TRYING [4]
% 0.21/0.40  TRYING [4]
% 0.21/0.41  TRYING [4,4,2]
% 0.21/0.41  TRYING [4,4,2]
% 0.21/0.42  TRYING [5]
% 0.21/0.43  TRYING [4,4,3]
% 0.21/0.44  TRYING [4,4,3]
% 0.21/0.44  % (24578)First to succeed.
% 0.21/0.44  TRYING [5]
% 0.21/0.44  % (24578)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24575"
% 0.21/0.44  % (24580)Also succeeded, but the first one will report.
% 0.21/0.44  % (24578)Refutation found. Thanks to Tanya!
% 0.21/0.44  % SZS status Theorem for theBenchmark
% 0.21/0.44  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.44  % (24578)------------------------------
% 0.21/0.44  % (24578)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.44  % (24578)Termination reason: Refutation
% 0.21/0.44  
% 0.21/0.44  % (24578)Memory used [KB]: 1908
% 0.21/0.44  % (24578)Time elapsed: 0.066 s
% 0.21/0.44  % (24578)Instructions burned: 134 (million)
% 0.21/0.44  % (24575)Success in time 0.071 s
%------------------------------------------------------------------------------