TSTP Solution File: GRP001+6 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 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 : n017.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 : Fri Sep  1 15:37:59 EDT 2023

% Result   : Theorem 0.16s 0.40s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (   9 unt;   0 def)
%            Number of atoms       :  177 (   0 equ)
%            Maximal formula atoms :   32 (   7 avg)
%            Number of connectives :  211 (  59   ~;  48   |;  86   &)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   9 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  245 (; 214   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f364,plain,
    $false,
    inference(subsumption_resolution,[],[f362,f20]) ).

fof(f20,plain,
    ~ product(sK2,sK1,sK3),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ( ~ product(sK2,sK1,sK3)
    & product(sK1,sK2,sK3)
    & ! [X4] : product(X4,X4,sK0)
    & ! [X5] : product(inverse(X5),X5,sK0)
    & ! [X6] : product(X6,inverse(X6),sK0)
    & ! [X7] : product(sK0,X7,X7)
    & ! [X8] : product(X8,sK0,X8)
    & ! [X9,X10,X11,X12,X13,X14] :
        ( product(X12,X11,X14)
        | ~ product(X9,X13,X14)
        | ~ product(X10,X11,X13)
        | ~ product(X9,X10,X12) )
    & ! [X15,X16,X17,X18,X19,X20] :
        ( product(X15,X19,X20)
        | ~ product(X18,X17,X20)
        | ~ product(X16,X17,X19)
        | ~ product(X15,X16,X18) )
    & ! [X21,X22] : product(X21,X22,sK4(X21,X22)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f6,f9,f8,f7]) ).

fof(f7,plain,
    ( ? [X0] :
        ( ? [X1,X2,X3] :
            ( ~ product(X2,X1,X3)
            & product(X1,X2,X3) )
        & ! [X4] : product(X4,X4,X0)
        & ! [X5] : product(inverse(X5),X5,X0)
        & ! [X6] : product(X6,inverse(X6),X0)
        & ! [X7] : product(X0,X7,X7)
        & ! [X8] : product(X8,X0,X8)
        & ! [X9,X10,X11,X12,X13,X14] :
            ( product(X12,X11,X14)
            | ~ product(X9,X13,X14)
            | ~ product(X10,X11,X13)
            | ~ product(X9,X10,X12) )
        & ! [X15,X16,X17,X18,X19,X20] :
            ( product(X15,X19,X20)
            | ~ product(X18,X17,X20)
            | ~ product(X16,X17,X19)
            | ~ product(X15,X16,X18) )
        & ! [X21,X22] :
          ? [X23] : product(X21,X22,X23) )
   => ( ? [X1,X2,X3] :
          ( ~ product(X2,X1,X3)
          & product(X1,X2,X3) )
      & ! [X4] : product(X4,X4,sK0)
      & ! [X5] : product(inverse(X5),X5,sK0)
      & ! [X6] : product(X6,inverse(X6),sK0)
      & ! [X7] : product(sK0,X7,X7)
      & ! [X8] : product(X8,sK0,X8)
      & ! [X9,X10,X11,X12,X13,X14] :
          ( product(X12,X11,X14)
          | ~ product(X9,X13,X14)
          | ~ product(X10,X11,X13)
          | ~ product(X9,X10,X12) )
      & ! [X15,X16,X17,X18,X19,X20] :
          ( product(X15,X19,X20)
          | ~ product(X18,X17,X20)
          | ~ product(X16,X17,X19)
          | ~ product(X15,X16,X18) )
      & ! [X21,X22] :
        ? [X23] : product(X21,X22,X23) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ( ? [X1,X2,X3] :
        ( ~ product(X2,X1,X3)
        & product(X1,X2,X3) )
   => ( ~ product(sK2,sK1,sK3)
      & product(sK1,sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ! [X21,X22] :
      ( ? [X23] : product(X21,X22,X23)
     => product(X21,X22,sK4(X21,X22)) ),
    introduced(choice_axiom,[]) ).

fof(f6,plain,
    ? [X0] :
      ( ? [X1,X2,X3] :
          ( ~ product(X2,X1,X3)
          & product(X1,X2,X3) )
      & ! [X4] : product(X4,X4,X0)
      & ! [X5] : product(inverse(X5),X5,X0)
      & ! [X6] : product(X6,inverse(X6),X0)
      & ! [X7] : product(X0,X7,X7)
      & ! [X8] : product(X8,X0,X8)
      & ! [X9,X10,X11,X12,X13,X14] :
          ( product(X12,X11,X14)
          | ~ product(X9,X13,X14)
          | ~ product(X10,X11,X13)
          | ~ product(X9,X10,X12) )
      & ! [X15,X16,X17,X18,X19,X20] :
          ( product(X15,X19,X20)
          | ~ product(X18,X17,X20)
          | ~ product(X16,X17,X19)
          | ~ product(X15,X16,X18) )
      & ! [X21,X22] :
        ? [X23] : product(X21,X22,X23) ),
    inference(rectify,[],[f5]) ).

fof(f5,plain,
    ? [X0] :
      ( ? [X21,X22,X23] :
          ( ~ product(X22,X21,X23)
          & product(X21,X22,X23) )
      & ! [X20] : product(X20,X20,X0)
      & ! [X1] : product(inverse(X1),X1,X0)
      & ! [X2] : product(X2,inverse(X2),X0)
      & ! [X3] : product(X0,X3,X3)
      & ! [X4] : product(X4,X0,X4)
      & ! [X5,X6,X7,X8,X9,X10] :
          ( product(X8,X7,X10)
          | ~ product(X5,X9,X10)
          | ~ product(X6,X7,X9)
          | ~ product(X5,X6,X8) )
      & ! [X11,X12,X13,X14,X15,X16] :
          ( product(X11,X15,X16)
          | ~ product(X14,X13,X16)
          | ~ product(X12,X13,X15)
          | ~ product(X11,X12,X14) )
      & ! [X17,X18] :
        ? [X19] : product(X17,X18,X19) ),
    inference(flattening,[],[f4]) ).

fof(f4,plain,
    ? [X0] :
      ( ? [X21,X22,X23] :
          ( ~ product(X22,X21,X23)
          & product(X21,X22,X23) )
      & ! [X20] : product(X20,X20,X0)
      & ! [X1] : product(inverse(X1),X1,X0)
      & ! [X2] : product(X2,inverse(X2),X0)
      & ! [X3] : product(X0,X3,X3)
      & ! [X4] : product(X4,X0,X4)
      & ! [X5,X6,X7,X8,X9,X10] :
          ( product(X8,X7,X10)
          | ~ product(X5,X9,X10)
          | ~ product(X6,X7,X9)
          | ~ product(X5,X6,X8) )
      & ! [X11,X12,X13,X14,X15,X16] :
          ( product(X11,X15,X16)
          | ~ product(X14,X13,X16)
          | ~ product(X12,X13,X15)
          | ~ product(X11,X12,X14) )
      & ! [X17,X18] :
        ? [X19] : product(X17,X18,X19) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,plain,
    ~ ! [X0] :
        ( ( ! [X1] : product(inverse(X1),X1,X0)
          & ! [X2] : product(X2,inverse(X2),X0)
          & ! [X3] : product(X0,X3,X3)
          & ! [X4] : product(X4,X0,X4)
          & ! [X5,X6,X7,X8,X9,X10] :
              ( ( product(X5,X9,X10)
                & product(X6,X7,X9)
                & product(X5,X6,X8) )
             => product(X8,X7,X10) )
          & ! [X11,X12,X13,X14,X15,X16] :
              ( ( product(X14,X13,X16)
                & product(X12,X13,X15)
                & product(X11,X12,X14) )
             => product(X11,X15,X16) )
          & ! [X17,X18] :
            ? [X19] : product(X17,X18,X19) )
       => ( ! [X20] : product(X20,X20,X0)
         => ! [X21,X22,X23] :
              ( product(X21,X22,X23)
             => product(X22,X21,X23) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
        ( ( ! [X1] : product(inverse(X1),X1,X0)
          & ! [X1] : product(X1,inverse(X1),X0)
          & ! [X1] : product(X0,X1,X1)
          & ! [X1] : product(X1,X0,X1)
          & ! [X1,X2,X3,X4,X5,X6] :
              ( ( product(X1,X5,X6)
                & product(X2,X3,X5)
                & product(X1,X2,X4) )
             => product(X4,X3,X6) )
          & ! [X1,X2,X3,X4,X5,X6] :
              ( ( product(X4,X3,X6)
                & product(X2,X3,X5)
                & product(X1,X2,X4) )
             => product(X1,X5,X6) )
          & ! [X1,X2] :
            ? [X3] : product(X1,X2,X3) )
       => ( ! [X1] : product(X1,X1,X0)
         => ! [X4,X5,X6] :
              ( product(X4,X5,X6)
             => product(X5,X4,X6) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ! [X0] :
      ( ( ! [X1] : product(inverse(X1),X1,X0)
        & ! [X1] : product(X1,inverse(X1),X0)
        & ! [X1] : product(X0,X1,X1)
        & ! [X1] : product(X1,X0,X1)
        & ! [X1,X2,X3,X4,X5,X6] :
            ( ( product(X1,X5,X6)
              & product(X2,X3,X5)
              & product(X1,X2,X4) )
           => product(X4,X3,X6) )
        & ! [X1,X2,X3,X4,X5,X6] :
            ( ( product(X4,X3,X6)
              & product(X2,X3,X5)
              & product(X1,X2,X4) )
           => product(X1,X5,X6) )
        & ! [X1,X2] :
          ? [X3] : product(X1,X2,X3) )
     => ( ! [X1] : product(X1,X1,X0)
       => ! [X4,X5,X6] :
            ( product(X4,X5,X6)
           => product(X5,X4,X6) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.3uKzVx9AtG/Vampire---4.8_28282',commutativity) ).

fof(f362,plain,
    product(sK2,sK1,sK3),
    inference(resolution,[],[f337,f45]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( ~ product(X0,X1,X2)
      | product(X0,X2,X1) ),
    inference(resolution,[],[f22,f18]) ).

fof(f18,plain,
    ! [X4] : product(X4,X4,sK0),
    inference(cnf_transformation,[],[f10]) ).

fof(f22,plain,
    ! [X6,X7,X4,X5] :
      ( ~ product(X4,X7,sK0)
      | ~ product(X7,X6,X5)
      | product(X4,X5,X6) ),
    inference(resolution,[],[f12,f15]) ).

fof(f15,plain,
    ! [X7] : product(sK0,X7,X7),
    inference(cnf_transformation,[],[f10]) ).

fof(f12,plain,
    ! [X18,X19,X16,X17,X15,X20] :
      ( ~ product(X18,X17,X20)
      | product(X15,X19,X20)
      | ~ product(X16,X17,X19)
      | ~ product(X15,X16,X18) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f337,plain,
    product(sK2,sK3,sK1),
    inference(resolution,[],[f82,f79]) ).

fof(f79,plain,
    product(sK1,sK3,sK2),
    inference(resolution,[],[f45,f19]) ).

fof(f19,plain,
    product(sK1,sK2,sK3),
    inference(cnf_transformation,[],[f10]) ).

fof(f82,plain,
    ! [X2,X0,X1] :
      ( ~ product(X2,X1,X0)
      | product(X0,X1,X2) ),
    inference(resolution,[],[f33,f18]) ).

fof(f33,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(X3,X1,sK0)
      | product(X0,X1,X2)
      | ~ product(X2,X3,X0) ),
    inference(resolution,[],[f13,f14]) ).

fof(f14,plain,
    ! [X8] : product(X8,sK0,X8),
    inference(cnf_transformation,[],[f10]) ).

fof(f13,plain,
    ! [X10,X11,X9,X14,X12,X13] :
      ( ~ product(X9,X13,X14)
      | product(X12,X11,X14)
      | ~ product(X10,X11,X13)
      | ~ product(X9,X10,X12) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 0.09/0.12  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.32  % Computer : n017.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Wed Aug 30 16:52:59 EDT 2023
% 0.11/0.32  % CPUTime    : 
% 0.16/0.38  % (28389)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38  % (28391)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on Vampire---4 for (569ds/0Mi)
% 0.16/0.38  % (28395)dis+11_4:5_nm=4_216 on Vampire---4 for (216ds/0Mi)
% 0.16/0.38  % (28390)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on Vampire---4 for (1451ds/0Mi)
% 0.16/0.38  % (28396)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on Vampire---4 for (1451ds/0Mi)
% 0.16/0.38  % (28394)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on Vampire---4 for (396ds/0Mi)
% 0.16/0.38  % (28393)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on Vampire---4 for (470ds/0Mi)
% 0.16/0.38  TRYING [1]
% 0.16/0.38  TRYING [1]
% 0.16/0.38  TRYING [1]
% 0.16/0.38  TRYING [1]
% 0.16/0.38  % (28392)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 Vampire---4 for (476ds/0Mi)
% 0.16/0.38  TRYING [2]
% 0.16/0.38  TRYING [2]
% 0.16/0.38  TRYING [2]
% 0.16/0.39  TRYING [3]
% 0.16/0.39  TRYING [3]
% 0.16/0.39  TRYING [3]
% 0.16/0.39  TRYING [2]
% 0.16/0.39  TRYING [3]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  % (28395)First to succeed.
% 0.16/0.40  % (28390)Also succeeded, but the first one will report.
% 0.16/0.40  % (28395)Refutation found. Thanks to Tanya!
% 0.16/0.40  % SZS status Theorem for Vampire---4
% 0.16/0.40  % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.40  % (28395)------------------------------
% 0.16/0.40  % (28395)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.16/0.40  % (28395)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.16/0.40  % (28395)Termination reason: Refutation
% 0.16/0.40  
% 0.16/0.40  % (28395)Memory used [KB]: 5500
% 0.16/0.40  % (28395)Time elapsed: 0.015 s
% 0.16/0.40  % (28395)------------------------------
% 0.16/0.40  % (28395)------------------------------
% 0.16/0.40  % (28389)Success in time 0.067 s
% 0.16/0.40  % Vampire---4.8 exiting
%------------------------------------------------------------------------------