TSTP Solution File: GRP012+5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP012+5 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n023.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 05:52:18 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   34 (  13 unt;   0 def)
%            Number of atoms       :  195 (   0 equ)
%            Maximal formula atoms :   32 (   5 avg)
%            Number of connectives :  229 (  68   ~;  55   |;  91   &)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  257 ( 220   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f509,plain,
    $false,
    inference(subsumption_resolution,[],[f506,f392]) ).

fof(f392,plain,
    ~ product(sK3,sK4,sK0),
    inference(resolution,[],[f386,f44]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( product(inverse(X0),X2,X1)
      | ~ product(X0,X1,X2) ),
    inference(resolution,[],[f22,f17]) ).

fof(f17,plain,
    ! [X5] : product(inverse(X5),X5,sK0),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ( ~ product(inverse(sK3),inverse(sK4),sK0)
    & product(sK2,sK1,sK4)
    & product(inverse(sK1),inverse(sK2),sK3)
    & ! [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,sK5(X21,X22)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f6,f9,f8,f7]) ).

fof(f7,plain,
    ( ? [X0] :
        ( ? [X1,X2,X3,X4] :
            ( ~ product(inverse(X3),inverse(X4),X0)
            & product(X2,X1,X4)
            & product(inverse(X1),inverse(X2),X3) )
        & ! [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) )
   => ( ? [X4,X3,X2,X1] :
          ( ~ product(inverse(X3),inverse(X4),sK0)
          & product(X2,X1,X4)
          & product(inverse(X1),inverse(X2),X3) )
      & ! [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,
    ( ? [X4,X3,X2,X1] :
        ( ~ product(inverse(X3),inverse(X4),sK0)
        & product(X2,X1,X4)
        & product(inverse(X1),inverse(X2),X3) )
   => ( ~ product(inverse(sK3),inverse(sK4),sK0)
      & product(sK2,sK1,sK4)
      & product(inverse(sK1),inverse(sK2),sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ! [X21,X22] :
      ( ? [X23] : product(X21,X22,X23)
     => product(X21,X22,sK5(X21,X22)) ),
    introduced(choice_axiom,[]) ).

fof(f6,plain,
    ? [X0] :
      ( ? [X1,X2,X3,X4] :
          ( ~ product(inverse(X3),inverse(X4),X0)
          & product(X2,X1,X4)
          & product(inverse(X1),inverse(X2),X3) )
      & ! [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] :
      ( ? [X20,X21,X22,X23] :
          ( ~ product(inverse(X22),inverse(X23),X0)
          & product(X21,X20,X23)
          & product(inverse(X20),inverse(X21),X22) )
      & ! [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] :
      ( ? [X20,X21,X22,X23] :
          ( ~ product(inverse(X22),inverse(X23),X0)
          & product(X21,X20,X23)
          & product(inverse(X20),inverse(X21),X22) )
      & ! [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,X21,X22,X23] :
            ( ( product(X21,X20,X23)
              & product(inverse(X20),inverse(X21),X22) )
           => product(inverse(X22),inverse(X23),X0) ) ),
    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) )
       => ! [X4,X5,X6,X1] :
            ( ( product(X5,X4,X1)
              & product(inverse(X4),inverse(X5),X6) )
           => product(inverse(X6),inverse(X1),X0) ) ),
    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) )
     => ! [X4,X5,X6,X1] :
          ( ( product(X5,X4,X1)
            & product(inverse(X4),inverse(X5),X6) )
         => product(inverse(X6),inverse(X1),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distribution) ).

fof(f22,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(X0,X3,sK0)
      | ~ product(X3,X2,X1)
      | product(X0,X1,X2) ),
    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(f386,plain,
    ~ product(inverse(sK3),sK0,sK4),
    inference(resolution,[],[f92,f20]) ).

fof(f20,plain,
    ~ product(inverse(sK3),inverse(sK4),sK0),
    inference(cnf_transformation,[],[f10]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( product(X0,inverse(X1),sK0)
      | ~ product(X0,sK0,X1) ),
    inference(resolution,[],[f23,f15]) ).

fof(f23,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(X2,inverse(X3),X1)
      | product(X0,X1,sK0)
      | ~ product(X0,X2,X3) ),
    inference(resolution,[],[f12,f16]) ).

fof(f16,plain,
    ! [X6] : product(X6,inverse(X6),sK0),
    inference(cnf_transformation,[],[f10]) ).

fof(f506,plain,
    product(sK3,sK4,sK0),
    inference(resolution,[],[f115,f420]) ).

fof(f420,plain,
    product(inverse(sK2),sK4,sK1),
    inference(resolution,[],[f279,f43]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( ~ product(inverse(X0),X1,X2)
      | product(X0,X2,X1) ),
    inference(resolution,[],[f22,f16]) ).

fof(f279,plain,
    product(inverse(inverse(sK2)),sK1,sK4),
    inference(resolution,[],[f256,f84]) ).

fof(f84,plain,
    ! [X0] :
      ( ~ product(sK2,sK0,X0)
      | product(X0,sK1,sK4) ),
    inference(resolution,[],[f37,f15]) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( ~ product(X2,X1,sK1)
      | product(X0,X1,sK4)
      | ~ product(sK2,X2,X0) ),
    inference(resolution,[],[f13,f19]) ).

fof(f19,plain,
    product(sK2,sK1,sK4),
    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]) ).

fof(f256,plain,
    ! [X0] : product(X0,sK0,inverse(inverse(X0))),
    inference(resolution,[],[f43,f16]) ).

fof(f115,plain,
    ! [X0] :
      ( ~ product(inverse(sK2),X0,sK1)
      | product(sK3,X0,sK0) ),
    inference(resolution,[],[f35,f18]) ).

fof(f18,plain,
    product(inverse(sK1),inverse(sK2),sK3),
    inference(cnf_transformation,[],[f10]) ).

fof(f35,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(inverse(X3),X2,X0)
      | ~ product(X2,X1,X3)
      | product(X0,X1,sK0) ),
    inference(resolution,[],[f13,f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRP012+5 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n023.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 20:54:08 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (18656)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (18658)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (18660)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  % (18657)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38  % (18662)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38  % (18661)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38  % (18659)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  TRYING [1]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  % (18663)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 [2]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.39  TRYING [4]
% 0.14/0.39  TRYING [4]
% 0.14/0.39  TRYING [4]
% 0.14/0.39  TRYING [4]
% 0.14/0.40  % (18662)First to succeed.
% 0.14/0.40  % (18662)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18656"
% 0.14/0.40  % (18662)Refutation found. Thanks to Tanya!
% 0.14/0.40  % SZS status Theorem for theBenchmark
% 0.14/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40  % (18662)------------------------------
% 0.14/0.40  % (18662)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40  % (18662)Termination reason: Refutation
% 0.14/0.40  
% 0.14/0.40  % (18662)Memory used [KB]: 887
% 0.14/0.40  % (18662)Time elapsed: 0.021 s
% 0.14/0.40  % (18662)Instructions burned: 35 (million)
% 0.14/0.40  % (18656)Success in time 0.036 s
%------------------------------------------------------------------------------