TSTP Solution File: KRS084+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KRS084+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n022.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 : Mon May 20 23:21:54 EDT 2024

% Result   : Unsatisfiable 0.08s 0.31s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   68 (  18 unt;   0 def)
%            Number of atoms       :  229 (   6 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  248 (  87   ~;  74   |;  65   &)
%                                         (  12 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :  116 (  93   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f373,plain,
    $false,
    inference(subsumption_resolution,[],[f362,f160]) ).

fof(f160,plain,
    cc(sK5(i2003_11_14_17_19_35232)),
    inference(unit_resulting_resolution,[],[f157,f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ cd(X0)
      | cc(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ( cd(X0)
        | ~ cc(X0)
        | ! [X1] :
            ( cc(X1)
            | ~ rf(X0,X1) ) )
      & ( ( cc(X0)
          & ~ cc(sK2(X0))
          & rf(X0,sK2(X0)) )
        | ~ cd(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f77,f78]) ).

fof(f78,plain,
    ! [X0] :
      ( ? [X2] :
          ( ~ cc(X2)
          & rf(X0,X2) )
     => ( ~ cc(sK2(X0))
        & rf(X0,sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f77,plain,
    ! [X0] :
      ( ( cd(X0)
        | ~ cc(X0)
        | ! [X1] :
            ( cc(X1)
            | ~ rf(X0,X1) ) )
      & ( ( cc(X0)
          & ? [X2] :
              ( ~ cc(X2)
              & rf(X0,X2) ) )
        | ~ cd(X0) ) ),
    inference(rectify,[],[f76]) ).

fof(f76,plain,
    ! [X0] :
      ( ( cd(X0)
        | ~ cc(X0)
        | ! [X1] :
            ( cc(X1)
            | ~ rf(X0,X1) ) )
      & ( ( cc(X0)
          & ? [X1] :
              ( ~ cc(X1)
              & rf(X0,X1) ) )
        | ~ cd(X0) ) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ( cd(X0)
        | ~ cc(X0)
        | ! [X1] :
            ( cc(X1)
            | ~ rf(X0,X1) ) )
      & ( ( cc(X0)
          & ? [X1] :
              ( ~ cc(X1)
              & rf(X0,X1) ) )
        | ~ cd(X0) ) ),
    inference(nnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( cd(X0)
    <=> ( cc(X0)
        & ? [X1] :
            ( ~ cc(X1)
            & rf(X0,X1) ) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,axiom,
    ! [X3] :
      ( cd(X3)
    <=> ( cc(X3)
        & ? [X4] :
            ( ~ cc(X4)
            & rf(X3,X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

fof(f157,plain,
    cd(sK5(i2003_11_14_17_19_35232)),
    inference(unit_resulting_resolution,[],[f151,f107]) ).

fof(f107,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | cd(sK5(X0)) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cd(X1)
            | ~ rinvF(X0,X1) ) )
      & ( ( cd(sK5(X0))
          & rinvF(X0,sK5(X0)) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f86,f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ? [X2] :
          ( cd(X2)
          & rinvF(X0,X2) )
     => ( cd(sK5(X0))
        & rinvF(X0,sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cd(X1)
            | ~ rinvF(X0,X1) ) )
      & ( ? [X2] :
            ( cd(X2)
            & rinvF(X0,X2) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f85]) ).

fof(f85,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X3] :
            ( ~ cd(X3)
            | ~ rinvF(X0,X3) ) )
      & ( ? [X3] :
            ( cd(X3)
            & rinvF(X0,X3) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ? [X3] :
          ( cd(X3)
          & rinvF(X0,X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f151,plain,
    sP0(i2003_11_14_17_19_35232),
    inference(unit_resulting_resolution,[],[f93,f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | cc(X0)
        | ~ sP1(X0)
        | ~ sP0(X0) )
      & ( ( ~ cc(X0)
          & sP1(X0)
          & sP0(X0) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(flattening,[],[f89]) ).

fof(f89,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | cc(X0)
        | ~ sP1(X0)
        | ~ sP0(X0) )
      & ( ( ~ cc(X0)
          & sP1(X0)
          & sP0(X0) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ~ cc(X0)
        & sP1(X0)
        & sP0(X0) ) ),
    inference(definition_folding,[],[f35,f72,f71]) ).

fof(f72,plain,
    ! [X0] :
      ( sP1(X0)
    <=> ! [X1] :
          ( ? [X2] :
              ( cd(X2)
              & rinvF(X1,X2) )
          | ~ rinvR(X0,X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f35,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ~ cc(X0)
        & ! [X1] :
            ( ? [X2] :
                ( cd(X2)
                & rinvF(X1,X2) )
            | ~ rinvR(X0,X1) )
        & ? [X3] :
            ( cd(X3)
            & rinvF(X0,X3) ) ) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ~ cc(X0)
        & ! [X1] :
            ( rinvR(X0,X1)
           => ? [X2] :
                ( cd(X2)
                & rinvF(X1,X2) ) )
        & ? [X3] :
            ( cd(X3)
            & rinvF(X0,X3) ) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( ~ cc(X3)
        & ! [X4] :
            ( rinvR(X3,X4)
           => ? [X5] :
                ( cd(X5)
                & rinvF(X4,X5) ) )
        & ? [X4] :
            ( cd(X4)
            & rinvF(X3,X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

fof(f93,plain,
    cUnsatisfiable(i2003_11_14_17_19_35232),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,axiom,
    cUnsatisfiable(i2003_11_14_17_19_35232),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

fof(f362,plain,
    ~ cc(sK5(i2003_11_14_17_19_35232)),
    inference(superposition,[],[f214,f325]) ).

fof(f325,plain,
    sK5(i2003_11_14_17_19_35232) = sK2(sK4(sK5(i2003_11_14_17_19_35232))),
    inference(unit_resulting_resolution,[],[f213,f307,f133]) ).

fof(f133,plain,
    ! [X2,X0,X1] :
      ( ~ rf(X0,X2)
      | X1 = X2
      | ~ rf(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ~ rf(X0,X2)
      | ~ rf(X0,X1) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ~ rf(X0,X2)
      | ~ rf(X0,X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ( rf(X0,X2)
        & rf(X0,X1) )
     => X1 = X2 ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X3,X4,X5] :
      ( ( rf(X3,X5)
        & rf(X3,X4) )
     => X4 = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

fof(f307,plain,
    rf(sK4(sK5(i2003_11_14_17_19_35232)),sK5(i2003_11_14_17_19_35232)),
    inference(unit_resulting_resolution,[],[f271,f123]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ~ rinvF(X0,X1)
      | rf(X1,X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ( rinvF(X0,X1)
        | ~ rf(X1,X0) )
      & ( rf(X1,X0)
        | ~ rinvF(X0,X1) ) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( rinvF(X0,X1)
    <=> rf(X1,X0) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X3,X4] :
      ( rinvF(X3,X4)
    <=> rf(X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f271,plain,
    rinvF(sK5(i2003_11_14_17_19_35232),sK4(sK5(i2003_11_14_17_19_35232))),
    inference(unit_resulting_resolution,[],[f153,f175,f102]) ).

fof(f102,plain,
    ! [X3,X0] :
      ( ~ rinvR(X0,X3)
      | rinvF(X3,sK4(X3))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ( ! [X2] :
              ( ~ cd(X2)
              | ~ rinvF(sK3(X0),X2) )
          & rinvR(X0,sK3(X0)) ) )
      & ( ! [X3] :
            ( ( cd(sK4(X3))
              & rinvF(X3,sK4(X3)) )
            | ~ rinvR(X0,X3) )
        | ~ sP1(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f81,f83,f82]) ).

fof(f82,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( ~ cd(X2)
              | ~ rinvF(X1,X2) )
          & rinvR(X0,X1) )
     => ( ! [X2] :
            ( ~ cd(X2)
            | ~ rinvF(sK3(X0),X2) )
        & rinvR(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ! [X3] :
      ( ? [X4] :
          ( cd(X4)
          & rinvF(X3,X4) )
     => ( cd(sK4(X3))
        & rinvF(X3,sK4(X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ? [X1] :
            ( ! [X2] :
                ( ~ cd(X2)
                | ~ rinvF(X1,X2) )
            & rinvR(X0,X1) ) )
      & ( ! [X3] :
            ( ? [X4] :
                ( cd(X4)
                & rinvF(X3,X4) )
            | ~ rinvR(X0,X3) )
        | ~ sP1(X0) ) ),
    inference(rectify,[],[f80]) ).

fof(f80,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ? [X1] :
            ( ! [X2] :
                ( ~ cd(X2)
                | ~ rinvF(X1,X2) )
            & rinvR(X0,X1) ) )
      & ( ! [X1] :
            ( ? [X2] :
                ( cd(X2)
                & rinvF(X1,X2) )
            | ~ rinvR(X0,X1) )
        | ~ sP1(X0) ) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f175,plain,
    rinvR(i2003_11_14_17_19_35232,sK5(i2003_11_14_17_19_35232)),
    inference(unit_resulting_resolution,[],[f173,f122]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ~ rr(X1,X0)
      | rinvR(X0,X1) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( rinvR(X0,X1)
        | ~ rr(X1,X0) )
      & ( rr(X1,X0)
        | ~ rinvR(X0,X1) ) ),
    inference(nnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( rinvR(X0,X1)
    <=> rr(X1,X0) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X3,X4] :
      ( rinvR(X3,X4)
    <=> rr(X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

fof(f173,plain,
    rr(sK5(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
    inference(unit_resulting_resolution,[],[f171,f113]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( ~ rf(X0,X1)
      | rr(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( rr(X0,X1)
      | ~ rf(X0,X1) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( rf(X0,X1)
     => rr(X0,X1) ),
    inference(rectify,[],[f25]) ).

fof(f25,axiom,
    ! [X3,X4] :
      ( rf(X3,X4)
     => rr(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

fof(f171,plain,
    rf(sK5(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
    inference(unit_resulting_resolution,[],[f168,f123]) ).

fof(f168,plain,
    rinvF(i2003_11_14_17_19_35232,sK5(i2003_11_14_17_19_35232)),
    inference(unit_resulting_resolution,[],[f151,f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | rinvF(X0,sK5(X0)) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f153,plain,
    sP1(i2003_11_14_17_19_35232),
    inference(unit_resulting_resolution,[],[f93,f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sP1(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f213,plain,
    rf(sK4(sK5(i2003_11_14_17_19_35232)),sK2(sK4(sK5(i2003_11_14_17_19_35232)))),
    inference(unit_resulting_resolution,[],[f209,f98]) ).

fof(f98,plain,
    ! [X0] :
      ( ~ cd(X0)
      | rf(X0,sK2(X0)) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f209,plain,
    cd(sK4(sK5(i2003_11_14_17_19_35232))),
    inference(unit_resulting_resolution,[],[f153,f175,f103]) ).

fof(f103,plain,
    ! [X3,X0] :
      ( ~ rinvR(X0,X3)
      | cd(sK4(X3))
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f214,plain,
    ~ cc(sK2(sK4(sK5(i2003_11_14_17_19_35232)))),
    inference(unit_resulting_resolution,[],[f209,f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ~ cd(X0)
      | ~ cc(sK2(X0)) ),
    inference(cnf_transformation,[],[f79]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08  % Problem    : KRS084+1 : TPTP v8.2.0. Released v3.1.0.
% 0.07/0.09  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.29  % Computer : n022.cluster.edu
% 0.08/0.29  % Model    : x86_64 x86_64
% 0.08/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29  % Memory   : 8042.1875MB
% 0.08/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29  % CPULimit   : 300
% 0.08/0.29  % WCLimit    : 300
% 0.08/0.29  % DateTime   : Sat May 18 22:02:22 EDT 2024
% 0.08/0.29  % CPUTime    : 
% 0.08/0.29  % (29524)Running in auto input_syntax mode. Trying TPTP
% 0.08/0.30  % (29528)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.08/0.30  % (29531)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.08/0.30  TRYING [1]
% 0.08/0.30  TRYING [2]
% 0.08/0.30  % (29530)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.08/0.30  % (29525)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.08/0.30  TRYING [3]
% 0.08/0.30  TRYING [4]
% 0.08/0.30  TRYING [1]
% 0.08/0.31  TRYING [2]
% 0.08/0.31  TRYING [5]
% 0.08/0.31  TRYING [3]
% 0.08/0.31  % (29531)First to succeed.
% 0.08/0.31  TRYING [4]
% 0.08/0.31  % (29531)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29524"
% 0.08/0.31  TRYING [5]
% 0.08/0.31  % (29531)Refutation found. Thanks to Tanya!
% 0.08/0.31  % SZS status Unsatisfiable for theBenchmark
% 0.08/0.31  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.31  % (29531)------------------------------
% 0.13/0.31  % (29531)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.31  % (29531)Termination reason: Refutation
% 0.13/0.31  
% 0.13/0.31  % (29531)Memory used [KB]: 915
% 0.13/0.31  % (29531)Time elapsed: 0.004 s
% 0.13/0.31  % (29531)Instructions burned: 11 (million)
% 0.13/0.31  % (29524)Success in time 0.014 s
%------------------------------------------------------------------------------