TSTP Solution File: NUN062+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 08:45:00 EDT 2024

% Result   : Theorem 0.14s 0.32s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   64 (  13 unt;   0 def)
%            Number of atoms       :  211 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  219 (  72   ~;  51   |;  85   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-2 aty)
%            Number of variables   :  181 ( 123   !;  58   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f326,plain,
    $false,
    inference(resolution,[],[f317,f306]) ).

fof(f306,plain,
    ! [X0] : id(sK30,X0),
    inference(resolution,[],[f300,f126]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | id(X1,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( id(X1,X0)
      | ~ id(X0,X1) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X14,X15] :
      ( id(X15,X14)
      | ~ id(X14,X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

fof(f300,plain,
    ! [X0] : id(X0,sK30),
    inference(resolution,[],[f299,f164]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( ~ sP8(X0,X1)
      | id(X0,X1) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ( r1(X0)
        & id(X0,X1) )
      | ~ sP8(X0,X1) ),
    inference(rectify,[],[f104]) ).

fof(f104,plain,
    ! [X1,X0] :
      ( ( r1(X1)
        & id(X1,X0) )
      | ~ sP8(X1,X0) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X1,X0] :
      ( ( r1(X1)
        & id(X1,X0) )
      | ~ sP8(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f299,plain,
    ! [X0] : sP8(X0,sK30),
    inference(resolution,[],[f298,f166]) ).

fof(f166,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sP8(X1,sK30) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X1] :
      ( ( ~ id(X1,sK30)
        & ~ r1(X1) )
      | sP8(X1,sK30) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f57,f106]) ).

fof(f106,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( ~ id(X1,X0)
          & ~ r1(X1) )
        | sP8(X1,X0) )
   => ! [X1] :
        ( ( ~ id(X1,sK30)
          & ~ r1(X1) )
        | sP8(X1,sK30) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ? [X0] :
    ! [X1] :
      ( ( ~ id(X1,X0)
        & ~ r1(X1) )
      | sP8(X1,X0) ),
    inference(definition_folding,[],[f1,f56]) ).

fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( ~ id(X1,X0)
        & ~ r1(X1) )
      | ( r1(X1)
        & id(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(f298,plain,
    ! [X0] : r1(X0),
    inference(subsumption_resolution,[],[f296,f196]) ).

fof(f196,plain,
    ! [X0] : r1(sK10(X0)),
    inference(resolution,[],[f195,f110]) ).

fof(f110,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] : id(X0,X0),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X13] : id(X13,X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f195,plain,
    ! [X0,X1] :
      ( ~ id(sK25(sK9,X0),X1)
      | r1(sK10(X0)) ),
    inference(resolution,[],[f142,f109]) ).

fof(f109,plain,
    ! [X2,X3,X1] :
      ( ~ r3(sK9,X2,X3)
      | ~ id(X3,X1)
      | r1(sK10(X2)) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X1,X2] :
      ( ! [X3] :
          ( ~ r3(sK9,X2,X3)
          | ~ id(X3,X1) )
      | ( r1(sK10(X2))
        & id(X2,sK10(X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f39,f59,f58]) ).

fof(f58,plain,
    ( ? [X0] :
      ! [X1,X2] :
        ( ! [X3] :
            ( ~ r3(X0,X2,X3)
            | ~ id(X3,X1) )
        | ? [X4] :
            ( r1(X4)
            & id(X2,X4) ) )
   => ! [X2,X1] :
        ( ! [X3] :
            ( ~ r3(sK9,X2,X3)
            | ~ id(X3,X1) )
        | ? [X4] :
            ( r1(X4)
            & id(X2,X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X2] :
      ( ? [X4] :
          ( r1(X4)
          & id(X2,X4) )
     => ( r1(sK10(X2))
        & id(X2,sK10(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ? [X0] :
    ! [X1,X2] :
      ( ! [X3] :
          ( ~ r3(X0,X2,X3)
          | ~ id(X3,X1) )
      | ? [X4] :
          ( r1(X4)
          & id(X2,X4) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ! [X0] :
      ? [X1,X2] :
        ( ? [X3] :
            ( r3(X0,X2,X3)
            & id(X3,X1) )
        & ! [X4] :
            ( ~ r1(X4)
            | ~ id(X2,X4) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X37] :
      ? [X45,X62] :
        ( ? [X46] :
            ( r3(X37,X62,X46)
            & id(X46,X45) )
        & ! [X39] :
            ( ~ r1(X39)
            | ~ id(X62,X39) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X37] :
    ? [X45,X62] :
      ( ? [X46] :
          ( r3(X37,X62,X46)
          & id(X46,X45) )
      & ! [X39] :
          ( ~ r1(X39)
          | ~ id(X62,X39) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbersid) ).

fof(f142,plain,
    ! [X0,X1] : r3(X0,X1,sK25(X0,X1)),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( r3(X0,X1,sK25(X0,X1))
      & r2(sK25(X0,X1),sK24(X0,X1))
      & r3(X0,sK27(X0,X1),sK26(X0,X1))
      & r2(X1,sK27(X0,X1))
      & id(sK26(X0,X1),sK24(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26,sK27])],[f32,f88,f87,f86,f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r3(X0,X1,X3)
              & r2(X3,X2) )
          & ? [X4] :
              ( ? [X5] :
                  ( r3(X0,X5,X4)
                  & r2(X1,X5) )
              & id(X4,X2) ) )
     => ( ? [X3] :
            ( r3(X0,X1,X3)
            & r2(X3,sK24(X0,X1)) )
        & ? [X4] :
            ( ? [X5] :
                ( r3(X0,X5,X4)
                & r2(X1,X5) )
            & id(X4,sK24(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,sK24(X0,X1)) )
     => ( r3(X0,X1,sK25(X0,X1))
        & r2(sK25(X0,X1),sK24(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,sK24(X0,X1)) )
     => ( ? [X5] :
            ( r3(X0,X5,sK26(X0,X1))
            & r2(X1,X5) )
        & id(sK26(X0,X1),sK24(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X5,sK26(X0,X1))
          & r2(X1,X5) )
     => ( r3(X0,sK27(X0,X1),sK26(X0,X1))
        & r2(X1,sK27(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,X2) )
      & ? [X4] :
          ( ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,X2) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X37,X38] :
    ? [X39] :
      ( ? [X42] :
          ( r3(X37,X38,X42)
          & r2(X42,X39) )
      & ? [X40] :
          ( ? [X41] :
              ( r3(X37,X41,X40)
              & r2(X38,X41) )
          & id(X40,X39) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).

fof(f296,plain,
    ! [X0] :
      ( r1(X0)
      | ~ r1(sK10(X0)) ),
    inference(resolution,[],[f272,f128]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( ~ sP2(X0,X1)
      | ~ r1(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ( ~ r1(X0)
        & ~ r1(X1) )
      | ~ sP2(X0,X1) ),
    inference(rectify,[],[f78]) ).

fof(f78,plain,
    ! [X1,X0] :
      ( ( ~ r1(X1)
        & ~ r1(X0) )
      | ~ sP2(X1,X0) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X1,X0] :
      ( ( ~ r1(X1)
        & ~ r1(X0) )
      | ~ sP2(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f272,plain,
    ! [X0] :
      ( sP2(sK10(X0),X0)
      | r1(X0) ),
    inference(resolution,[],[f129,f201]) ).

fof(f201,plain,
    ! [X0] : id(X0,sK10(X0)),
    inference(resolution,[],[f194,f110]) ).

fof(f194,plain,
    ! [X0,X1] :
      ( ~ id(sK25(sK9,X0),X1)
      | id(X0,sK10(X0)) ),
    inference(resolution,[],[f142,f108]) ).

fof(f108,plain,
    ! [X2,X3,X1] :
      ( ~ r3(sK9,X2,X3)
      | ~ id(X3,X1)
      | id(X2,sK10(X2)) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ~ id(X0,X1)
      | sP2(X1,X0)
      | r1(X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( r1(X1)
        & r1(X0) )
      | sP2(X1,X0)
      | ~ id(X0,X1) ),
    inference(definition_folding,[],[f28,f44]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( r1(X1)
        & r1(X0) )
      | ( ~ r1(X1)
        & ~ r1(X0) )
      | ~ id(X0,X1) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X19,X20] :
      ( ( r1(X20)
        & r1(X19) )
      | ( ~ r1(X20)
        & ~ r1(X19) )
      | ~ id(X19,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

fof(f317,plain,
    ! [X2,X0,X1] : ~ id(X0,sK23(X1,X2)),
    inference(resolution,[],[f316,f134]) ).

fof(f134,plain,
    ! [X0,X1] : r2(X1,sK23(X0,X1)),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( r4(X0,X1,sK21(X0,X1))
      & r3(sK21(X0,X1),X0,sK20(X0,X1))
      & r4(X0,sK23(X0,X1),sK22(X0,X1))
      & r2(X1,sK23(X0,X1))
      & id(sK22(X0,X1),sK20(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f31,f83,f82,f81,f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r4(X0,X1,X3)
              & r3(X3,X0,X2) )
          & ? [X4] :
              ( ? [X5] :
                  ( r4(X0,X5,X4)
                  & r2(X1,X5) )
              & id(X4,X2) ) )
     => ( ? [X3] :
            ( r4(X0,X1,X3)
            & r3(X3,X0,sK20(X0,X1)) )
        & ? [X4] :
            ( ? [X5] :
                ( r4(X0,X5,X4)
                & r2(X1,X5) )
            & id(X4,sK20(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r4(X0,X1,X3)
          & r3(X3,X0,sK20(X0,X1)) )
     => ( r4(X0,X1,sK21(X0,X1))
        & r3(sK21(X0,X1),X0,sK20(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,sK20(X0,X1)) )
     => ( ? [X5] :
            ( r4(X0,X5,sK22(X0,X1))
            & r2(X1,X5) )
        & id(sK22(X0,X1),sK20(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r4(X0,X5,sK22(X0,X1))
          & r2(X1,X5) )
     => ( r4(X0,sK23(X0,X1),sK22(X0,X1))
        & r2(X1,sK23(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r4(X0,X1,X3)
          & r3(X3,X0,X2) )
      & ? [X4] :
          ( ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,X2) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X43,X44] :
    ? [X45] :
      ( ? [X48] :
          ( r4(X43,X44,X48)
          & r3(X48,X43,X45) )
      & ? [X46] :
          ( ? [X47] :
              ( r4(X43,X47,X46)
              & r2(X44,X47) )
          & id(X46,X45) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).

fof(f316,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X0,X1)
      | ~ id(X2,X1) ),
    inference(subsumption_resolution,[],[f131,f298]) ).

fof(f131,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X0,X1)
      | ~ r1(X2)
      | ~ id(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | ! [X2] :
          ( ~ r1(X2)
          | ~ id(X2,X1) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X64,X65] :
      ( ~ r2(X64,X65)
      | ! [X66] :
          ( ~ r1(X66)
          | ~ id(X66,X65) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem    : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.02/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30  % Computer : n005.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Fri May  3 18:52:08 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.10/0.30  % (22452)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.31  % (22458)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.32  % (22454)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.32  % (22453)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.32  % (22455)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)
% 0.14/0.32  % (22457)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.32  % (22459)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)
% 0.14/0.32  TRYING [1]
% 0.14/0.32  TRYING [1]
% 0.14/0.32  TRYING [2]
% 0.14/0.32  TRYING [1]
% 0.14/0.32  TRYING [2]
% 0.14/0.32  TRYING [2]
% 0.14/0.32  % (22457)First to succeed.
% 0.14/0.32  % (22456)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.32  % (22457)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22452"
% 0.14/0.32  % (22457)Refutation found. Thanks to Tanya!
% 0.14/0.32  % SZS status Theorem for theBenchmark
% 0.14/0.32  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.32  % (22457)------------------------------
% 0.14/0.32  % (22457)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.32  % (22457)Termination reason: Refutation
% 0.14/0.32  
% 0.14/0.32  % (22457)Memory used [KB]: 929
% 0.14/0.32  % (22457)Time elapsed: 0.006 s
% 0.14/0.32  % (22457)Instructions burned: 9 (million)
% 0.14/0.32  % (22452)Success in time 0.021 s
%------------------------------------------------------------------------------