TSTP Solution File: NUN066+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUN066+1 : TPTP v8.1.2. Released v7.3.0.
% 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 : n001.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 20:50:26 EDT 2023

% Result   : Theorem 6.19s 1.35s
% Output   : Refutation 6.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   75 (  12 unt;   0 def)
%            Number of atoms       :  228 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  247 (  94   ~;  84   |;  61   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   2 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   0 con; 1-1 aty)
%            Number of variables   :  154 (; 116   !;  38   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f41151,plain,
    $false,
    inference(avatar_sat_refutation,[],[f40888,f41147]) ).

fof(f41147,plain,
    ~ spl25_222,
    inference(avatar_contradiction_clause,[],[f41146]) ).

fof(f41146,plain,
    ( $false
    | ~ spl25_222 ),
    inference(subsumption_resolution,[],[f40961,f17439]) ).

fof(f17439,plain,
    ( ! [X4] : ~ r1(X4)
    | ~ spl25_222 ),
    inference(avatar_component_clause,[],[f17438]) ).

fof(f17438,plain,
    ( spl25_222
  <=> ! [X4] : ~ r1(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_222])]) ).

fof(f40961,plain,
    ( ! [X13] : r1(X13)
    | ~ spl25_222 ),
    inference(resolution,[],[f17439,f17734]) ).

fof(f17734,plain,
    ! [X11] :
      ( r1(sK8(sK3(X11)))
      | r1(X11) ),
    inference(resolution,[],[f494,f89]) ).

fof(f89,plain,
    ! [X0] : id(sK8(X0),X0),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( r3(X0,sK9(X0),sK8(X0))
      & r1(sK9(X0))
      & id(sK8(X0),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f24,f54,f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) )
          & id(X1,X0) )
     => ( ? [X2] :
            ( r3(X0,X2,sK8(X0))
            & r1(X2) )
        & id(sK8(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK8(X0))
          & r1(X2) )
     => ( r3(X0,sK9(X0),sK8(X0))
        & r1(sK9(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) )
      & id(X1,X0) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X53] :
    ? [X54] :
      ( ? [X55] :
          ( r3(X53,X55,X54)
          & r1(X55) )
      & id(X54,X53) ),
    file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_4a) ).

fof(f494,plain,
    ! [X0,X1] :
      ( ~ id(X0,sK3(X1))
      | r1(X0)
      | r1(X1) ),
    inference(resolution,[],[f163,f478]) ).

fof(f478,plain,
    ! [X0] :
      ( sP0(X0)
      | r1(X0) ),
    inference(duplicate_literal_removal,[],[f471]) ).

fof(f471,plain,
    ! [X0] :
      ( r1(X0)
      | sP0(X0)
      | sP0(X0) ),
    inference(resolution,[],[f164,f82]) ).

fof(f82,plain,
    ! [X0] :
      ( id(X0,sK4(X0))
      | sP0(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ( r1(sK4(X0))
        & id(X0,sK4(X0)) )
      | sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f41,f48]) ).

fof(f48,plain,
    ! [X0] :
      ( ? [X1] :
          ( r1(X1)
          & id(X0,X1) )
     => ( r1(sK4(X0))
        & id(X0,sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ! [X0] :
      ( ? [X1] :
          ( r1(X1)
          & id(X0,X1) )
      | sP0(X0) ),
    inference(definition_folding,[],[f39,f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ? [X2] :
          ( id(X0,X2)
          & ? [X3] :
              ( r2(X3,X2)
              & ? [X4] :
                  ( r2(X4,X3)
                  & r1(X4) ) ) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f39,plain,
    ! [X0] :
      ( ? [X1] :
          ( r1(X1)
          & id(X0,X1) )
      | ? [X2] :
          ( id(X0,X2)
          & ? [X3] :
              ( r2(X3,X2)
              & ? [X4] :
                  ( r2(X4,X3)
                  & r1(X4) ) ) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ? [X0] :
        ( ! [X1] :
            ( ~ r1(X1)
            | ~ id(X0,X1) )
        & ! [X2] :
            ( ~ id(X0,X2)
            | ! [X3] :
                ( ~ r2(X3,X2)
                | ! [X4] :
                    ( ~ r2(X4,X3)
                    | ~ r1(X4) ) ) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ? [X62] :
        ( ! [X40] :
            ( ~ r1(X40)
            | ~ id(X62,X40) )
        & ! [X45] :
            ( ~ id(X62,X45)
            | ! [X46] :
                ( ~ r2(X46,X45)
                | ! [X39] :
                    ( ~ r2(X39,X46)
                    | ~ r1(X39) ) ) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ? [X62] :
      ( ! [X40] :
          ( ~ r1(X40)
          | ~ id(X62,X40) )
      & ! [X45] :
          ( ~ id(X62,X45)
          | ! [X46] :
              ( ~ r2(X46,X45)
              | ! [X39] :
                  ( ~ r2(X39,X46)
                  | ~ r1(X39) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',nonzerononetwoexistid) ).

fof(f164,plain,
    ! [X2,X3] :
      ( ~ id(X2,sK4(X3))
      | r1(X2)
      | sP0(X3) ),
    inference(resolution,[],[f102,f83]) ).

fof(f83,plain,
    ! [X0] :
      ( r1(sK4(X0))
      | sP0(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ~ r1(X1)
      | r1(X0)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

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/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_8) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ sP0(X1)
      | ~ id(X0,sK3(X1))
      | r1(X0) ),
    inference(resolution,[],[f102,f78]) ).

fof(f78,plain,
    ! [X0] :
      ( r1(sK3(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( ( id(X0,sK1(X0))
        & r2(sK2(X0),sK1(X0))
        & r2(sK3(X0),sK2(X0))
        & r1(sK3(X0)) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f43,f46,f45,f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ? [X1] :
          ( id(X0,X1)
          & ? [X2] :
              ( r2(X2,X1)
              & ? [X3] :
                  ( r2(X3,X2)
                  & r1(X3) ) ) )
     => ( id(X0,sK1(X0))
        & ? [X2] :
            ( r2(X2,sK1(X0))
            & ? [X3] :
                ( r2(X3,X2)
                & r1(X3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ! [X0] :
      ( ? [X2] :
          ( r2(X2,sK1(X0))
          & ? [X3] :
              ( r2(X3,X2)
              & r1(X3) ) )
     => ( r2(sK2(X0),sK1(X0))
        & ? [X3] :
            ( r2(X3,sK2(X0))
            & r1(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ! [X0] :
      ( ? [X3] :
          ( r2(X3,sK2(X0))
          & r1(X3) )
     => ( r2(sK3(X0),sK2(X0))
        & r1(sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0] :
      ( ? [X1] :
          ( id(X0,X1)
          & ? [X2] :
              ( r2(X2,X1)
              & ? [X3] :
                  ( r2(X3,X2)
                  & r1(X3) ) ) )
      | ~ sP0(X0) ),
    inference(rectify,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ? [X2] :
          ( id(X0,X2)
          & ? [X3] :
              ( r2(X3,X2)
              & ? [X4] :
                  ( r2(X4,X3)
                  & r1(X4) ) ) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f40]) ).

fof(f40888,plain,
    spl25_222,
    inference(avatar_split_clause,[],[f40887,f17438]) ).

fof(f40887,plain,
    ! [X0] : ~ r1(X0),
    inference(subsumption_resolution,[],[f40743,f318]) ).

fof(f318,plain,
    ! [X2] : ~ r1(sK13(X2)),
    inference(resolution,[],[f215,f84]) ).

fof(f84,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/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_5) ).

fof(f215,plain,
    ! [X2,X3] :
      ( ~ id(X2,sK13(X3))
      | ~ r1(X2) ),
    inference(resolution,[],[f105,f159]) ).

fof(f159,plain,
    ! [X2] : r2(X2,sK13(X2)),
    inference(resolution,[],[f99,f84]) ).

fof(f99,plain,
    ! [X2,X0] :
      ( ~ id(X2,sK13(X0))
      | r2(X0,X2) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X2] :
      ( ( ~ id(X2,sK13(X0))
        & ~ r2(X0,X2) )
      | ( r2(X0,X2)
        & id(X2,sK13(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f26,f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( ~ id(X2,X1)
            & ~ r2(X0,X2) )
          | ( r2(X0,X2)
            & id(X2,X1) ) )
     => ! [X2] :
          ( ( ~ id(X2,sK13(X0))
            & ~ r2(X0,X2) )
          | ( r2(X0,X2)
            & id(X2,sK13(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( ~ id(X2,X1)
        & ~ r2(X0,X2) )
      | ( r2(X0,X2)
        & id(X2,X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( ~ id(X4,X3)
        & ~ r2(X2,X4) )
      | ( r2(X2,X4)
        & id(X4,X3) ) ),
    file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_2) ).

fof(f105,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/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_7a) ).

fof(f40743,plain,
    ! [X0] :
      ( ~ r1(X0)
      | r1(sK13(X0)) ),
    inference(resolution,[],[f40742,f555]) ).

fof(f555,plain,
    ! [X0,X1] :
      ( ~ id(X0,sK2(X1))
      | ~ r1(X0)
      | r1(X1) ),
    inference(resolution,[],[f219,f478]) ).

fof(f219,plain,
    ! [X12,X13] :
      ( ~ sP0(X13)
      | ~ id(X12,sK2(X13))
      | ~ r1(X12) ),
    inference(resolution,[],[f105,f79]) ).

fof(f79,plain,
    ! [X0] :
      ( r2(sK3(X0),sK2(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f40742,plain,
    ! [X2] : id(X2,sK2(sK13(X2))),
    inference(subsumption_resolution,[],[f40741,f318]) ).

fof(f40741,plain,
    ! [X2] :
      ( id(X2,sK2(sK13(X2)))
      | r1(sK13(X2)) ),
    inference(subsumption_resolution,[],[f40738,f322]) ).

fof(f322,plain,
    ! [X3] : sP0(sK13(X3)),
    inference(subsumption_resolution,[],[f319,f83]) ).

fof(f319,plain,
    ! [X3] :
      ( ~ r1(sK4(sK13(X3)))
      | sP0(sK13(X3)) ),
    inference(resolution,[],[f215,f147]) ).

fof(f147,plain,
    ! [X2] :
      ( id(sK4(X2),X2)
      | sP0(X2) ),
    inference(resolution,[],[f100,f82]) ).

fof(f100,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/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_6) ).

fof(f40738,plain,
    ! [X2] :
      ( id(X2,sK2(sK13(X2)))
      | ~ sP0(sK13(X2))
      | r1(sK13(X2)) ),
    inference(resolution,[],[f3161,f479]) ).

fof(f479,plain,
    ! [X0] :
      ( id(X0,sK1(X0))
      | r1(X0) ),
    inference(resolution,[],[f478,f81]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | id(X0,sK1(X0)) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f3161,plain,
    ! [X50,X49] :
      ( ~ id(sK13(X49),sK1(X50))
      | id(X49,sK2(X50))
      | ~ sP0(X50) ),
    inference(resolution,[],[f309,f80]) ).

fof(f80,plain,
    ! [X0] :
      ( r2(sK2(X0),sK1(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f309,plain,
    ! [X3,X4,X5] :
      ( ~ r2(X3,X4)
      | id(X5,X3)
      | ~ id(sK13(X5),X4) ),
    inference(resolution,[],[f106,f159]) ).

fof(f106,plain,
    ! [X2,X3,X0,X1] :
      ( ~ r2(X0,X3)
      | ~ r2(X1,X2)
      | id(X0,X1)
      | ~ id(X3,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( id(X0,X1)
      | ! [X2] :
          ( ~ r2(X1,X2)
          | ! [X3] :
              ( ~ r2(X0,X3)
              | ~ id(X3,X2) ) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X49,X50] :
      ( id(X49,X50)
      | ! [X51] :
          ( ~ r2(X50,X51)
          | ! [X52] :
              ( ~ r2(X49,X52)
              | ~ id(X52,X51) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_3a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUN066+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35  % Computer : n001.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
% 0.14/0.35  % DateTime   : Wed Aug 30 16:49:24 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.41  % (14883)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41  % (14902)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on Vampire---4 for (1451ds/0Mi)
% 0.21/0.41  % (14903)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on Vampire---4 for (569ds/0Mi)
% 0.21/0.41  % (14904)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)
% 0.21/0.41  % (14906)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on Vampire---4 for (396ds/0Mi)
% 0.21/0.41  % (14905)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.41  % (14907)dis+11_4:5_nm=4_216 on Vampire---4 for (216ds/0Mi)
% 0.21/0.41  % (14908)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)
% 0.21/0.42  TRYING [1]
% 0.21/0.42  TRYING [2]
% 0.21/0.42  TRYING [1]
% 0.21/0.42  TRYING [1]
% 0.21/0.42  TRYING [1]
% 0.21/0.42  TRYING [2]
% 0.21/0.42  TRYING [2]
% 0.21/0.42  TRYING [2]
% 0.21/0.42  TRYING [3]
% 0.21/0.42  TRYING [3]
% 0.21/0.42  TRYING [3]
% 0.21/0.42  TRYING [3]
% 0.21/0.43  TRYING [4]
% 0.21/0.43  TRYING [4]
% 0.21/0.45  TRYING [5]
% 0.21/0.45  TRYING [5]
% 0.21/0.46  TRYING [4]
% 0.21/0.47  TRYING [4]
% 0.21/0.50  TRYING [6]
% 0.21/0.52  TRYING [6]
% 0.21/0.61  TRYING [7]
% 0.21/0.62  TRYING [5]
% 0.21/0.68  TRYING [5]
% 0.21/0.70  TRYING [7]
% 5.69/1.23  TRYING [8]
% 6.19/1.34  % (14907)First to succeed.
% 6.19/1.35  % (14907)Refutation found. Thanks to Tanya!
% 6.19/1.35  % SZS status Theorem for Vampire---4
% 6.19/1.35  % SZS output start Proof for Vampire---4
% See solution above
% 6.19/1.35  % (14907)------------------------------
% 6.19/1.35  % (14907)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 6.19/1.35  % (14907)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 6.19/1.35  % (14907)Termination reason: Refutation
% 6.19/1.35  
% 6.19/1.35  % (14907)Memory used [KB]: 25202
% 6.19/1.35  % (14907)Time elapsed: 0.935 s
% 6.19/1.35  % (14907)------------------------------
% 6.19/1.35  % (14907)------------------------------
% 6.19/1.35  % (14883)Success in time 0.981 s
% 6.19/1.35  % Vampire---4.8 exiting
%------------------------------------------------------------------------------