TSTP Solution File: NUN073+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUN073+2 : 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 : 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 : Thu Aug 31 12:52:35 EDT 2023

% Result   : Theorem 0.20s 0.42s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   48 (  20 unt;   0 def)
%            Number of atoms       :  150 (  47 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  167 (  65   ~;  45   |;  50   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-1 aty)
%            Number of variables   :   87 (;  60   !;  27   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f170,plain,
    $false,
    inference(resolution,[],[f161,f120]) ).

fof(f120,plain,
    ! [X0] : ~ r2(X0,sK24),
    inference(forward_demodulation,[],[f117,f116]) ).

fof(f116,plain,
    sK4 = sK24,
    inference(resolution,[],[f60,f103]) ).

fof(f103,plain,
    ! [X1] :
      ( sK24 = X1
      | ~ r1(X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X1] :
      ( ( sK24 = X1
        & r1(X1) )
      | ( sK24 != X1
        & ~ r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f1,f58]) ).

fof(f58,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( X0 = X1
          & r1(X1) )
        | ( X0 != X1
          & ~ r1(X1) ) )
   => ! [X1] :
        ( ( sK24 = X1
          & r1(X1) )
        | ( sK24 != X1
          & ~ r1(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( X0 = X1
        & r1(X1) )
      | ( X0 != X1
        & ~ r1(X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.b4X87j061Q/Vampire---4.8_28264',axiom_1) ).

fof(f60,plain,
    r1(sK4),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( r2(sK1,sK0)
    & r2(sK2,sK1)
    & r1(sK2)
    & sK0 = sK3
    & r2(sK4,sK3)
    & r1(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f25,f30,f29,f28,f27,f26]) ).

fof(f26,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( r2(X1,X0)
            & ? [X2] :
                ( r2(X2,X1)
                & r1(X2) ) )
        & ? [X3] :
            ( X0 = X3
            & ? [X4] :
                ( r2(X4,X3)
                & r1(X4) ) ) )
   => ( ? [X1] :
          ( r2(X1,sK0)
          & ? [X2] :
              ( r2(X2,X1)
              & r1(X2) ) )
      & ? [X3] :
          ( sK0 = X3
          & ? [X4] :
              ( r2(X4,X3)
              & r1(X4) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ( ? [X1] :
        ( r2(X1,sK0)
        & ? [X2] :
            ( r2(X2,X1)
            & r1(X2) ) )
   => ( r2(sK1,sK0)
      & ? [X2] :
          ( r2(X2,sK1)
          & r1(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ( ? [X2] :
        ( r2(X2,sK1)
        & r1(X2) )
   => ( r2(sK2,sK1)
      & r1(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ( ? [X3] :
        ( sK0 = X3
        & ? [X4] :
            ( r2(X4,X3)
            & r1(X4) ) )
   => ( sK0 = sK3
      & ? [X4] :
          ( r2(X4,sK3)
          & r1(X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ( ? [X4] :
        ( r2(X4,sK3)
        & r1(X4) )
   => ( r2(sK4,sK3)
      & r1(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ? [X0] :
      ( ? [X1] :
          ( r2(X1,X0)
          & ? [X2] :
              ( r2(X2,X1)
              & r1(X2) ) )
      & ? [X3] :
          ( X0 = X3
          & ? [X4] :
              ( r2(X4,X3)
              & r1(X4) ) ) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0] :
        ( ! [X1] :
            ( ~ r2(X1,X0)
            | ! [X2] :
                ( ~ r2(X2,X1)
                | ~ r1(X2) ) )
        | ! [X3] :
            ( X0 != X3
            | ! [X4] :
                ( ~ r2(X4,X3)
                | ~ r1(X4) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X38] :
        ( ! [X22] :
            ( ~ r2(X22,X38)
            | ! [X16] :
                ( ~ r2(X16,X22)
                | ~ r1(X16) ) )
        | ! [X21] :
            ( X21 != X38
            | ! [X15] :
                ( ~ r2(X15,X21)
                | ~ r1(X15) ) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X38] :
      ( ! [X22] :
          ( ~ r2(X22,X38)
          | ! [X16] :
              ( ~ r2(X16,X22)
              | ~ r1(X16) ) )
      | ! [X21] :
          ( X21 != X38
          | ! [X15] :
              ( ~ r2(X15,X21)
              | ~ r1(X15) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.b4X87j061Q/Vampire---4.8_28264',oneuneqtwo) ).

fof(f117,plain,
    ! [X0] : ~ r2(X0,sK4),
    inference(resolution,[],[f60,f107]) ).

fof(f107,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | ~ r1(X2) ),
    inference(equality_resolution,[],[f81]) ).

fof(f81,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X0,X1)
      | X1 != X2
      | ~ r1(X2) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | ! [X2] :
          ( X1 != X2
          | ~ r1(X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X40,X41] :
      ( ~ r2(X40,X41)
      | ! [X42] :
          ( X41 != X42
          | ~ r1(X42) ) ),
    file('/export/starexec/sandbox/tmp/tmp.b4X87j061Q/Vampire---4.8_28264',axiom_7a) ).

fof(f161,plain,
    r2(sK24,sK24),
    inference(backward_demodulation,[],[f119,f158]) ).

fof(f158,plain,
    sK0 = sK24,
    inference(resolution,[],[f130,f145]) ).

fof(f145,plain,
    r2(sK0,sK0),
    inference(backward_demodulation,[],[f65,f140]) ).

fof(f140,plain,
    sK0 = sK1,
    inference(forward_demodulation,[],[f138,f133]) ).

fof(f133,plain,
    sK0 = sK13(sK24),
    inference(resolution,[],[f119,f79]) ).

fof(f79,plain,
    ! [X2,X0] :
      ( sK13(X0) = X2
      | ~ r2(X0,X2) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X2] :
      ( ( sK13(X0) = X2
        & r2(X0,X2) )
      | ( sK13(X0) != X2
        & ~ r2(X0,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f18,f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( X1 = X2
            & r2(X0,X2) )
          | ( X1 != X2
            & ~ r2(X0,X2) ) )
     => ! [X2] :
          ( ( sK13(X0) = X2
            & r2(X0,X2) )
          | ( sK13(X0) != X2
            & ~ r2(X0,X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( X1 = X2
        & r2(X0,X2) )
      | ( X1 != X2
        & ~ r2(X0,X2) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( X3 = X4
        & r2(X2,X4) )
      | ( X3 != X4
        & ~ r2(X2,X4) ) ),
    file('/export/starexec/sandbox/tmp/tmp.b4X87j061Q/Vampire---4.8_28264',axiom_2) ).

fof(f138,plain,
    sK1 = sK13(sK24),
    inference(resolution,[],[f124,f79]) ).

fof(f124,plain,
    r2(sK24,sK1),
    inference(backward_demodulation,[],[f64,f121]) ).

fof(f121,plain,
    sK2 = sK24,
    inference(resolution,[],[f63,f103]) ).

fof(f63,plain,
    r1(sK2),
    inference(cnf_transformation,[],[f31]) ).

fof(f64,plain,
    r2(sK2,sK1),
    inference(cnf_transformation,[],[f31]) ).

fof(f65,plain,
    r2(sK1,sK0),
    inference(cnf_transformation,[],[f31]) ).

fof(f130,plain,
    ! [X0] :
      ( ~ r2(X0,sK0)
      | sK24 = X0 ),
    inference(resolution,[],[f119,f108]) ).

fof(f108,plain,
    ! [X3,X0,X1] :
      ( X0 = X1
      | ~ r2(X1,X3)
      | ~ r2(X0,X3) ),
    inference(equality_resolution,[],[f82]) ).

fof(f82,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | ~ r2(X1,X2)
      | X2 != X3
      | ~ r2(X0,X3) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ! [X2] :
          ( ~ r2(X1,X2)
          | ! [X3] :
              ( X2 != X3
              | ~ r2(X0,X3) ) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X25,X26] :
      ( X25 = X26
      | ! [X27] :
          ( ~ r2(X26,X27)
          | ! [X28] :
              ( X27 != X28
              | ~ r2(X25,X28) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.b4X87j061Q/Vampire---4.8_28264',axiom_3a) ).

fof(f119,plain,
    r2(sK24,sK0),
    inference(backward_demodulation,[],[f115,f116]) ).

fof(f115,plain,
    r2(sK4,sK0),
    inference(forward_demodulation,[],[f61,f62]) ).

fof(f62,plain,
    sK0 = sK3,
    inference(cnf_transformation,[],[f31]) ).

fof(f61,plain,
    r2(sK4,sK3),
    inference(cnf_transformation,[],[f31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUN073+2 : TPTP v8.1.2. Released v7.3.0.
% 0.03/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun Aug 27 09:46:11 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.35  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.b4X87j061Q/Vampire---4.8_28264
% 0.13/0.35  % (28372)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41  % (28374)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.20/0.41  % (28377)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.20/0.41  % (28376)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.20/0.41  % (28373)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.20/0.41  % (28378)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.20/0.41  % (28379)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.20/0.41  % (28375)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.20/0.42  % (28376)First to succeed.
% 0.20/0.42  % (28377)Also succeeded, but the first one will report.
% 0.20/0.42  % (28378)Also succeeded, but the first one will report.
% 0.20/0.42  % (28376)Refutation found. Thanks to Tanya!
% 0.20/0.42  % SZS status Theorem for Vampire---4
% 0.20/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.42  % (28376)------------------------------
% 0.20/0.42  % (28376)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.42  % (28376)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.42  % (28376)Termination reason: Refutation
% 0.20/0.42  
% 0.20/0.42  % (28376)Memory used [KB]: 9978
% 0.20/0.42  % (28376)Time elapsed: 0.007 s
% 0.20/0.42  % (28376)------------------------------
% 0.20/0.42  % (28376)------------------------------
% 0.20/0.42  % (28372)Success in time 0.065 s
% 0.20/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------