TSTP Solution File: NUM625+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM625+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n013.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 12:13:21 EDT 2023

% Result   : Theorem 0.24s 0.46s
% Output   : Refutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   51 (  18 unt;   0 def)
%            Number of atoms       :  243 (  44 equ)
%            Maximal formula atoms :   22 (   4 avg)
%            Number of connectives :  310 ( 118   ~; 110   |;  66   &)
%                                         (   9 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   2 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   76 (;  68   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1300,plain,
    $false,
    inference(avatar_sat_refutation,[],[f698,f1297]) ).

fof(f1297,plain,
    ~ spl25_3,
    inference(avatar_contradiction_clause,[],[f1296]) ).

fof(f1296,plain,
    ( $false
    | ~ spl25_3 ),
    inference(subsumption_resolution,[],[f1295,f634]) ).

fof(f634,plain,
    ( aSet0(xQ)
    | ~ spl25_3 ),
    inference(avatar_component_clause,[],[f633]) ).

fof(f633,plain,
    ( spl25_3
  <=> aSet0(xQ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_3])]) ).

fof(f1295,plain,
    ( ~ aSet0(xQ)
    | ~ spl25_3 ),
    inference(subsumption_resolution,[],[f1294,f721]) ).

fof(f721,plain,
    ( aElement0(xp)
    | ~ spl25_3 ),
    inference(subsumption_resolution,[],[f720,f634]) ).

fof(f720,plain,
    ( aElement0(xp)
    | ~ aSet0(xQ) ),
    inference(resolution,[],[f344,f458]) ).

fof(f458,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,X0)
      | aElement0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f176]) ).

fof(f176,plain,
    ! [X0] :
      ( ! [X1] :
          ( aElement0(X1)
          | ~ aElementOf0(X1,X0) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aElementOf0(X1,X0)
         => aElement0(X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',mEOfElem) ).

fof(f344,plain,
    aElementOf0(xp,xQ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,axiom,
    aElementOf0(xp,xQ),
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5173) ).

fof(f1294,plain,
    ( ~ aElement0(xp)
    | ~ aSet0(xQ) ),
    inference(subsumption_resolution,[],[f1275,f606]) ).

fof(f606,plain,
    aElementOf0(xp,xP),
    inference(forward_demodulation,[],[f346,f339]) ).

fof(f339,plain,
    xp = xx,
    inference(cnf_transformation,[],[f120]) ).

fof(f120,axiom,
    xp = xx,
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5496) ).

fof(f346,plain,
    aElementOf0(xx,xP),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,axiom,
    aElementOf0(xx,xP),
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5348) ).

fof(f1275,plain,
    ( ~ aElementOf0(xp,xP)
    | ~ aElement0(xp)
    | ~ aSet0(xQ) ),
    inference(superposition,[],[f594,f608]) ).

fof(f608,plain,
    xP = sdtmndt0(xQ,xp),
    inference(forward_demodulation,[],[f378,f348]) ).

fof(f348,plain,
    xp = szmzizndt0(xQ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,axiom,
    xp = szmzizndt0(xQ),
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5147) ).

fof(f378,plain,
    xP = sdtmndt0(xQ,szmzizndt0(xQ)),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,axiom,
    ( xP = sdtmndt0(xQ,szmzizndt0(xQ))
    & aSet0(xP) ),
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5164) ).

fof(f594,plain,
    ! [X0,X4] :
      ( ~ aElementOf0(X4,sdtmndt0(X0,X4))
      | ~ aElement0(X4)
      | ~ aSet0(X0) ),
    inference(equality_resolution,[],[f593]) ).

fof(f593,plain,
    ! [X2,X0,X4] :
      ( ~ aElementOf0(X4,X2)
      | sdtmndt0(X0,X4) != X2
      | ~ aElement0(X4)
      | ~ aSet0(X0) ),
    inference(equality_resolution,[],[f527]) ).

fof(f527,plain,
    ! [X2,X0,X1,X4] :
      ( X1 != X4
      | ~ aElementOf0(X4,X2)
      | sdtmndt0(X0,X1) != X2
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f323]) ).

fof(f323,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X0,X1) = X2
            | ( ( sK21(X0,X1,X2) = X1
                | ~ aElementOf0(sK21(X0,X1,X2),X0)
                | ~ aElement0(sK21(X0,X1,X2))
                | ~ aElementOf0(sK21(X0,X1,X2),X2) )
              & ( ( sK21(X0,X1,X2) != X1
                  & aElementOf0(sK21(X0,X1,X2),X0)
                  & aElement0(sK21(X0,X1,X2)) )
                | aElementOf0(sK21(X0,X1,X2),X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X4] :
                  ( ( aElementOf0(X4,X2)
                    | X1 = X4
                    | ~ aElementOf0(X4,X0)
                    | ~ aElement0(X4) )
                  & ( ( X1 != X4
                      & aElementOf0(X4,X0)
                      & aElement0(X4) )
                    | ~ aElementOf0(X4,X2) ) )
              & aSet0(X2) )
            | sdtmndt0(X0,X1) != X2 ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f321,f322]) ).

fof(f322,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( X1 = X3
            | ~ aElementOf0(X3,X0)
            | ~ aElement0(X3)
            | ~ aElementOf0(X3,X2) )
          & ( ( X1 != X3
              & aElementOf0(X3,X0)
              & aElement0(X3) )
            | aElementOf0(X3,X2) ) )
     => ( ( sK21(X0,X1,X2) = X1
          | ~ aElementOf0(sK21(X0,X1,X2),X0)
          | ~ aElement0(sK21(X0,X1,X2))
          | ~ aElementOf0(sK21(X0,X1,X2),X2) )
        & ( ( sK21(X0,X1,X2) != X1
            & aElementOf0(sK21(X0,X1,X2),X0)
            & aElement0(sK21(X0,X1,X2)) )
          | aElementOf0(sK21(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f321,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X0,X1) = X2
            | ? [X3] :
                ( ( X1 = X3
                  | ~ aElementOf0(X3,X0)
                  | ~ aElement0(X3)
                  | ~ aElementOf0(X3,X2) )
                & ( ( X1 != X3
                    & aElementOf0(X3,X0)
                    & aElement0(X3) )
                  | aElementOf0(X3,X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X4] :
                  ( ( aElementOf0(X4,X2)
                    | X1 = X4
                    | ~ aElementOf0(X4,X0)
                    | ~ aElement0(X4) )
                  & ( ( X1 != X4
                      & aElementOf0(X4,X0)
                      & aElement0(X4) )
                    | ~ aElementOf0(X4,X2) ) )
              & aSet0(X2) )
            | sdtmndt0(X0,X1) != X2 ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(rectify,[],[f320]) ).

fof(f320,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X0,X1) = X2
            | ? [X3] :
                ( ( X1 = X3
                  | ~ aElementOf0(X3,X0)
                  | ~ aElement0(X3)
                  | ~ aElementOf0(X3,X2) )
                & ( ( X1 != X3
                    & aElementOf0(X3,X0)
                    & aElement0(X3) )
                  | aElementOf0(X3,X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X3] :
                  ( ( aElementOf0(X3,X2)
                    | X1 = X3
                    | ~ aElementOf0(X3,X0)
                    | ~ aElement0(X3) )
                  & ( ( X1 != X3
                      & aElementOf0(X3,X0)
                      & aElement0(X3) )
                    | ~ aElementOf0(X3,X2) ) )
              & aSet0(X2) )
            | sdtmndt0(X0,X1) != X2 ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f319]) ).

fof(f319,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X0,X1) = X2
            | ? [X3] :
                ( ( X1 = X3
                  | ~ aElementOf0(X3,X0)
                  | ~ aElement0(X3)
                  | ~ aElementOf0(X3,X2) )
                & ( ( X1 != X3
                    & aElementOf0(X3,X0)
                    & aElement0(X3) )
                  | aElementOf0(X3,X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X3] :
                  ( ( aElementOf0(X3,X2)
                    | X1 = X3
                    | ~ aElementOf0(X3,X0)
                    | ~ aElement0(X3) )
                  & ( ( X1 != X3
                      & aElementOf0(X3,X0)
                      & aElement0(X3) )
                    | ~ aElementOf0(X3,X2) ) )
              & aSet0(X2) )
            | sdtmndt0(X0,X1) != X2 ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f227]) ).

fof(f227,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( X1 != X3
                  & aElementOf0(X3,X0)
                  & aElement0(X3) ) )
            & aSet0(X2) ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f226]) ).

fof(f226,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( X1 != X3
                  & aElementOf0(X3,X0)
                  & aElement0(X3) ) )
            & aSet0(X2) ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aSet0(X0) )
     => ! [X2] :
          ( sdtmndt0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( X1 != X3
                  & aElementOf0(X3,X0)
                  & aElement0(X3) ) )
            & aSet0(X2) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',mDefDiff) ).

fof(f698,plain,
    spl25_3,
    inference(avatar_split_clause,[],[f697,f633]) ).

fof(f697,plain,
    aSet0(xQ),
    inference(subsumption_resolution,[],[f685,f425]) ).

fof(f425,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,axiom,
    ( isCountable0(szNzAzT0)
    & aSet0(szNzAzT0) ),
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',mNATSet) ).

fof(f685,plain,
    ( aSet0(xQ)
    | ~ aSet0(szNzAzT0) ),
    inference(resolution,[],[f342,f462]) ).

fof(f462,plain,
    ! [X0,X1] :
      ( ~ aSubsetOf0(X1,X0)
      | aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f284]) ).

fof(f284,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ( ~ aElementOf0(sK12(X0,X1),X0)
              & aElementOf0(sK12(X0,X1),X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f282,f283]) ).

fof(f283,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK12(X0,X1),X0)
        & aElementOf0(sK12(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f282,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(rectify,[],[f281]) ).

fof(f281,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(flattening,[],[f280]) ).

fof(f280,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f182]) ).

fof(f182,plain,
    ! [X0] :
      ( ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X0)
                | ~ aElementOf0(X2,X1) )
            & aSet0(X1) ) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,X0) )
            & aSet0(X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',mDefSub) ).

fof(f342,plain,
    aSubsetOf0(xQ,szNzAzT0),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,axiom,
    aSubsetOf0(xQ,szNzAzT0),
    file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5106) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem    : NUM625+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.16  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37  % Computer : n013.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Fri Aug 25 10:50:32 EDT 2023
% 0.16/0.38  % CPUTime    : 
% 0.16/0.38  This is a FOF_CAX_RFO_SEQ problem
% 0.16/0.38  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485
% 0.16/0.38  % (22610)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.44  % (22619)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.24/0.44  % (22613)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.24/0.44  % (22615)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.24/0.44  % (22614)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.24/0.44  % (22617)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.24/0.44  % (22618)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.24/0.45  % (22611)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.24/0.46  % (22619)First to succeed.
% 0.24/0.46  % (22619)Refutation found. Thanks to Tanya!
% 0.24/0.46  % SZS status Theorem for Vampire---4
% 0.24/0.46  % SZS output start Proof for Vampire---4
% See solution above
% 0.24/0.46  % (22619)------------------------------
% 0.24/0.46  % (22619)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.46  % (22619)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.46  % (22619)Termination reason: Refutation
% 0.24/0.46  
% 0.24/0.46  % (22619)Memory used [KB]: 6268
% 0.24/0.46  % (22619)Time elapsed: 0.018 s
% 0.24/0.46  % (22619)------------------------------
% 0.24/0.46  % (22619)------------------------------
% 0.24/0.46  % (22610)Success in time 0.077 s
% 0.24/0.46  % Vampire---4.8 exiting
%------------------------------------------------------------------------------