TSTP Solution File: NUM555+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM555+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 : n009.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 20:20:41 EDT 2023

% Result   : Theorem 1.28s 0.59s
% Output   : Refutation 1.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   30 (  10 unt;   0 def)
%            Number of atoms       :  172 (  34 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  227 (  85   ~;  77   |;  54   &)
%                                         (   9 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   61 (;  57   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3186,plain,
    $false,
    inference(resolution,[],[f3184,f230]) ).

fof(f230,plain,
    aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(flattening,[],[f72]) ).

fof(f72,negated_conjecture,
    ~ ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(negated_conjecture,[],[f71]) ).

fof(f71,conjecture,
    ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
    file('/export/starexec/sandbox2/tmp/tmp.6zQlQoskOX/Vampire---4.8_4485',m__) ).

fof(f3184,plain,
    ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(resolution,[],[f3178,f242]) ).

fof(f242,plain,
    aSet0(xQ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    ( xk = sbrdtbr0(xQ)
    & isFinite0(xQ)
    & aSet0(xQ) ),
    file('/export/starexec/sandbox2/tmp/tmp.6zQlQoskOX/Vampire---4.8_4485',m__2291) ).

fof(f3178,plain,
    ( ~ aSet0(xQ)
    | ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
    inference(resolution,[],[f3125,f237]) ).

fof(f237,plain,
    aElement0(xy),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,axiom,
    ( aElementOf0(xy,xQ)
    & aElement0(xy) ),
    file('/export/starexec/sandbox2/tmp/tmp.6zQlQoskOX/Vampire---4.8_4485',m__2304) ).

fof(f3125,plain,
    ! [X138] :
      ( ~ aElement0(X138)
      | ~ aElementOf0(xx,sdtmndt0(xQ,X138))
      | ~ aSet0(xQ) ),
    inference(resolution,[],[f835,f231]) ).

fof(f231,plain,
    ~ aElementOf0(xx,xQ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,axiom,
    ~ aElementOf0(xx,xQ),
    file('/export/starexec/sandbox2/tmp/tmp.6zQlQoskOX/Vampire---4.8_4485',m__2323) ).

fof(f835,plain,
    ! [X2,X3,X4] :
      ( aElementOf0(X4,X3)
      | ~ aSet0(X3)
      | ~ aElementOf0(X4,sdtmndt0(X3,X2))
      | ~ aElement0(X2) ),
    inference(resolution,[],[f833,f325]) ).

fof(f325,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP3(X0,X1,X2)
      | ~ aElementOf0(X4,X2)
      | aElementOf0(X4,X1) ),
    inference(cnf_transformation,[],[f215]) ).

fof(f215,plain,
    ! [X0,X1,X2] :
      ( ( sP3(X0,X1,X2)
        | ( ( sK14(X0,X1,X2) = X0
            | ~ aElementOf0(sK14(X0,X1,X2),X1)
            | ~ aElement0(sK14(X0,X1,X2))
            | ~ aElementOf0(sK14(X0,X1,X2),X2) )
          & ( ( sK14(X0,X1,X2) != X0
              & aElementOf0(sK14(X0,X1,X2),X1)
              & aElement0(sK14(X0,X1,X2)) )
            | aElementOf0(sK14(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( aElementOf0(X4,X2)
              | X0 = X4
              | ~ aElementOf0(X4,X1)
              | ~ aElement0(X4) )
            & ( ( X0 != X4
                & aElementOf0(X4,X1)
                & aElement0(X4) )
              | ~ aElementOf0(X4,X2) ) )
        | ~ sP3(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f213,f214]) ).

fof(f214,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( X0 = X3
            | ~ aElementOf0(X3,X1)
            | ~ aElement0(X3)
            | ~ aElementOf0(X3,X2) )
          & ( ( X0 != X3
              & aElementOf0(X3,X1)
              & aElement0(X3) )
            | aElementOf0(X3,X2) ) )
     => ( ( sK14(X0,X1,X2) = X0
          | ~ aElementOf0(sK14(X0,X1,X2),X1)
          | ~ aElement0(sK14(X0,X1,X2))
          | ~ aElementOf0(sK14(X0,X1,X2),X2) )
        & ( ( sK14(X0,X1,X2) != X0
            & aElementOf0(sK14(X0,X1,X2),X1)
            & aElement0(sK14(X0,X1,X2)) )
          | aElementOf0(sK14(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f213,plain,
    ! [X0,X1,X2] :
      ( ( sP3(X0,X1,X2)
        | ? [X3] :
            ( ( X0 = X3
              | ~ aElementOf0(X3,X1)
              | ~ aElement0(X3)
              | ~ aElementOf0(X3,X2) )
            & ( ( X0 != X3
                & aElementOf0(X3,X1)
                & aElement0(X3) )
              | aElementOf0(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( aElementOf0(X4,X2)
              | X0 = X4
              | ~ aElementOf0(X4,X1)
              | ~ aElement0(X4) )
            & ( ( X0 != X4
                & aElementOf0(X4,X1)
                & aElement0(X4) )
              | ~ aElementOf0(X4,X2) ) )
        | ~ sP3(X0,X1,X2) ) ),
    inference(rectify,[],[f212]) ).

fof(f212,plain,
    ! [X1,X0,X2] :
      ( ( sP3(X1,X0,X2)
        | ? [X3] :
            ( ( X1 = X3
              | ~ aElementOf0(X3,X0)
              | ~ aElement0(X3)
              | ~ aElementOf0(X3,X2) )
            & ( ( X1 != X3
                & aElementOf0(X3,X0)
                & aElement0(X3) )
              | aElementOf0(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( aElementOf0(X3,X2)
              | X1 = X3
              | ~ aElementOf0(X3,X0)
              | ~ aElement0(X3) )
            & ( ( X1 != X3
                & aElementOf0(X3,X0)
                & aElement0(X3) )
              | ~ aElementOf0(X3,X2) ) )
        | ~ sP3(X1,X0,X2) ) ),
    inference(flattening,[],[f211]) ).

fof(f211,plain,
    ! [X1,X0,X2] :
      ( ( sP3(X1,X0,X2)
        | ? [X3] :
            ( ( X1 = X3
              | ~ aElementOf0(X3,X0)
              | ~ aElement0(X3)
              | ~ aElementOf0(X3,X2) )
            & ( ( X1 != X3
                & aElementOf0(X3,X0)
                & aElement0(X3) )
              | aElementOf0(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( aElementOf0(X3,X2)
              | X1 = X3
              | ~ aElementOf0(X3,X0)
              | ~ aElement0(X3) )
            & ( ( X1 != X3
                & aElementOf0(X3,X0)
                & aElement0(X3) )
              | ~ aElementOf0(X3,X2) ) )
        | ~ sP3(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f167]) ).

fof(f167,plain,
    ! [X1,X0,X2] :
      ( sP3(X1,X0,X2)
    <=> ! [X3] :
          ( aElementOf0(X3,X2)
        <=> ( X1 != X3
            & aElementOf0(X3,X0)
            & aElement0(X3) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f833,plain,
    ! [X0,X1] :
      ( sP3(X0,X1,sdtmndt0(X1,X0))
      | ~ aElement0(X0)
      | ~ aSet0(X1) ),
    inference(equality_resolution,[],[f333]) ).

fof(f333,plain,
    ! [X2,X0,X1] :
      ( sdtmndt0(X0,X1) != X2
      | sP3(X1,X0,X2)
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f217]) ).

fof(f217,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X0,X1) = X2
            | ~ sP3(X1,X0,X2)
            | ~ aSet0(X2) )
          & ( ( sP3(X1,X0,X2)
              & aSet0(X2) )
            | sdtmndt0(X0,X1) != X2 ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f216]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X0,X1) = X2
            | ~ sP3(X1,X0,X2)
            | ~ aSet0(X2) )
          & ( ( sP3(X1,X0,X2)
              & aSet0(X2) )
            | sdtmndt0(X0,X1) != X2 ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f168]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X0,X1) = X2
        <=> ( sP3(X1,X0,X2)
            & aSet0(X2) ) )
      | ~ aElement0(X1)
      | ~ aSet0(X0) ),
    inference(definition_folding,[],[f137,f167]) ).

fof(f137,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,[],[f136]) ).

fof(f136,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/sandbox2/tmp/tmp.6zQlQoskOX/Vampire---4.8_4485',mDefDiff) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem    : NUM555+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.13  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Aug 30 14:59:50 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.13/0.37  % (4657)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38  % (4658)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.13/0.38  % (4662)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.13/0.38  % (4659)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.13/0.38  % (4661)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.13/0.38  % (4660)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.13/0.38  % (4663)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 Vampire---4 for (522ds/0Mi)
% 0.13/0.38  % (4664)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 Vampire---4 for (497ds/0Mi)
% 0.13/0.38  TRYING [1]
% 0.13/0.38  TRYING [2]
% 0.20/0.39  TRYING [3]
% 0.20/0.39  TRYING [1]
% 0.20/0.39  TRYING [2]
% 0.20/0.40  TRYING [4]
% 0.20/0.41  TRYING [3]
% 0.20/0.44  TRYING [5]
% 0.20/0.45  TRYING [4]
% 0.20/0.51  TRYING [1]
% 0.20/0.51  TRYING [2]
% 0.20/0.51  TRYING [3]
% 1.13/0.53  TRYING [5]
% 1.28/0.54  TRYING [4]
% 1.28/0.58  % (4663)First to succeed.
% 1.28/0.59  % (4663)Refutation found. Thanks to Tanya!
% 1.28/0.59  % SZS status Theorem for Vampire---4
% 1.28/0.59  % SZS output start Proof for Vampire---4
% See solution above
% 1.28/0.59  % (4663)------------------------------
% 1.28/0.59  % (4663)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 1.28/0.59  % (4663)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 1.28/0.59  % (4663)Termination reason: Refutation
% 1.28/0.59  
% 1.28/0.59  % (4663)Memory used [KB]: 4861
% 1.28/0.59  % (4663)Time elapsed: 0.204 s
% 1.28/0.59  % (4663)------------------------------
% 1.28/0.59  % (4663)------------------------------
% 1.28/0.59  % (4657)Success in time 0.241 s
% 1.28/0.59  % Vampire---4.8 exiting
%------------------------------------------------------------------------------