TSTP Solution File: RNG102+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : RNG102+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n024.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 : Wed May  1 03:41:53 EDT 2024

% Result   : Theorem 0.60s 0.76s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   33 (   6 unt;   1 typ;   0 def)
%            Number of atoms       :  266 (  45 equ)
%            Maximal formula atoms :   17 (   8 avg)
%            Number of connectives :  192 (  74   ~;  69   |;  40   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  116 ( 116 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   5 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   76 (  57   !;  18   ?;  23   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_14,type,
    sQ12_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f207,plain,
    $false,
    inference(subsumption_resolution,[],[f206,f91]) ).

tff(f91,plain,
    aElement0(xc),
    inference(cnf_transformation,[],[f38]) ).

tff(f38,axiom,
    aElement0(xc),
    file('/export/starexec/sandbox/tmp/tmp.DSGkztsmNS/Vampire---4.8_10997',m__1905) ).

tff(f206,plain,
    ~ aElement0(xc),
    inference(subsumption_resolution,[],[f205,f93]) ).

tff(f93,plain,
    aElementOf0(xy,slsdtgt0(xc)),
    inference(cnf_transformation,[],[f39]) ).

tff(f39,axiom,
    ( aElement0(xz)
    & aElementOf0(xy,slsdtgt0(xc))
    & aElementOf0(xx,slsdtgt0(xc)) ),
    file('/export/starexec/sandbox/tmp/tmp.DSGkztsmNS/Vampire---4.8_10997',m__1933) ).

tff(f205,plain,
    ( ~ aElementOf0(xy,slsdtgt0(xc))
    | ~ aElement0(xc) ),
    inference(resolution,[],[f201,f141]) ).

tff(f141,plain,
    ! [X0: $i,X5: $i] :
      ( aElement0(sK11(X0,X5))
      | ~ aElementOf0(X5,slsdtgt0(X0))
      | ~ aElement0(X0) ),
    inference(equality_resolution,[],[f119]) ).

tff(f119,plain,
    ! [X0: $i,X1: $i,X5: $i] :
      ( aElement0(sK11(X0,X5))
      | ~ aElementOf0(X5,X1)
      | ( slsdtgt0(X0) != X1 )
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f90]) ).

tff(f90,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( slsdtgt0(X0) = X1 )
            | ( ( ! [X3] :
                    ( ( sdtasdt0(X0,X3) != sK9(X0,X1) )
                    | ~ aElement0(X3) )
                | ~ aElementOf0(sK9(X0,X1),X1) )
              & ( ( ( sK9(X0,X1) = sdtasdt0(X0,sK10(X0,X1)) )
                  & aElement0(sK10(X0,X1)) )
                | aElementOf0(sK9(X0,X1),X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X5] :
                  ( ( aElementOf0(X5,X1)
                    | ! [X6] :
                        ( ( sdtasdt0(X0,X6) != X5 )
                        | ~ aElement0(X6) ) )
                  & ( ( ( sdtasdt0(X0,sK11(X0,X5)) = X5 )
                      & aElement0(sK11(X0,X5)) )
                    | ~ aElementOf0(X5,X1) ) )
              & aSet0(X1) )
            | ( slsdtgt0(X0) != X1 ) ) )
      | ~ aElement0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f86,f89,f88,f87]) ).

tff(f87,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( ( sdtasdt0(X0,X3) != X2 )
                | ~ aElement0(X3) )
            | ~ aElementOf0(X2,X1) )
          & ( ? [X4] :
                ( ( sdtasdt0(X0,X4) = X2 )
                & aElement0(X4) )
            | aElementOf0(X2,X1) ) )
     => ( ( ! [X3] :
              ( ( sdtasdt0(X0,X3) != sK9(X0,X1) )
              | ~ aElement0(X3) )
          | ~ aElementOf0(sK9(X0,X1),X1) )
        & ( ? [X4] :
              ( ( sdtasdt0(X0,X4) = sK9(X0,X1) )
              & aElement0(X4) )
          | aElementOf0(sK9(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f88,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ( sdtasdt0(X0,X4) = sK9(X0,X1) )
          & aElement0(X4) )
     => ( ( sK9(X0,X1) = sdtasdt0(X0,sK10(X0,X1)) )
        & aElement0(sK10(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f89,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( ( sdtasdt0(X0,X7) = X5 )
          & aElement0(X7) )
     => ( ( sdtasdt0(X0,sK11(X0,X5)) = X5 )
        & aElement0(sK11(X0,X5)) ) ),
    introduced(choice_axiom,[]) ).

tff(f86,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( slsdtgt0(X0) = X1 )
            | ? [X2] :
                ( ( ! [X3] :
                      ( ( sdtasdt0(X0,X3) != X2 )
                      | ~ aElement0(X3) )
                  | ~ aElementOf0(X2,X1) )
                & ( ? [X4] :
                      ( ( sdtasdt0(X0,X4) = X2 )
                      & aElement0(X4) )
                  | aElementOf0(X2,X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X5] :
                  ( ( aElementOf0(X5,X1)
                    | ! [X6] :
                        ( ( sdtasdt0(X0,X6) != X5 )
                        | ~ aElement0(X6) ) )
                  & ( ? [X7] :
                        ( ( sdtasdt0(X0,X7) = X5 )
                        & aElement0(X7) )
                    | ~ aElementOf0(X5,X1) ) )
              & aSet0(X1) )
            | ( slsdtgt0(X0) != X1 ) ) )
      | ~ aElement0(X0) ),
    inference(rectify,[],[f85]) ).

tff(f85,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( slsdtgt0(X0) = X1 )
            | ? [X2] :
                ( ( ! [X3] :
                      ( ( sdtasdt0(X0,X3) != X2 )
                      | ~ aElement0(X3) )
                  | ~ aElementOf0(X2,X1) )
                & ( ? [X3] :
                      ( ( sdtasdt0(X0,X3) = X2 )
                      & aElement0(X3) )
                  | aElementOf0(X2,X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( ( aElementOf0(X2,X1)
                    | ! [X3] :
                        ( ( sdtasdt0(X0,X3) != X2 )
                        | ~ aElement0(X3) ) )
                  & ( ? [X3] :
                        ( ( sdtasdt0(X0,X3) = X2 )
                        & aElement0(X3) )
                    | ~ aElementOf0(X2,X1) ) )
              & aSet0(X1) )
            | ( slsdtgt0(X0) != X1 ) ) )
      | ~ aElement0(X0) ),
    inference(flattening,[],[f84]) ).

tff(f84,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( slsdtgt0(X0) = X1 )
            | ? [X2] :
                ( ( ! [X3] :
                      ( ( sdtasdt0(X0,X3) != X2 )
                      | ~ aElement0(X3) )
                  | ~ aElementOf0(X2,X1) )
                & ( ? [X3] :
                      ( ( sdtasdt0(X0,X3) = X2 )
                      & aElement0(X3) )
                  | aElementOf0(X2,X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( ( aElementOf0(X2,X1)
                    | ! [X3] :
                        ( ( sdtasdt0(X0,X3) != X2 )
                        | ~ aElement0(X3) ) )
                  & ( ? [X3] :
                        ( ( sdtasdt0(X0,X3) = X2 )
                        & aElement0(X3) )
                    | ~ aElementOf0(X2,X1) ) )
              & aSet0(X1) )
            | ( slsdtgt0(X0) != X1 ) ) )
      | ~ aElement0(X0) ),
    inference(nnf_transformation,[],[f58]) ).

tff(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( slsdtgt0(X0) = X1 )
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
              <=> ? [X3] :
                    ( ( sdtasdt0(X0,X3) = X2 )
                    & aElement0(X3) ) )
            & aSet0(X1) ) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f37]) ).

tff(f37,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ! [X1] :
          ( ( slsdtgt0(X0) = X1 )
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
              <=> ? [X3] :
                    ( ( sdtasdt0(X0,X3) = X2 )
                    & aElement0(X3) ) )
            & aSet0(X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.DSGkztsmNS/Vampire---4.8_10997',mDefPrIdeal) ).

tff(f201,plain,
    ~ aElement0(sK11(xc,xy)),
    inference(subsumption_resolution,[],[f200,f91]) ).

tff(f200,plain,
    ( ~ aElement0(xc)
    | ~ aElement0(sK11(xc,xy)) ),
    inference(subsumption_resolution,[],[f199,f93]) ).

tff(f199,plain,
    ( ~ aElementOf0(xy,slsdtgt0(xc))
    | ~ aElement0(xc)
    | ~ aElement0(sK11(xc,xy)) ),
    inference(resolution,[],[f198,f145]) ).

tff(f145,plain,
    ! [X0: $i] :
      ( ~ sQ12_eqProxy($i,xy,sdtasdt0(xc,X0))
      | ~ aElement0(X0) ),
    inference(equality_proxy_replacement,[],[f97,f143]) ).

tff(f143,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ12_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ12_eqProxy])]) ).

tff(f97,plain,
    ! [X0: $i] :
      ( ( xy != sdtasdt0(xc,X0) )
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f46]) ).

tff(f46,plain,
    ! [X0] :
      ( ( xy != sdtasdt0(xc,X0) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f42]) ).

tff(f42,negated_conjecture,
    ~ ? [X0] :
        ( ( xy = sdtasdt0(xc,X0) )
        & aElement0(X0) ),
    inference(negated_conjecture,[],[f41]) ).

tff(f41,conjecture,
    ? [X0] :
      ( ( xy = sdtasdt0(xc,X0) )
      & aElement0(X0) ),
    file('/export/starexec/sandbox/tmp/tmp.DSGkztsmNS/Vampire---4.8_10997',m__) ).

tff(f198,plain,
    ! [X0: $i,X5: $i] :
      ( sQ12_eqProxy($i,X5,sdtasdt0(X0,sK11(X0,X5)))
      | ~ aElementOf0(X5,slsdtgt0(X0))
      | ~ aElement0(X0) ),
    inference(forward_literal_rewriting,[],[f159,f172]) ).

tff(f172,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ12_eqProxy(X0,X2,X1)
      | ~ sQ12_eqProxy(X0,X1,X2) ),
    inference(equality_proxy_axiom,[],[f143]) ).

tff(f159,plain,
    ! [X0: $i,X5: $i] :
      ( sQ12_eqProxy($i,sdtasdt0(X0,sK11(X0,X5)),X5)
      | ~ aElementOf0(X5,slsdtgt0(X0))
      | ~ aElement0(X0) ),
    inference(equality_proxy_replacement,[],[f140,f143]) ).

tff(f140,plain,
    ! [X0: $i,X5: $i] :
      ( ( sdtasdt0(X0,sK11(X0,X5)) = X5 )
      | ~ aElementOf0(X5,slsdtgt0(X0))
      | ~ aElement0(X0) ),
    inference(equality_resolution,[],[f120]) ).

tff(f120,plain,
    ! [X0: $i,X1: $i,X5: $i] :
      ( ( sdtasdt0(X0,sK11(X0,X5)) = X5 )
      | ~ aElementOf0(X5,X1)
      | ( slsdtgt0(X0) != X1 )
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f90]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : RNG102+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Apr 30 17:31:06 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.DSGkztsmNS/Vampire---4.8_10997
% 0.60/0.76  % (11255)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.76  % (11261)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.60/0.76  % (11257)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.76  % (11256)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.60/0.76  % (11258)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.60/0.76  % (11259)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.76  % (11260)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.60/0.76  % (11255)First to succeed.
% 0.60/0.76  % (11255)Refutation found. Thanks to Tanya!
% 0.60/0.76  % SZS status Theorem for Vampire---4
% 0.60/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.76  % (11255)------------------------------
% 0.60/0.76  % (11255)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.76  % (11255)Termination reason: Refutation
% 0.60/0.76  
% 0.60/0.76  % (11255)Memory used [KB]: 1100
% 0.60/0.76  % (11255)Time elapsed: 0.004 s
% 0.60/0.76  % (11255)Instructions burned: 7 (million)
% 0.60/0.76  % (11255)------------------------------
% 0.60/0.76  % (11255)------------------------------
% 0.60/0.76  % (11250)Success in time 0.39 s
% 0.60/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------