TSTP Solution File: SEU130+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU130+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n012.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 : Sun May  5 09:20:23 EDT 2024

% Result   : Theorem 0.60s 0.77s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   52 (   9 unt;   1 typ;   0 def)
%            Number of atoms       :  322 (  24 equ)
%            Maximal formula atoms :   14 (   6 avg)
%            Number of connectives :  236 (  94   ~;  86   |;  42   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  129 ( 129 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   5 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   97 (  85   !;  11   ?;  33   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_4,type,
    sQ4_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f211,plain,
    $false,
    inference(avatar_sat_refutation,[],[f190,f194,f208]) ).

tff(f208,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f207]) ).

tff(f207,plain,
    ( $false
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f206,f84]) ).

tff(f84,plain,
    ~ subset(sK0,set_intersection2(sK0,sK1)),
    inference(subsumption_resolution,[],[f83,f53]) ).

tff(f53,plain,
    ! [X0: $i,X1: $i] : subset(set_intersection2(X0,X1),X0),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,axiom,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    file('/export/starexec/sandbox2/tmp/tmp.QrO1y47v12/Vampire---4.8_29706',t17_xboole_1) ).

tff(f83,plain,
    ( ~ subset(set_intersection2(sK0,sK1),sK0)
    | ~ subset(sK0,set_intersection2(sK0,sK1)) ),
    inference(resolution,[],[f70,f64]) ).

tff(f64,plain,
    ~ sQ4_eqProxy($i,sK0,set_intersection2(sK0,sK1)),
    inference(equality_proxy_replacement,[],[f40,f63]) ).

tff(f63,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ4_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ4_eqProxy])]) ).

tff(f40,plain,
    sK0 != set_intersection2(sK0,sK1),
    inference(cnf_transformation,[],[f27]) ).

tff(f27,plain,
    ( ( sK0 != set_intersection2(sK0,sK1) )
    & subset(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f24,f26]) ).

tff(f26,plain,
    ( ? [X0,X1] :
        ( ( set_intersection2(X0,X1) != X0 )
        & subset(X0,X1) )
   => ( ( sK0 != set_intersection2(sK0,sK1) )
      & subset(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f24,plain,
    ? [X0,X1] :
      ( ( set_intersection2(X0,X1) != X0 )
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

tff(f15,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => ( set_intersection2(X0,X1) = X0 ) ),
    inference(negated_conjecture,[],[f14]) ).

tff(f14,conjecture,
    ! [X0,X1] :
      ( subset(X0,X1)
     => ( set_intersection2(X0,X1) = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.QrO1y47v12/Vampire---4.8_29706',t28_xboole_1) ).

tff(f70,plain,
    ! [X0: $i,X1: $i] :
      ( sQ4_eqProxy($i,X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(equality_proxy_replacement,[],[f51,f63]) ).

tff(f51,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0,X1] :
      ( ( ( X0 = X1 )
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | ( X0 != X1 ) ) ),
    inference(flattening,[],[f33]) ).

tff(f33,plain,
    ! [X0,X1] :
      ( ( ( X0 = X1 )
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | ( X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f3]) ).

tff(f3,axiom,
    ! [X0,X1] :
      ( ( X0 = X1 )
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.QrO1y47v12/Vampire---4.8_29706',d10_xboole_0) ).

tff(f206,plain,
    ( subset(sK0,set_intersection2(sK0,sK1))
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f202,f39]) ).

tff(f39,plain,
    subset(sK0,sK1),
    inference(cnf_transformation,[],[f27]) ).

tff(f202,plain,
    ( ~ subset(sK0,sK1)
    | subset(sK0,set_intersection2(sK0,sK1))
    | ~ spl5_1 ),
    inference(resolution,[],[f185,f56]) ).

tff(f56,plain,
    ! [X0: $i,X1: $i] :
      ( in(sK3(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK3(X0,X1),X1)
          & in(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f36,f37]) ).

tff(f37,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK3(X0,X1),X1)
        & in(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f36,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f35]) ).

tff(f35,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f25]) ).

tff(f25,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

tff(f4,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.QrO1y47v12/Vampire---4.8_29706',d3_tarski) ).

tff(f185,plain,
    ( ! [X0: $i] :
        ( ~ in(sK3(sK0,set_intersection2(sK0,sK1)),X0)
        | ~ subset(X0,sK1) )
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f184]) ).

tff(f184,plain,
    ( spl5_1
  <=> ! [X0] :
        ( ~ in(sK3(sK0,set_intersection2(sK0,sK1)),X0)
        | ~ subset(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

tff(f194,plain,
    spl5_2,
    inference(avatar_contradiction_clause,[],[f193]) ).

tff(f193,plain,
    ( $false
    | spl5_2 ),
    inference(subsumption_resolution,[],[f191,f84]) ).

tff(f191,plain,
    ( subset(sK0,set_intersection2(sK0,sK1))
    | spl5_2 ),
    inference(resolution,[],[f189,f56]) ).

tff(f189,plain,
    ( ~ in(sK3(sK0,set_intersection2(sK0,sK1)),sK0)
    | spl5_2 ),
    inference(avatar_component_clause,[],[f187]) ).

tff(f187,plain,
    ( spl5_2
  <=> in(sK3(sK0,set_intersection2(sK0,sK1)),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

tff(f190,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f178,f187,f184]) ).

tff(f178,plain,
    ! [X0: $i] :
      ( ~ in(sK3(sK0,set_intersection2(sK0,sK1)),sK0)
      | ~ in(sK3(sK0,set_intersection2(sK0,sK1)),X0)
      | ~ subset(X0,sK1) ),
    inference(resolution,[],[f118,f84]) ).

tff(f118,plain,
    ! [X2: $i,X3: $i,X0: $i,X1: $i] :
      ( subset(X0,set_intersection2(X1,X2))
      | ~ in(sK3(X0,set_intersection2(X1,X2)),X1)
      | ~ in(sK3(X0,set_intersection2(X1,X2)),X3)
      | ~ subset(X3,X2) ),
    inference(resolution,[],[f85,f55]) ).

tff(f55,plain,
    ! [X3: $i,X0: $i,X1: $i] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

tff(f85,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ in(sK3(X0,set_intersection2(X1,X2)),X2)
      | ~ in(sK3(X0,set_intersection2(X1,X2)),X1)
      | subset(X0,set_intersection2(X1,X2)) ),
    inference(resolution,[],[f58,f57]) ).

tff(f57,plain,
    ! [X0: $i,X1: $i] :
      ( ~ in(sK3(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

tff(f58,plain,
    ! [X0: $i,X1: $i,X4: $i] :
      ( in(X4,set_intersection2(X0,X1))
      | ~ in(X4,X1)
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f45]) ).

tff(f45,plain,
    ! [X2: $i,X0: $i,X1: $i,X4: $i] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | ~ in(X4,X0)
      | ( set_intersection2(X0,X1) != X2 ) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0,X1,X2] :
      ( ( ( set_intersection2(X0,X1) = X2 )
        | ( ( ~ in(sK2(X0,X1,X2),X1)
            | ~ in(sK2(X0,X1,X2),X0)
            | ~ in(sK2(X0,X1,X2),X2) )
          & ( ( in(sK2(X0,X1,X2),X1)
              & in(sK2(X0,X1,X2),X0) )
            | in(sK2(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | ( set_intersection2(X0,X1) != X2 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f30,f31]) ).

tff(f31,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK2(X0,X1,X2),X1)
          | ~ in(sK2(X0,X1,X2),X0)
          | ~ in(sK2(X0,X1,X2),X2) )
        & ( ( in(sK2(X0,X1,X2),X1)
            & in(sK2(X0,X1,X2),X0) )
          | in(sK2(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ! [X0,X1,X2] :
      ( ( ( set_intersection2(X0,X1) = X2 )
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | ( set_intersection2(X0,X1) != X2 ) ) ),
    inference(rectify,[],[f29]) ).

tff(f29,plain,
    ! [X0,X1,X2] :
      ( ( ( set_intersection2(X0,X1) = X2 )
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | ( set_intersection2(X0,X1) != X2 ) ) ),
    inference(flattening,[],[f28]) ).

tff(f28,plain,
    ! [X0,X1,X2] :
      ( ( ( set_intersection2(X0,X1) = X2 )
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | ( set_intersection2(X0,X1) != X2 ) ) ),
    inference(nnf_transformation,[],[f5]) ).

tff(f5,axiom,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2 )
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.QrO1y47v12/Vampire---4.8_29706',d3_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU130+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35  % Computer : n012.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   : Fri May  3 11:28:25 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.QrO1y47v12/Vampire---4.8_29706
% 0.60/0.76  % (29891)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  % (29894)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  % (29893)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  % (29895)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  % (29892)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  % (29896)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  % (29897)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  % (29898)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.60/0.76  % (29898)Refutation not found, incomplete strategy% (29898)------------------------------
% 0.60/0.76  % (29898)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (29894)Refutation not found, incomplete strategy% (29894)------------------------------
% 0.60/0.76  % (29894)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (29894)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76  
% 0.60/0.76  % (29894)Memory used [KB]: 957
% 0.60/0.76  % (29894)Time elapsed: 0.002 s
% 0.60/0.76  % (29894)Instructions burned: 2 (million)
% 0.60/0.76  % (29898)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76  
% 0.60/0.76  % (29898)Memory used [KB]: 954
% 0.60/0.76  % (29898)Time elapsed: 0.002 s
% 0.60/0.76  % (29898)Instructions burned: 2 (million)
% 0.60/0.76  % (29896)Refutation not found, incomplete strategy% (29896)------------------------------
% 0.60/0.76  % (29896)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76  % (29896)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76  
% 0.60/0.76  % (29896)Memory used [KB]: 969
% 0.60/0.76  % (29896)Time elapsed: 0.003 s
% 0.60/0.76  % (29896)Instructions burned: 2 (million)
% 0.60/0.76  % (29894)------------------------------
% 0.60/0.76  % (29894)------------------------------
% 0.60/0.76  % (29898)------------------------------
% 0.60/0.76  % (29898)------------------------------
% 0.60/0.76  % (29896)------------------------------
% 0.60/0.76  % (29896)------------------------------
% 0.60/0.76  % (29891)First to succeed.
% 0.60/0.77  % (29891)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29890"
% 0.60/0.77  % (29897)Also succeeded, but the first one will report.
% 0.60/0.77  % (29891)Refutation found. Thanks to Tanya!
% 0.60/0.77  % SZS status Theorem for Vampire---4
% 0.60/0.77  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.77  % (29891)------------------------------
% 0.60/0.77  % (29891)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77  % (29891)Termination reason: Refutation
% 0.60/0.77  
% 0.60/0.77  % (29891)Memory used [KB]: 1081
% 0.60/0.77  % (29891)Time elapsed: 0.005 s
% 0.60/0.77  % (29891)Instructions burned: 12 (million)
% 0.60/0.77  % (29890)Success in time 0.403 s
% 0.60/0.77  % Vampire---4.8 exiting
%------------------------------------------------------------------------------