TSTP Solution File: SET662+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n021.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 03:48:31 EDT 2024

% Result   : Theorem 0.62s 0.83s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   49 (  10 unt;   0 def)
%            Number of atoms       :  151 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  169 (  67   ~;  59   |;   8   &)
%                                         (  12 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :   57 (  55   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f131,plain,
    $false,
    inference(avatar_sat_refutation,[],[f94,f121,f130]) ).

fof(f130,plain,
    ~ spl8_2,
    inference(avatar_contradiction_clause,[],[f129]) ).

fof(f129,plain,
    ( $false
    | ~ spl8_2 ),
    inference(subsumption_resolution,[],[f125,f49]) ).

fof(f49,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/tmp/tmp.oRmyvG0wiK/Vampire---4.8_3070',p20) ).

fof(f125,plain,
    ( ~ ilf_type(cross_product(sK0,sK1),set_type)
    | ~ spl8_2 ),
    inference(resolution,[],[f93,f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.oRmyvG0wiK/Vampire---4.8_3070',p13) ).

fof(f93,plain,
    ( empty(power_set(cross_product(sK0,sK1)))
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f91]) ).

fof(f91,plain,
    ( spl8_2
  <=> empty(power_set(cross_product(sK0,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f121,plain,
    spl8_1,
    inference(avatar_contradiction_clause,[],[f120]) ).

fof(f120,plain,
    ( $false
    | spl8_1 ),
    inference(subsumption_resolution,[],[f119,f50]) ).

fof(f50,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox/tmp/tmp.oRmyvG0wiK/Vampire---4.8_3070',p5a) ).

fof(f119,plain,
    ( ~ empty(empty_set)
    | spl8_1 ),
    inference(subsumption_resolution,[],[f118,f49]) ).

fof(f118,plain,
    ( ~ ilf_type(empty_set,set_type)
    | ~ empty(empty_set)
    | spl8_1 ),
    inference(subsumption_resolution,[],[f105,f49]) ).

fof(f105,plain,
    ( ~ ilf_type(sK6(empty_set,cross_product(sK0,sK1)),set_type)
    | ~ ilf_type(empty_set,set_type)
    | ~ empty(empty_set)
    | spl8_1 ),
    inference(resolution,[],[f96,f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ member(X1,X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0] :
      ( ( empty(X0)
      <=> ! [X1] :
            ( ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( empty(X0)
      <=> ! [X1] :
            ( ilf_type(X1,set_type)
           => ~ member(X1,X0) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.oRmyvG0wiK/Vampire---4.8_3070',p11) ).

fof(f96,plain,
    ( member(sK6(empty_set,cross_product(sK0,sK1)),empty_set)
    | spl8_1 ),
    inference(unit_resulting_resolution,[],[f49,f49,f89,f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( member(sK6(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.oRmyvG0wiK/Vampire---4.8_3070',p12) ).

fof(f89,plain,
    ( ~ member(empty_set,power_set(cross_product(sK0,sK1)))
    | spl8_1 ),
    inference(avatar_component_clause,[],[f87]) ).

fof(f87,plain,
    ( spl8_1
  <=> member(empty_set,power_set(cross_product(sK0,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f94,plain,
    ( ~ spl8_1
    | spl8_2 ),
    inference(avatar_split_clause,[],[f85,f91,f87]) ).

fof(f85,plain,
    ( empty(power_set(cross_product(sK0,sK1)))
    | ~ member(empty_set,power_set(cross_product(sK0,sK1))) ),
    inference(subsumption_resolution,[],[f84,f49]) ).

fof(f84,plain,
    ( empty(power_set(cross_product(sK0,sK1)))
    | ~ member(empty_set,power_set(cross_product(sK0,sK1)))
    | ~ ilf_type(empty_set,set_type) ),
    inference(subsumption_resolution,[],[f83,f49]) ).

fof(f83,plain,
    ( empty(power_set(cross_product(sK0,sK1)))
    | ~ ilf_type(power_set(cross_product(sK0,sK1)),set_type)
    | ~ member(empty_set,power_set(cross_product(sK0,sK1)))
    | ~ ilf_type(empty_set,set_type) ),
    inference(resolution,[],[f79,f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | empty(X1)
      | ~ ilf_type(X1,set_type)
      | ~ member(X0,X1)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ( ilf_type(X1,set_type)
            & ~ empty(X1) )
         => ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.oRmyvG0wiK/Vampire---4.8_3070',p14) ).

fof(f79,plain,
    ~ ilf_type(empty_set,member_type(power_set(cross_product(sK0,sK1)))),
    inference(unit_resulting_resolution,[],[f49,f49,f77,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | ilf_type(X1,subset_type(X0)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.oRmyvG0wiK/Vampire---4.8_3070',p7) ).

fof(f77,plain,
    ~ ilf_type(empty_set,subset_type(cross_product(sK0,sK1))),
    inference(unit_resulting_resolution,[],[f49,f49,f47,f54]) ).

fof(f54,plain,
    ! [X3,X0,X1] :
      ( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | ilf_type(X3,relation_type(X0,X1)) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
                | ~ ilf_type(X2,relation_type(X0,X1)) )
            & ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
                | ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ilf_type(X2,subset_type(cross_product(X0,X1))) )
            & ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X0,X1)))
               => ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
               => ilf_type(X3,subset_type(cross_product(X0,X1))) )
            & ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
               => ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.oRmyvG0wiK/Vampire---4.8_3070',p2) ).

fof(f47,plain,
    ~ ilf_type(empty_set,relation_type(sK0,sK1)),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ ilf_type(empty_set,relation_type(X0,X1))
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ilf_type(empty_set,relation_type(X0,X1)) ) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f22,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ilf_type(empty_set,relation_type(X0,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.oRmyvG0wiK/Vampire---4.8_3070',prove_relset_1_25) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem    : SET662+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.13  % 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
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Apr 30 17:17:55 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.34  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.oRmyvG0wiK/Vampire---4.8_3070
% 0.62/0.82  % (3180)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.62/0.82  % (3178)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 (2995ds/34Mi)
% 0.62/0.82  % (3179)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 (2995ds/51Mi)
% 0.62/0.82  % (3181)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.62/0.82  % (3182)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 (2995ds/34Mi)
% 0.62/0.82  % (3183)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.62/0.82  % (3184)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 (2995ds/83Mi)
% 0.62/0.82  % (3183)Refutation not found, incomplete strategy% (3183)------------------------------
% 0.62/0.82  % (3183)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.82  % (3183)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.82  
% 0.62/0.82  % (3183)Memory used [KB]: 1021
% 0.62/0.82  % (3183)Time elapsed: 0.002 s
% 0.62/0.82  % (3178)Refutation not found, incomplete strategy% (3178)------------------------------
% 0.62/0.82  % (3178)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.82  % (3178)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.82  
% 0.62/0.82  % (3178)Memory used [KB]: 1038
% 0.62/0.82  % (3178)Time elapsed: 0.003 s
% 0.62/0.82  % (3178)Instructions burned: 2 (million)
% 0.62/0.82  % (3178)------------------------------
% 0.62/0.82  % (3178)------------------------------
% 0.62/0.82  % (3183)Instructions burned: 2 (million)
% 0.62/0.82  % (3181)Refutation not found, incomplete strategy% (3181)------------------------------
% 0.62/0.82  % (3181)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.82  % (3181)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.82  
% 0.62/0.82  % (3181)Memory used [KB]: 1023
% 0.62/0.82  % (3181)Time elapsed: 0.003 s
% 0.62/0.82  % (3181)Instructions burned: 2 (million)
% 0.62/0.82  % (3181)------------------------------
% 0.62/0.82  % (3181)------------------------------
% 0.62/0.82  % (3183)------------------------------
% 0.62/0.82  % (3183)------------------------------
% 0.62/0.82  % (3185)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 (2995ds/56Mi)
% 0.62/0.82  % (3182)Refutation not found, incomplete strategy% (3182)------------------------------
% 0.62/0.82  % (3182)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.82  % (3182)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.82  
% 0.62/0.82  % (3182)Memory used [KB]: 1034
% 0.62/0.82  % (3182)Time elapsed: 0.003 s
% 0.62/0.82  % (3182)Instructions burned: 4 (million)
% 0.62/0.82  % (3182)------------------------------
% 0.62/0.82  % (3182)------------------------------
% 0.62/0.83  % (3184)First to succeed.
% 0.62/0.83  % (3185)Refutation not found, incomplete strategy% (3185)------------------------------
% 0.62/0.83  % (3185)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.83  % (3185)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.83  
% 0.62/0.83  % (3185)Memory used [KB]: 1023
% 0.62/0.83  % (3185)Time elapsed: 0.002 s
% 0.62/0.83  % (3185)Instructions burned: 2 (million)
% 0.62/0.83  % (3185)------------------------------
% 0.62/0.83  % (3185)------------------------------
% 0.62/0.83  % (3180)Also succeeded, but the first one will report.
% 0.62/0.83  % (3184)Refutation found. Thanks to Tanya!
% 0.62/0.83  % SZS status Theorem for Vampire---4
% 0.62/0.83  % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.83  % (3184)------------------------------
% 0.62/0.83  % (3184)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.83  % (3184)Termination reason: Refutation
% 0.62/0.83  
% 0.62/0.83  % (3184)Memory used [KB]: 1056
% 0.62/0.83  % (3184)Time elapsed: 0.004 s
% 0.62/0.83  % (3184)Instructions burned: 6 (million)
% 0.62/0.83  % (3184)------------------------------
% 0.62/0.83  % (3184)------------------------------
% 0.62/0.83  % (3177)Success in time 0.482 s
% 0.62/0.83  % Vampire---4.8 exiting
%------------------------------------------------------------------------------