TSTP Solution File: SET640+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET640+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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n020.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 03:48:27 EDT 2024

% Result   : Theorem 0.62s 0.82s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   56 (  13 unt;   0 def)
%            Number of atoms       :  200 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  228 (  84   ~;  79   |;  17   &)
%                                         (  13 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :   87 (  79   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f522,plain,
    $false,
    inference(avatar_sat_refutation,[],[f458,f493,f521]) ).

fof(f521,plain,
    ~ spl15_10,
    inference(avatar_contradiction_clause,[],[f520]) ).

fof(f520,plain,
    ( $false
    | ~ spl15_10 ),
    inference(subsumption_resolution,[],[f515,f56]) ).

fof(f56,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p19) ).

fof(f515,plain,
    ( ~ ilf_type(cross_product(sK1,sK2),set_type)
    | ~ spl15_10 ),
    inference(resolution,[],[f457,f81]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p12) ).

fof(f457,plain,
    ( empty(power_set(cross_product(sK1,sK2)))
    | ~ spl15_10 ),
    inference(avatar_component_clause,[],[f455]) ).

fof(f455,plain,
    ( spl15_10
  <=> empty(power_set(cross_product(sK1,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).

fof(f493,plain,
    ~ spl15_9,
    inference(avatar_contradiction_clause,[],[f492]) ).

fof(f492,plain,
    ( $false
    | ~ spl15_9 ),
    inference(subsumption_resolution,[],[f463,f113]) ).

fof(f113,plain,
    ~ member(sK4(sK3,cross_product(sK1,sK2)),cross_product(sK1,sK2)),
    inference(unit_resulting_resolution,[],[f56,f56,f107,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ member(sK4(X0,X1),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,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,[],[f27]) ).

fof(f27,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,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,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( subset(X0,X1)
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p6) ).

fof(f107,plain,
    ~ subset(sK3,cross_product(sK1,sK2)),
    inference(unit_resulting_resolution,[],[f56,f51,f56,f56,f52,f63]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X2)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ subset(X0,X1)
      | ~ ilf_type(X0,set_type)
      | subset(X0,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( subset(X0,X2)
              | ~ subset(X1,X2)
              | ~ subset(X0,X1)
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( subset(X0,X2)
              | ~ subset(X1,X2)
              | ~ subset(X0,X1)
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ( ( subset(X1,X2)
                  & subset(X0,X1) )
               => subset(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p1) ).

fof(f52,plain,
    ~ subset(sK0,cross_product(sK1,sK2)),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ subset(X0,cross_product(X1,X2))
                  & subset(X0,X3)
                  & ilf_type(X3,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ subset(X0,cross_product(X1,X2))
                  & subset(X0,X3)
                  & ilf_type(X3,relation_type(X1,X2)) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,set_type)
               => ! [X3] :
                    ( ilf_type(X3,relation_type(X1,X2))
                   => ( subset(X0,X3)
                     => subset(X0,cross_product(X1,X2)) ) ) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X1,X2))
                 => ( subset(X0,X3)
                   => subset(X0,cross_product(X1,X2)) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',prove_relset_1_2) ).

fof(f51,plain,
    subset(sK0,sK3),
    inference(cnf_transformation,[],[f24]) ).

fof(f463,plain,
    ( member(sK4(sK3,cross_product(sK1,sK2)),cross_product(sK1,sK2))
    | ~ spl15_9 ),
    inference(unit_resulting_resolution,[],[f112,f56,f56,f56,f453,f83]) ).

fof(f83,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ member(X2,X0)
      | member(X2,X1)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,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,[],[f42]) ).

fof(f42,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,[],[f11]) ).

fof(f11,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/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p11) ).

fof(f453,plain,
    ( member(sK3,power_set(cross_product(sK1,sK2)))
    | ~ spl15_9 ),
    inference(avatar_component_clause,[],[f451]) ).

fof(f451,plain,
    ( spl15_9
  <=> member(sK3,power_set(cross_product(sK1,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).

fof(f112,plain,
    member(sK4(sK3,cross_product(sK1,sK2)),sK3),
    inference(unit_resulting_resolution,[],[f56,f56,f107,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( member(sK4(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f458,plain,
    ( spl15_9
    | spl15_10 ),
    inference(avatar_split_clause,[],[f449,f455,f451]) ).

fof(f449,plain,
    ( empty(power_set(cross_product(sK1,sK2)))
    | member(sK3,power_set(cross_product(sK1,sK2))) ),
    inference(subsumption_resolution,[],[f448,f56]) ).

fof(f448,plain,
    ( empty(power_set(cross_product(sK1,sK2)))
    | member(sK3,power_set(cross_product(sK1,sK2)))
    | ~ ilf_type(sK3,set_type) ),
    inference(subsumption_resolution,[],[f447,f56]) ).

fof(f447,plain,
    ( empty(power_set(cross_product(sK1,sK2)))
    | ~ ilf_type(power_set(cross_product(sK1,sK2)),set_type)
    | member(sK3,power_set(cross_product(sK1,sK2)))
    | ~ ilf_type(sK3,set_type) ),
    inference(resolution,[],[f199,f89]) ).

fof(f89,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,[],[f47]) ).

fof(f47,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,[],[f46]) ).

fof(f46,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,[],[f13]) ).

fof(f13,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/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p13) ).

fof(f199,plain,
    ilf_type(sK3,member_type(power_set(cross_product(sK1,sK2)))),
    inference(unit_resulting_resolution,[],[f56,f56,f106,f73]) ).

fof(f73,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,[],[f36]) ).

fof(f36,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/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p8) ).

fof(f106,plain,
    ilf_type(sK3,subset_type(cross_product(sK1,sK2))),
    inference(unit_resulting_resolution,[],[f56,f56,f50,f65]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,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,[],[f22]) ).

fof(f22,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,[],[f4]) ).

fof(f4,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/sandbox2/tmp/tmp.BFVmAO6CVp/Vampire---4.8_30336',p4) ).

fof(f50,plain,
    ilf_type(sK3,relation_type(sK1,sK2)),
    inference(cnf_transformation,[],[f24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET640+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15  % 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
% 0.15/0.36  % Computer : n020.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 17:11:32 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  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.BFVmAO6CVp/Vampire---4.8_30336
% 0.62/0.80  % (30559)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)
% 0.62/0.80  % (30560)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)
% 0.62/0.80  % (30554)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)
% 0.62/0.80  % (30556)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.62/0.80  % (30557)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)
% 0.62/0.80  % (30555)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)
% 0.62/0.80  % (30558)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)
% 0.62/0.80  % (30561)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)
% 0.62/0.81  % (30560)First to succeed.
% 0.62/0.82  % (30560)Refutation found. Thanks to Tanya!
% 0.62/0.82  % SZS status Theorem for Vampire---4
% 0.62/0.82  % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.82  % (30560)------------------------------
% 0.62/0.82  % (30560)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.82  % (30560)Termination reason: Refutation
% 0.62/0.82  
% 0.62/0.82  % (30560)Memory used [KB]: 1221
% 0.62/0.82  % (30560)Time elapsed: 0.014 s
% 0.62/0.82  % (30560)Instructions burned: 22 (million)
% 0.62/0.82  % (30560)------------------------------
% 0.62/0.82  % (30560)------------------------------
% 0.62/0.82  % (30520)Success in time 0.427 s
% 0.62/0.82  % Vampire---4.8 exiting
%------------------------------------------------------------------------------