TSTP Solution File: SET162+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET162+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 : n017.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 09:04:28 EDT 2024

% Result   : Theorem 0.55s 0.74s
% Output   : Refutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   33 (  10 unt;   1 typ;   0 def)
%            Number of atoms       :  190 (  17 equ)
%            Maximal formula atoms :   10 (   5 avg)
%            Number of connectives :  115 (  43   ~;  51   |;  15   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   86 (  86 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   63 (  57   !;   5   ?;  32   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_4,type,
    sQ2_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f129,plain,
    $false,
    inference(resolution,[],[f112,f40]) ).

tff(f40,plain,
    ~ sQ2_eqProxy($i,sK0,union(sK0,empty_set)),
    inference(equality_proxy_replacement,[],[f22,f39]) ).

tff(f39,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ2_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ2_eqProxy])]) ).

tff(f22,plain,
    sK0 != union(sK0,empty_set),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    sK0 != union(sK0,empty_set),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).

tff(f12,plain,
    ( ? [X0] : ( union(X0,empty_set) != X0 )
   => ( sK0 != union(sK0,empty_set) ) ),
    introduced(choice_axiom,[]) ).

tff(f11,plain,
    ? [X0] : ( union(X0,empty_set) != X0 ),
    inference(ennf_transformation,[],[f10]) ).

tff(f10,negated_conjecture,
    ~ ! [X0] : ( union(X0,empty_set) = X0 ),
    inference(negated_conjecture,[],[f9]) ).

tff(f9,conjecture,
    ! [X0] : ( union(X0,empty_set) = X0 ),
    file('/export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729',prove_union_empty_set) ).

tff(f112,plain,
    ! [X0: $i] : sQ2_eqProxy($i,X0,union(X0,empty_set)),
    inference(subsumption_resolution,[],[f107,f80]) ).

tff(f80,plain,
    ! [X0: $i,X1: $i] :
      ( ~ member(sK1(X0,union(X0,X1)),X0)
      | sQ2_eqProxy($i,X0,union(X0,X1)) ),
    inference(factoring,[],[f62]) ).

tff(f62,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ member(sK1(X0,union(X1,X2)),X1)
      | ~ member(sK1(X0,union(X1,X2)),X0)
      | sQ2_eqProxy($i,X0,union(X1,X2)) ),
    inference(resolution,[],[f41,f32]) ).

tff(f32,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f21]) ).

tff(f21,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f20]) ).

tff(f20,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729',union_defn) ).

tff(f41,plain,
    ! [X0: $i,X1: $i] :
      ( ~ member(sK1(X0,X1),X1)
      | sQ2_eqProxy($i,X0,X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f26,f39]) ).

tff(f26,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ member(sK1(X0,X1),X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f17]) ).

tff(f17,plain,
    ! [X0,X1] :
      ( ( ( X0 = X1 )
        | ( ( ~ member(sK1(X0,X1),X1)
            | ~ member(sK1(X0,X1),X0) )
          & ( member(sK1(X0,X1),X1)
            | member(sK1(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | ( X0 != X1 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f16]) ).

tff(f16,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK1(X0,X1),X1)
          | ~ member(sK1(X0,X1),X0) )
        & ( member(sK1(X0,X1),X1)
          | member(sK1(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f15,plain,
    ! [X0,X1] :
      ( ( ( X0 = X1 )
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | ( X0 != X1 ) ) ),
    inference(rectify,[],[f14]) ).

tff(f14,plain,
    ! [X0,X1] :
      ( ( ( X0 = X1 )
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | ( X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f8]) ).

tff(f8,axiom,
    ! [X0,X1] :
      ( ( X0 = X1 )
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729',equal_member_defn) ).

tff(f107,plain,
    ! [X0: $i] :
      ( member(sK1(X0,union(X0,empty_set)),X0)
      | sQ2_eqProxy($i,X0,union(X0,empty_set)) ),
    inference(duplicate_literal_removal,[],[f104]) ).

tff(f104,plain,
    ! [X0: $i] :
      ( member(sK1(X0,union(X0,empty_set)),X0)
      | sQ2_eqProxy($i,X0,union(X0,empty_set))
      | sQ2_eqProxy($i,X0,union(X0,empty_set)) ),
    inference(resolution,[],[f84,f80]) ).

tff(f84,plain,
    ! [X0: $i,X1: $i] :
      ( member(sK1(X0,union(X1,empty_set)),X1)
      | member(sK1(X0,union(X1,empty_set)),X0)
      | sQ2_eqProxy($i,X0,union(X1,empty_set)) ),
    inference(resolution,[],[f66,f34]) ).

tff(f34,plain,
    ! [X0: $i] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729',empty_set_defn) ).

tff(f66,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( member(sK1(X0,union(X1,X2)),X2)
      | member(sK1(X0,union(X1,X2)),X0)
      | member(sK1(X0,union(X1,X2)),X1)
      | sQ2_eqProxy($i,X0,union(X1,X2)) ),
    inference(resolution,[],[f42,f31]) ).

tff(f31,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f21]) ).

tff(f42,plain,
    ! [X0: $i,X1: $i] :
      ( member(sK1(X0,X1),X1)
      | sQ2_eqProxy($i,X0,X1)
      | member(sK1(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f25,f39]) ).

tff(f25,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | member(sK1(X0,X1),X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET162+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.15  % 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
% 0.15/0.36  % Computer : n017.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   : Fri May  3 16:57:38 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.SYnmTIlvIo/Vampire---4.8_2729
% 0.55/0.73  % (3062)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)
% 0.55/0.73  % (3065)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)
% 0.55/0.74  % (3062)First to succeed.
% 0.55/0.74  % (3065)Refutation not found, incomplete strategy% (3065)------------------------------
% 0.55/0.74  % (3065)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74  % (3065)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.74  
% 0.55/0.74  % (3065)Memory used [KB]: 980
% 0.55/0.74  % (3065)Time elapsed: 0.004 s
% 0.55/0.74  % (3065)Instructions burned: 3 (million)
% 0.55/0.74  % (3064)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.74  % (3065)------------------------------
% 0.55/0.74  % (3065)------------------------------
% 0.55/0.74  % (3066)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)
% 0.55/0.74  % (3063)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)
% 0.55/0.74  % (3067)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)
% 0.55/0.74  % (3062)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2970"
% 0.55/0.74  % (3062)Refutation found. Thanks to Tanya!
% 0.55/0.74  % SZS status Theorem for Vampire---4
% 0.55/0.74  % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.74  % (3062)------------------------------
% 0.55/0.74  % (3062)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.74  % (3062)Termination reason: Refutation
% 0.55/0.74  
% 0.55/0.74  % (3062)Memory used [KB]: 1054
% 0.55/0.74  % (3062)Time elapsed: 0.004 s
% 0.55/0.74  % (3062)Instructions burned: 7 (million)
% 0.55/0.74  % (2970)Success in time 0.372 s
% 0.55/0.74  % Vampire---4.8 exiting
%------------------------------------------------------------------------------