TSTP Solution File: SET930+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n032.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 03:49:32 EDT 2024

% Result   : Theorem 0.49s 0.72s
% Output   : Refutation 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   39 (   7 unt;   0 def)
%            Number of atoms       :  125 (  58 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  160 (  74   ~;  45   |;  35   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   55 (  49   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f222,plain,
    $false,
    inference(avatar_sat_refutation,[],[f111,f175,f209,f221]) ).

fof(f221,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f137,f93,f89]) ).

fof(f89,plain,
    ( spl5_1
  <=> in(sK2,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f93,plain,
    ( spl5_2
  <=> in(sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f137,plain,
    ( ~ in(sK3,sK4)
    | in(sK2,sK4) ),
    inference(trivial_inequality_removal,[],[f123]) ).

fof(f123,plain,
    ( singleton(sK2) != singleton(sK2)
    | ~ in(sK3,sK4)
    | in(sK2,sK4) ),
    inference(superposition,[],[f41,f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
      | ~ in(X1,X2)
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
        | ( X0 != X1
          & ~ in(X1,X2) )
        | in(X0,X2) )
      & ( ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) )
        | set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
        | ( X0 != X1
          & ~ in(X1,X2) )
        | in(X0,X2) )
      & ( ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) )
        | set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
    <=> ( ( X0 = X1
          | in(X1,X2) )
        & ~ in(X0,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.qjpKwUKkNk/Vampire---4.8_12407',l39_zfmisc_1) ).

fof(f41,plain,
    set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ( unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4)
    & set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3)
    & set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
    & empty_set != set_difference(unordered_pair(sK2,sK3),sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f23]) ).

fof(f23,plain,
    ( ? [X0,X1,X2] :
        ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
        & set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
        & set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
        & empty_set != set_difference(unordered_pair(X0,X1),X2) )
   => ( unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4)
      & set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3)
      & set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
      & empty_set != set_difference(unordered_pair(sK2,sK3),sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ? [X0,X1,X2] :
      ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
      & set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
      & set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
      & empty_set != set_difference(unordered_pair(X0,X1),X2) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ~ ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
          & set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
          & set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
          & empty_set != set_difference(unordered_pair(X0,X1),X2) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1,X2] :
      ~ ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
        & set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
        & set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
        & empty_set != set_difference(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.qjpKwUKkNk/Vampire---4.8_12407',t74_zfmisc_1) ).

fof(f209,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f205,f93,f89]) ).

fof(f205,plain,
    ( in(sK3,sK4)
    | in(sK2,sK4) ),
    inference(trivial_inequality_removal,[],[f182]) ).

fof(f182,plain,
    ( unordered_pair(sK2,sK3) != unordered_pair(sK2,sK3)
    | in(sK3,sK4)
    | in(sK2,sK4) ),
    inference(superposition,[],[f43,f36]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
      | in(X1,X2)
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
        | in(X1,X2)
        | in(X0,X2) )
      & ( ( ~ in(X1,X2)
          & ~ in(X0,X2) )
        | unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
        | in(X1,X2)
        | in(X0,X2) )
      & ( ( ~ in(X1,X2)
          & ~ in(X0,X2) )
        | unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
    <=> ( ~ in(X1,X2)
        & ~ in(X0,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.qjpKwUKkNk/Vampire---4.8_12407',t72_zfmisc_1) ).

fof(f43,plain,
    unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4),
    inference(cnf_transformation,[],[f24]) ).

fof(f175,plain,
    ( spl5_2
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f173,f89,f93]) ).

fof(f173,plain,
    ( ~ in(sK2,sK4)
    | in(sK3,sK4) ),
    inference(trivial_inequality_removal,[],[f155]) ).

fof(f155,plain,
    ( singleton(sK3) != singleton(sK3)
    | ~ in(sK2,sK4)
    | in(sK3,sK4) ),
    inference(superposition,[],[f42,f118]) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( singleton(X0) = set_difference(unordered_pair(X1,X0),X2)
      | ~ in(X1,X2)
      | in(X0,X2) ),
    inference(superposition,[],[f30,f26]) ).

fof(f26,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/tmp/tmp.qjpKwUKkNk/Vampire---4.8_12407',commutativity_k2_tarski) ).

fof(f42,plain,
    set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3),
    inference(cnf_transformation,[],[f24]) ).

fof(f111,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f86,f93,f89]) ).

fof(f86,plain,
    ( ~ in(sK3,sK4)
    | ~ in(sK2,sK4) ),
    inference(trivial_inequality_removal,[],[f71]) ).

fof(f71,plain,
    ( empty_set != empty_set
    | ~ in(sK3,sK4)
    | ~ in(sK2,sK4) ),
    inference(superposition,[],[f40,f39]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( empty_set = set_difference(unordered_pair(X0,X1),X2)
      | ~ in(X1,X2)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( empty_set = set_difference(unordered_pair(X0,X1),X2)
    <=> ( in(X1,X2)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.qjpKwUKkNk/Vampire---4.8_12407',t73_zfmisc_1) ).

fof(f40,plain,
    empty_set != set_difference(unordered_pair(sK2,sK3),sK4),
    inference(cnf_transformation,[],[f24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem    : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.09  % 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
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit   : 300
% 0.08/0.28  % WCLimit    : 300
% 0.08/0.28  % DateTime   : Tue Apr 30 17:19:21 EDT 2024
% 0.08/0.28  % CPUTime    : 
% 0.08/0.28  This is a FOF_THM_RFO_SEQ problem
% 0.08/0.28  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.qjpKwUKkNk/Vampire---4.8_12407
% 0.49/0.71  % (12680)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)
% 0.49/0.71  % (12679)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.49/0.71  % (12677)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)
% 0.49/0.71  % (12681)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)
% 0.49/0.71  % (12678)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)
% 0.49/0.71  % (12683)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)
% 0.49/0.71  % (12684)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)
% 0.49/0.71  % (12682)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)
% 0.49/0.72  % (12684)Refutation not found, incomplete strategy% (12684)------------------------------
% 0.49/0.72  % (12684)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.49/0.72  % (12684)Termination reason: Refutation not found, incomplete strategy
% 0.49/0.72  
% 0.49/0.72  % (12684)Memory used [KB]: 980
% 0.49/0.72  % (12684)Time elapsed: 0.003 s
% 0.49/0.72  % (12684)Instructions burned: 3 (million)
% 0.49/0.72  % (12684)------------------------------
% 0.49/0.72  % (12684)------------------------------
% 0.49/0.72  % (12681)Refutation not found, incomplete strategy% (12681)------------------------------
% 0.49/0.72  % (12681)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.49/0.72  % (12681)Termination reason: Refutation not found, incomplete strategy
% 0.49/0.72  % (12683)Refutation not found, incomplete strategy% (12683)------------------------------
% 0.49/0.72  % (12683)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.49/0.72  % (12683)Termination reason: Refutation not found, incomplete strategy
% 0.49/0.72  
% 0.49/0.72  % (12683)Memory used [KB]: 957
% 0.49/0.72  % (12683)Time elapsed: 0.003 s
% 0.49/0.72  % (12683)Instructions burned: 3 (million)
% 0.49/0.72  % (12683)------------------------------
% 0.49/0.72  % (12683)------------------------------
% 0.49/0.72  % (12680)Refutation not found, incomplete strategy% (12680)------------------------------
% 0.49/0.72  % (12680)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.49/0.72  
% 0.49/0.72  % (12681)Memory used [KB]: 1046
% 0.49/0.72  % (12681)Time elapsed: 0.003 s
% 0.49/0.72  % (12681)Instructions burned: 3 (million)
% 0.49/0.72  % (12681)------------------------------
% 0.49/0.72  % (12681)------------------------------
% 0.49/0.72  % (12680)Termination reason: Refutation not found, incomplete strategy
% 0.49/0.72  
% 0.49/0.72  % (12680)Memory used [KB]: 969
% 0.49/0.72  % (12680)Time elapsed: 0.003 s
% 0.49/0.72  % (12680)Instructions burned: 3 (million)
% 0.49/0.72  % (12680)------------------------------
% 0.49/0.72  % (12680)------------------------------
% 0.49/0.72  % (12677)Refutation not found, incomplete strategy% (12677)------------------------------
% 0.49/0.72  % (12677)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.49/0.72  % (12677)Termination reason: Refutation not found, incomplete strategy
% 0.49/0.72  
% 0.49/0.72  % (12677)Memory used [KB]: 982
% 0.49/0.72  % (12677)Time elapsed: 0.004 s
% 0.49/0.72  % (12677)Instructions burned: 4 (million)
% 0.49/0.72  % (12677)------------------------------
% 0.49/0.72  % (12677)------------------------------
% 0.49/0.72  % (12678)First to succeed.
% 0.49/0.72  % (12682)Also succeeded, but the first one will report.
% 0.49/0.72  % (12687)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.49/0.72  % (12689)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.49/0.72  % (12688)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.49/0.72  % (12678)Refutation found. Thanks to Tanya!
% 0.49/0.72  % SZS status Theorem for Vampire---4
% 0.49/0.72  % SZS output start Proof for Vampire---4
% See solution above
% 0.49/0.72  % (12678)------------------------------
% 0.49/0.72  % (12678)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.49/0.72  % (12678)Termination reason: Refutation
% 0.49/0.72  
% 0.49/0.72  % (12678)Memory used [KB]: 1072
% 0.49/0.72  % (12678)Time elapsed: 0.007 s
% 0.49/0.72  % (12678)Instructions burned: 8 (million)
% 0.49/0.72  % (12678)------------------------------
% 0.49/0.72  % (12678)------------------------------
% 0.49/0.72  % (12572)Success in time 0.428 s
% 0.49/0.72  % Vampire---4.8 exiting
%------------------------------------------------------------------------------