TSTP Solution File: DAT047_1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : DAT047_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n024.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 05:04:23 EDT 2024

% Result   : Theorem 0.61s 0.76s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   62 (  14 unt;   6 typ;   0 def)
%            Number of atoms       :  129 (  52 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  123 (  50   ~;  47   |;  13   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number arithmetic     :  153 (   0 atm;  28 fun;  88 num;  37 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :   12 (   4 usr;   6 con; 0-2 aty)
%            Number of variables   :   64 (  64   !;   0   ?;  64   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    collection: $tType ).

tff(func_def_0,type,
    empty: collection ).

tff(func_def_1,type,
    add: ( $int * collection ) > collection ).

tff(func_def_2,type,
    remove: ( $int * collection ) > collection ).

tff(func_def_3,type,
    count: collection > $int ).

tff(pred_def_1,type,
    in: ( $int * collection ) > $o ).

tff(f113,plain,
    $false,
    inference(avatar_sat_refutation,[],[f89,f107,f112]) ).

tff(f112,plain,
    ~ spl0_1,
    inference(avatar_contradiction_clause,[],[f111]) ).

tff(f111,plain,
    ( $false
    | ~ spl0_1 ),
    inference(subsumption_resolution,[],[f110,f54]) ).

tff(f54,plain,
    ! [X0: $int] : ~ in(X0,empty),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $int] : ~ in(X0,empty),
    file('/export/starexec/sandbox2/tmp/tmp.Rig5IoZLoS/Vampire---4.8_25174',ax1) ).

tff(f110,plain,
    ( in(5,empty)
    | ~ spl0_1 ),
    inference(evaluation,[],[f109]) ).

tff(f109,plain,
    ( in(5,empty)
    | ( 5 = 3 )
    | ~ spl0_1 ),
    inference(resolution,[],[f108,f60]) ).

tff(f60,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ~ in(X0,add(X2,X1))
      | in(X0,X1)
      | ( X0 = X2 ) ),
    inference(cnf_transformation,[],[f45]) ).

tff(f45,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( X0 = X2 )
        | in(X0,X1)
        | ~ in(X0,add(X2,X1)) )
      & ( in(X0,add(X2,X1))
        | ( ( X0 != X2 )
          & ~ in(X0,X1) ) ) ),
    inference(flattening,[],[f44]) ).

tff(f44,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( X0 = X2 )
        | in(X0,X1)
        | ~ in(X0,add(X2,X1)) )
      & ( in(X0,add(X2,X1))
        | ( ( X0 != X2 )
          & ~ in(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( X0 = X2 )
        | in(X0,X1) )
    <=> in(X0,add(X2,X1)) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X5: $int,X6: collection,X7: $int] :
      ( ( ( X5 = X7 )
        | in(X5,X6) )
    <=> in(X5,add(X7,X6)) ),
    file('/export/starexec/sandbox2/tmp/tmp.Rig5IoZLoS/Vampire---4.8_25174',ax4) ).

tff(f108,plain,
    ( in(5,add(3,empty))
    | ~ spl0_1 ),
    inference(resolution,[],[f84,f65]) ).

tff(f65,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ~ in(X0,remove(X2,X1))
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f48]) ).

tff(f48,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( ( X0 != X2 )
          & in(X0,X1) )
        | ~ in(X0,remove(X2,X1)) )
      & ( in(X0,remove(X2,X1))
        | ( X0 = X2 )
        | ~ in(X0,X1) ) ),
    inference(flattening,[],[f47]) ).

tff(f47,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( ( X0 != X2 )
          & in(X0,X1) )
        | ~ in(X0,remove(X2,X1)) )
      & ( in(X0,remove(X2,X1))
        | ( X0 = X2 )
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( ( X0 != X2 )
        & in(X0,X1) )
    <=> in(X0,remove(X2,X1)) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X8: $int,X9: collection,X10: $int] :
      ( ( ( X8 != X10 )
        & in(X8,X9) )
    <=> in(X8,remove(X10,X9)) ),
    file('/export/starexec/sandbox2/tmp/tmp.Rig5IoZLoS/Vampire---4.8_25174',ax5) ).

tff(f84,plain,
    ( in(5,remove(3,add(3,empty)))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f82]) ).

tff(f82,plain,
    ( spl0_1
  <=> in(5,remove(3,add(3,empty))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

tff(f107,plain,
    spl0_2,
    inference(avatar_contradiction_clause,[],[f106]) ).

tff(f106,plain,
    ( $false
    | spl0_2 ),
    inference(evaluation,[],[f105]) ).

tff(f105,plain,
    ( ( 1 != $sum(0,1) )
    | spl0_2 ),
    inference(forward_demodulation,[],[f104,f73]) ).

tff(f73,plain,
    0 = count(empty),
    inference(equality_resolution,[],[f52]) ).

tff(f52,plain,
    ! [X0: collection] :
      ( ( 0 = count(X0) )
      | ( empty != X0 ) ),
    inference(cnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X0: collection] :
      ( ( ( empty = X0 )
        | ( 0 != count(X0) ) )
      & ( ( 0 = count(X0) )
        | ( empty != X0 ) ) ),
    inference(nnf_transformation,[],[f30]) ).

tff(f30,plain,
    ! [X0: collection] :
      ( ( empty = X0 )
    <=> ( 0 = count(X0) ) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X12: collection] :
      ( ( empty = X12 )
    <=> ( 0 = count(X12) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.Rig5IoZLoS/Vampire---4.8_25174',ax2) ).

tff(f104,plain,
    ( ( 1 != $sum(count(empty),1) )
    | spl0_2 ),
    inference(subsumption_resolution,[],[f102,f54]) ).

tff(f102,plain,
    ( ( 1 != $sum(count(empty),1) )
    | in(3,empty)
    | spl0_2 ),
    inference(superposition,[],[f101,f68]) ).

tff(f68,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(add(X0,X1)) = $sum(count(X1),1) )
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f49]) ).

tff(f49,plain,
    ! [X0: $int,X1: collection] :
      ( ( ~ in(X0,X1)
        | ( count(add(X0,X1)) != $sum(count(X1),1) ) )
      & ( ( count(add(X0,X1)) = $sum(count(X1),1) )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
    <=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X13: $int,X14: collection] :
      ( ~ in(X13,X14)
    <=> ( count(add(X13,X14)) = $sum(count(X14),1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.Rig5IoZLoS/Vampire---4.8_25174',ax3) ).

tff(f101,plain,
    ( ( 1 != count(add(3,empty)) )
    | spl0_2 ),
    inference(subsumption_resolution,[],[f100,f61]) ).

tff(f61,plain,
    ! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
    file('/export/starexec/sandbox2/tmp/tmp.Rig5IoZLoS/Vampire---4.8_25174',ax2) ).

tff(f100,plain,
    ( ( 1 != count(add(3,empty)) )
    | ~ in(3,add(3,empty))
    | spl0_2 ),
    inference(evaluation,[],[f98]) ).

tff(f98,plain,
    ( ( 1 != $sum(1,$sum(count(add(3,empty)),-1)) )
    | ~ in(3,add(3,empty))
    | spl0_2 ),
    inference(superposition,[],[f88,f77]) ).

tff(f77,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
      | ~ in(X0,X1) ),
    inference(evaluation,[],[f71]) ).

tff(f71,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f50]) ).

tff(f50,plain,
    ! [X0: $int,X1: collection] :
      ( ( in(X0,X1)
        | ( count(remove(X0,X1)) != $sum(count(X1),$uminus(1)) ) )
      & ( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f40]) ).

tff(f40,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
    <=> ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) ) ),
    inference(rectify,[],[f16]) ).

tff(f16,plain,
    ! [X17: $int,X18: collection] :
      ( in(X17,X18)
    <=> ( count(remove(X17,X18)) = $sum(count(X18),$uminus(1)) ) ),
    inference(theory_normalization,[],[f10]) ).

tff(f10,axiom,
    ! [X17: $int,X18: collection] :
      ( in(X17,X18)
    <=> ( count(remove(X17,X18)) = $difference(count(X18),1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.Rig5IoZLoS/Vampire---4.8_25174',ax5) ).

tff(f88,plain,
    ( ( 1 != $sum(1,count(remove(3,add(3,empty)))) )
    | spl0_2 ),
    inference(avatar_component_clause,[],[f86]) ).

tff(f86,plain,
    ( spl0_2
  <=> ( 1 = $sum(1,count(remove(3,add(3,empty)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

tff(f89,plain,
    ( spl0_1
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f80,f86,f82]) ).

tff(f80,plain,
    ( ( 1 != $sum(1,count(remove(3,add(3,empty)))) )
    | in(5,remove(3,add(3,empty))) ),
    inference(forward_demodulation,[],[f78,f17]) ).

tff(f17,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f78,plain,
    ( ( 1 != $sum(count(remove(3,add(3,empty))),1) )
    | in(5,remove(3,add(3,empty))) ),
    inference(superposition,[],[f51,f68]) ).

tff(f51,plain,
    1 != count(add(5,remove(3,add(3,empty)))),
    inference(cnf_transformation,[],[f29]) ).

tff(f29,plain,
    1 != count(add(5,remove(3,add(3,empty)))),
    inference(flattening,[],[f14]) ).

tff(f14,negated_conjecture,
    ( ~ 1 = count(add(5,remove(3,add(3,empty)))) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    1 = count(add(5,remove(3,add(3,empty)))),
    file('/export/starexec/sandbox2/tmp/tmp.Rig5IoZLoS/Vampire---4.8_25174',co1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : DAT047_1 : TPTP v8.1.2. Released v5.0.0.
% 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
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 12:59:05 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a TF0_THM_EQU_ARI problem
% 0.14/0.37  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.Rig5IoZLoS/Vampire---4.8_25174
% 0.61/0.76  % (25525)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)
% 0.61/0.76  % (25518)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)
% 0.61/0.76  % (25520)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.61/0.76  % (25519)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)
% 0.61/0.76  % (25521)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)
% 0.61/0.76  % (25522)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)
% 0.61/0.76  % (25523)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)
% 0.61/0.76  % (25524)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)
% 0.61/0.76  % (25523)First to succeed.
% 0.61/0.76  % (25518)Refutation not found, incomplete strategy% (25518)------------------------------
% 0.61/0.76  % (25518)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.76  % (25518)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.76  
% 0.61/0.76  % (25518)Memory used [KB]: 1080
% 0.61/0.76  % (25518)Time elapsed: 0.005 s
% 0.61/0.76  % (25518)Instructions burned: 6 (million)
% 0.61/0.76  % (25518)------------------------------
% 0.61/0.76  % (25518)------------------------------
% 0.61/0.76  % (25523)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25435"
% 0.61/0.76  % (25523)Refutation found. Thanks to Tanya!
% 0.61/0.76  % SZS status Theorem for Vampire---4
% 0.61/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.61/0.76  % (25523)------------------------------
% 0.61/0.76  % (25523)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.76  % (25523)Termination reason: Refutation
% 0.61/0.76  
% 0.61/0.76  % (25523)Memory used [KB]: 1081
% 0.61/0.76  % (25523)Time elapsed: 0.005 s
% 0.61/0.76  % (25523)Instructions burned: 6 (million)
% 0.61/0.76  % (25435)Success in time 0.385 s
% 0.61/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------