TSTP Solution File: DAT033_1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : DAT033_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 : n007.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 02:18:37 EDT 2024

% Result   : Theorem 0.61s 0.77s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   66 (   4 unt;   7 typ;   0 def)
%            Number of atoms       :  128 (  58 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  123 (  54   ~;  46   |;   8   &)
%                                         (  12 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number arithmetic     :  131 (   0 atm;  32 fun;  74 num;  25 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :   12 (   5 usr;   6 con; 0-2 aty)
%            Number of variables   :   52 (  50   !;   2   ?;  52   :)

% 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(func_def_11,type,
    sK0: collection ).

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

tff(f392,plain,
    $false,
    inference(avatar_sat_refutation,[],[f324,f361,f376,f391]) ).

tff(f391,plain,
    ( ~ spl1_3
    | ~ spl1_4 ),
    inference(avatar_contradiction_clause,[],[f390]) ).

tff(f390,plain,
    ( $false
    | ~ spl1_3
    | ~ spl1_4 ),
    inference(subsumption_resolution,[],[f386,f372]) ).

tff(f372,plain,
    ( ( count(remove(5,sK0)) != $sum(-1,count(sK0)) )
    | ~ spl1_3 ),
    inference(backward_demodulation,[],[f54,f368]) ).

tff(f368,plain,
    ( ( count(remove(3,sK0)) = $sum(-1,count(sK0)) )
    | ~ spl1_3 ),
    inference(resolution,[],[f218,f83]) ).

tff(f83,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
      | ( count(remove(X0,X1)) = $sum(-1,count(X1)) ) ),
    inference(backward_demodulation,[],[f79,f17]) ).

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

tff(f79,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
      | ~ in(X0,X1) ),
    inference(evaluation,[],[f66]) ).

tff(f66,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) )
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f49]) ).

tff(f49,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,[],[f35]) ).

tff(f35,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.DiEAvTyuv6/Vampire---4.8_31005',ax5) ).

tff(f218,plain,
    ( in(3,sK0)
    | ~ spl1_3 ),
    inference(avatar_component_clause,[],[f216]) ).

tff(f216,plain,
    ( spl1_3
  <=> in(3,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

tff(f54,plain,
    count(remove(5,sK0)) != count(remove(3,sK0)),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,plain,
    ( ( count(remove(5,sK0)) != count(remove(3,sK0)) )
    & ( count(add(5,sK0)) = count(add(3,sK0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f40,f42]) ).

tff(f42,plain,
    ( ? [X0: collection] :
        ( ( count(remove(5,X0)) != count(remove(3,X0)) )
        & ( count(add(5,X0)) = count(add(3,X0)) ) )
   => ( ( count(remove(5,sK0)) != count(remove(3,sK0)) )
      & ( count(add(5,sK0)) = count(add(3,sK0)) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f40,plain,
    ? [X0: collection] :
      ( ( count(remove(5,X0)) != count(remove(3,X0)) )
      & ( count(add(5,X0)) = count(add(3,X0)) ) ),
    inference(ennf_transformation,[],[f14]) ).

tff(f14,negated_conjecture,
    ~ ! [X0: collection] :
        ( ( count(add(5,X0)) = count(add(3,X0)) )
       => ( count(remove(5,X0)) = count(remove(3,X0)) ) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    ! [X0: collection] :
      ( ( count(add(5,X0)) = count(add(3,X0)) )
     => ( count(remove(5,X0)) = count(remove(3,X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.DiEAvTyuv6/Vampire---4.8_31005',co1) ).

tff(f386,plain,
    ( ( count(remove(5,sK0)) = $sum(-1,count(sK0)) )
    | ~ spl1_4 ),
    inference(resolution,[],[f385,f83]) ).

tff(f385,plain,
    ( in(5,sK0)
    | ~ spl1_4 ),
    inference(trivial_inequality_removal,[],[f380]) ).

tff(f380,plain,
    ( ( count(sK0) != count(sK0) )
    | in(5,sK0)
    | ~ spl1_4 ),
    inference(superposition,[],[f57,f221]) ).

tff(f221,plain,
    ( ( count(add(5,sK0)) = count(sK0) )
    | ~ spl1_4 ),
    inference(avatar_component_clause,[],[f220]) ).

tff(f220,plain,
    ( spl1_4
  <=> ( count(add(5,sK0)) = count(sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

tff(f57,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(add(X0,X1)) != count(X1) )
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f44,plain,
    ! [X0: $int,X1: collection] :
      ( ( in(X0,X1)
        | ( count(add(X0,X1)) != count(X1) ) )
      & ( ( count(add(X0,X1)) = count(X1) )
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f30]) ).

tff(f30,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
    <=> ( count(add(X0,X1)) = count(X1) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X15: $int,X16: collection] :
      ( in(X15,X16)
    <=> ( count(add(X15,X16)) = count(X16) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.DiEAvTyuv6/Vampire---4.8_31005',ax4) ).

tff(f376,plain,
    ( spl1_4
    | ~ spl1_3 ),
    inference(avatar_split_clause,[],[f373,f216,f220]) ).

tff(f373,plain,
    ( ( count(add(5,sK0)) = count(sK0) )
    | ~ spl1_3 ),
    inference(backward_demodulation,[],[f53,f370]) ).

tff(f370,plain,
    ( ( count(add(3,sK0)) = count(sK0) )
    | ~ spl1_3 ),
    inference(resolution,[],[f218,f56]) ).

tff(f56,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
      | ( count(add(X0,X1)) = count(X1) ) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f53,plain,
    count(add(5,sK0)) = count(add(3,sK0)),
    inference(cnf_transformation,[],[f43]) ).

tff(f361,plain,
    ( spl1_3
    | ~ spl1_5 ),
    inference(avatar_contradiction_clause,[],[f360]) ).

tff(f360,plain,
    ( $false
    | spl1_3
    | ~ spl1_5 ),
    inference(subsumption_resolution,[],[f359,f325]) ).

tff(f325,plain,
    ( ( count(remove(5,sK0)) != count(sK0) )
    | spl1_3 ),
    inference(backward_demodulation,[],[f54,f322]) ).

tff(f322,plain,
    ( ( count(remove(3,sK0)) = count(sK0) )
    | spl1_3 ),
    inference(resolution,[],[f217,f64]) ).

tff(f64,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
      | ( count(X1) = count(remove(X0,X1)) ) ),
    inference(cnf_transformation,[],[f48]) ).

tff(f48,plain,
    ! [X0: $int,X1: collection] :
      ( ( ~ in(X0,X1)
        | ( count(X1) != count(remove(X0,X1)) ) )
      & ( ( count(X1) = count(remove(X0,X1)) )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
    <=> ( count(X1) = count(remove(X0,X1)) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X19: $int,X20: collection] :
      ( ~ in(X19,X20)
    <=> ( count(remove(X19,X20)) = count(X20) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.DiEAvTyuv6/Vampire---4.8_31005',ax6) ).

tff(f217,plain,
    ( ~ in(3,sK0)
    | spl1_3 ),
    inference(avatar_component_clause,[],[f216]) ).

tff(f359,plain,
    ( ( count(remove(5,sK0)) = count(sK0) )
    | ~ spl1_5 ),
    inference(resolution,[],[f357,f64]) ).

tff(f357,plain,
    ( ~ in(5,sK0)
    | ~ spl1_5 ),
    inference(trivial_inequality_removal,[],[f349]) ).

tff(f349,plain,
    ( ( $sum(1,count(sK0)) != $sum(1,count(sK0)) )
    | ~ in(5,sK0)
    | ~ spl1_5 ),
    inference(superposition,[],[f82,f318]) ).

tff(f318,plain,
    ( ( count(add(5,sK0)) = $sum(1,count(sK0)) )
    | ~ spl1_5 ),
    inference(avatar_component_clause,[],[f317]) ).

tff(f317,plain,
    ( spl1_5
  <=> ( count(add(5,sK0)) = $sum(1,count(sK0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).

tff(f82,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(add(X0,X1)) != $sum(1,count(X1)) )
      | ~ in(X0,X1) ),
    inference(backward_demodulation,[],[f59,f17]) ).

tff(f59,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
      | ( count(add(X0,X1)) != $sum(count(X1),1) ) ),
    inference(cnf_transformation,[],[f45]) ).

tff(f45,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,[],[f31]) ).

tff(f31,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.DiEAvTyuv6/Vampire---4.8_31005',ax3) ).

tff(f324,plain,
    ( spl1_5
    | spl1_3 ),
    inference(avatar_split_clause,[],[f323,f216,f317]) ).

tff(f323,plain,
    ( ( count(add(5,sK0)) = $sum(1,count(sK0)) )
    | spl1_3 ),
    inference(backward_demodulation,[],[f53,f321]) ).

tff(f321,plain,
    ( ( count(add(3,sK0)) = $sum(1,count(sK0)) )
    | spl1_3 ),
    inference(resolution,[],[f217,f81]) ).

tff(f81,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
      | ( count(add(X0,X1)) = $sum(1,count(X1)) ) ),
    inference(backward_demodulation,[],[f58,f17]) ).

tff(f58,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(add(X0,X1)) = $sum(count(X1),1) )
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : DAT033_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 : n007.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   : Tue Apr 30 16:24:48 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a TF0_THM_EQU_ARI problem
% 0.14/0.36  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.DiEAvTyuv6/Vampire---4.8_31005
% 0.54/0.75  % (31328)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)
% 0.54/0.75  % (31321)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)
% 0.54/0.75  % (31323)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.54/0.75  % (31328)Refutation not found, incomplete strategy% (31328)------------------------------
% 0.54/0.75  % (31328)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.75  % (31328)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.75  
% 0.54/0.75  % (31328)Memory used [KB]: 1057
% 0.54/0.75  % (31328)Time elapsed: 0.002 s
% 0.54/0.75  % (31328)Instructions burned: 3 (million)
% 0.54/0.75  % (31328)------------------------------
% 0.54/0.75  % (31328)------------------------------
% 0.54/0.75  % (31322)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)
% 0.54/0.75  % (31325)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)
% 0.54/0.75  % (31324)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)
% 0.54/0.75  % (31327)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)
% 0.54/0.75  % (31326)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)
% 0.54/0.76  % (31326)Refutation not found, incomplete strategy% (31326)------------------------------
% 0.54/0.76  % (31326)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.76  % (31326)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.76  % (31330)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 (2996ds/55Mi)
% 0.54/0.76  
% 0.54/0.76  % (31326)Memory used [KB]: 1070
% 0.54/0.76  % (31326)Time elapsed: 0.004 s
% 0.54/0.76  % (31326)Instructions burned: 4 (million)
% 0.54/0.76  % (31326)------------------------------
% 0.54/0.76  % (31326)------------------------------
% 0.54/0.76  % (31321)Refutation not found, incomplete strategy% (31321)------------------------------
% 0.54/0.76  % (31321)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.76  % (31321)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.76  
% 0.54/0.76  % (31321)Memory used [KB]: 1079
% 0.54/0.76  % (31321)Time elapsed: 0.005 s
% 0.54/0.76  % (31321)Instructions burned: 5 (million)
% 0.54/0.76  % (31321)------------------------------
% 0.54/0.76  % (31321)------------------------------
% 0.54/0.76  % (31332)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 (2996ds/50Mi)
% 0.54/0.76  % (31334)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 (2996ds/208Mi)
% 0.54/0.76  % (31332)Refutation not found, incomplete strategy% (31332)------------------------------
% 0.54/0.76  % (31332)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.76  % (31332)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.76  
% 0.54/0.76  % (31332)Memory used [KB]: 1051
% 0.54/0.76  % (31332)Time elapsed: 0.004 s
% 0.54/0.76  % (31332)Instructions burned: 4 (million)
% 0.54/0.76  % (31332)------------------------------
% 0.54/0.76  % (31332)------------------------------
% 0.61/0.77  % (31323)First to succeed.
% 0.61/0.77  % (31336)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.61/0.77  % (31323)Refutation found. Thanks to Tanya!
% 0.61/0.77  % SZS status Theorem for Vampire---4
% 0.61/0.77  % SZS output start Proof for Vampire---4
% See solution above
% 0.61/0.77  % (31323)------------------------------
% 0.61/0.77  % (31323)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.61/0.77  % (31323)Termination reason: Refutation
% 0.61/0.77  
% 0.61/0.77  % (31323)Memory used [KB]: 1167
% 0.61/0.77  % (31323)Time elapsed: 0.016 s
% 0.61/0.77  % (31323)Instructions burned: 22 (million)
% 0.61/0.77  % (31323)------------------------------
% 0.61/0.77  % (31323)------------------------------
% 0.61/0.77  % (31155)Success in time 0.398 s
% 0.61/0.77  % Vampire---4.8 exiting
%------------------------------------------------------------------------------