TSTP Solution File: DAT026_1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : DAT026_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n021.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 Aug 30 22:21:29 EDT 2023

% Result   : Theorem 0.23s 0.44s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   63 (  30 unt;   9 typ;   0 def)
%            Number of atoms       :  141 (  27 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  138 (  51   ~;  30   |;  42   &)
%                                         (   4 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  210 (  49 atm;  32 fun;  69 num;  60 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (   7 usr;   8 con; 0-2 aty)
%            Number of variables   :   84 (;  66   !;  18   ?;  84   :)

% 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_8,type,
    sK0: collection ).

tff(func_def_9,type,
    sK1: collection ).

tff(func_def_10,type,
    sK2: $int ).

tff(func_def_11,type,
    sK3: $int ).

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

tff(f427,plain,
    $false,
    inference(subsumption_resolution,[],[f423,f174]) ).

tff(f174,plain,
    ~ $less(2,sK3),
    inference(evaluation,[],[f171]) ).

tff(f171,plain,
    ~ $less($sum(1,1),sK3),
    inference(unit_resulting_resolution,[],[f68,f142,f15]) ).

tff(f15,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X0,X2)
      | ~ $less(X1,X2)
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_146,[]) ).

tff(f142,plain,
    ~ $less(1,sK3),
    inference(unit_resulting_resolution,[],[f68,f83,f15]) ).

tff(f83,plain,
    ~ $less(1,$sum(1,sK3)),
    inference(forward_demodulation,[],[f75,f9]) ).

tff(f9,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_138,[]) ).

tff(f75,plain,
    ~ $less(1,$sum(sK3,1)),
    inference(unit_resulting_resolution,[],[f67,f20]) ).

tff(f20,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(X0,1))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_164,[]) ).

tff(f67,plain,
    $less(sK3,1),
    inference(evaluation,[],[f62]) ).

tff(f62,plain,
    $less(sK3,$sum(0,1)),
    inference(unit_resulting_resolution,[],[f39,f18]) ).

tff(f18,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_150,[]) ).

tff(f39,plain,
    ~ $less(0,sK3),
    inference(cnf_transformation,[],[f30]) ).

tff(f30,plain,
    ( ~ $less(0,sK3)
    & in(sK3,sK0)
    & ( sK0 = add($sum(sK2,2),remove(sK2,sK1)) )
    & in(sK2,sK1)
    & ! [X4: $int] :
        ( $less(0,X4)
        | ~ in(X4,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f27,f29,f28]) ).

tff(f28,plain,
    ( ? [X0: collection,X1: collection,X2: $int] :
        ( ? [X3: $int] :
            ( ~ $less(0,X3)
            & in(X3,X0) )
        & ( add($sum(X2,2),remove(X2,X1)) = X0 )
        & in(X2,X1)
        & ! [X4: $int] :
            ( $less(0,X4)
            | ~ in(X4,X1) ) )
   => ( ? [X3: $int] :
          ( ~ $less(0,X3)
          & in(X3,sK0) )
      & ( sK0 = add($sum(sK2,2),remove(sK2,sK1)) )
      & in(sK2,sK1)
      & ! [X4: $int] :
          ( $less(0,X4)
          | ~ in(X4,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f29,plain,
    ( ? [X3: $int] :
        ( ~ $less(0,X3)
        & in(X3,sK0) )
   => ( ~ $less(0,sK3)
      & in(sK3,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f27,plain,
    ? [X0: collection,X1: collection,X2: $int] :
      ( ? [X3: $int] :
          ( ~ $less(0,X3)
          & in(X3,X0) )
      & ( add($sum(X2,2),remove(X2,X1)) = X0 )
      & in(X2,X1)
      & ! [X4: $int] :
          ( $less(0,X4)
          | ~ in(X4,X1) ) ),
    inference(rectify,[],[f26]) ).

tff(f26,plain,
    ? [X0: collection,X1: collection,X2: $int] :
      ( ? [X4: $int] :
          ( ~ $less(0,X4)
          & in(X4,X0) )
      & ( add($sum(X2,2),remove(X2,X1)) = X0 )
      & in(X2,X1)
      & ! [X3: $int] :
          ( $less(0,X3)
          | ~ in(X3,X1) ) ),
    inference(flattening,[],[f25]) ).

tff(f25,plain,
    ? [X0: collection,X1: collection,X2: $int] :
      ( ? [X4: $int] :
          ( ~ $less(0,X4)
          & in(X4,X0) )
      & ( add($sum(X2,2),remove(X2,X1)) = X0 )
      & in(X2,X1)
      & ! [X3: $int] :
          ( $less(0,X3)
          | ~ in(X3,X1) ) ),
    inference(ennf_transformation,[],[f8]) ).

tff(f8,plain,
    ~ ! [X0: collection,X1: collection,X2: $int] :
        ( ( ( add($sum(X2,2),remove(X2,X1)) = X0 )
          & in(X2,X1)
          & ! [X3: $int] :
              ( in(X3,X1)
             => $less(0,X3) ) )
       => ! [X4: $int] :
            ( in(X4,X0)
           => $less(0,X4) ) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X0: collection,X1: collection,X2: $int] :
        ( ( ( add($sum(X2,2),remove(X2,X1)) = X0 )
          & in(X2,X1)
          & ! [X3: $int] :
              ( in(X3,X1)
             => $greater(X3,0) ) )
       => ! [X4: $int] :
            ( in(X4,X0)
           => $greater(X4,0) ) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X0: collection,X1: collection,X2: $int] :
      ( ( ( add($sum(X2,2),remove(X2,X1)) = X0 )
        & in(X2,X1)
        & ! [X3: $int] :
            ( in(X3,X1)
           => $greater(X3,0) ) )
     => ! [X4: $int] :
          ( in(X4,X0)
         => $greater(X4,0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.APCKrO65Jd/Vampire---4.8_2922',co1) ).

tff(f68,plain,
    ! [X0: $int] : $less(X0,$sum(1,X0)),
    inference(superposition,[],[f64,f9]) ).

tff(f64,plain,
    ! [X0: $int] : $less(X0,$sum(X0,1)),
    inference(unit_resulting_resolution,[],[f14,f18]) ).

tff(f14,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_145,[]) ).

tff(f423,plain,
    $less(2,sK3),
    inference(backward_demodulation,[],[f106,f419]) ).

tff(f419,plain,
    sK3 = $sum(2,sK2),
    inference(unit_resulting_resolution,[],[f38,f90,f373]) ).

tff(f373,plain,
    ! [X0: $int] :
      ( in(X0,remove(sK2,sK1))
      | ~ in(X0,sK0)
      | ( $sum(2,sK2) = X0 ) ),
    inference(superposition,[],[f48,f51]) ).

tff(f51,plain,
    sK0 = add($sum(2,sK2),remove(sK2,sK1)),
    inference(forward_demodulation,[],[f37,f9]) ).

tff(f37,plain,
    sK0 = add($sum(sK2,2),remove(sK2,sK1)),
    inference(cnf_transformation,[],[f30]) ).

tff(f48,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ~ in(X0,add(X2,X1))
      | in(X0,X1)
      | ( X0 = X2 ) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,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,[],[f33]) ).

tff(f33,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,[],[f24]) ).

tff(f24,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.APCKrO65Jd/Vampire---4.8_2922',ax4) ).

tff(f90,plain,
    ! [X0: $int] : ~ in(sK3,remove(X0,sK1)),
    inference(unit_resulting_resolution,[],[f53,f44]) ).

tff(f44,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ~ in(X0,remove(X2,X1))
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,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,[],[f31]) ).

tff(f31,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,[],[f23]) ).

tff(f23,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.APCKrO65Jd/Vampire---4.8_2922',ax5) ).

tff(f53,plain,
    ~ in(sK3,sK1),
    inference(unit_resulting_resolution,[],[f39,f35]) ).

tff(f35,plain,
    ! [X4: $int] :
      ( $less(0,X4)
      | ~ in(X4,sK1) ),
    inference(cnf_transformation,[],[f30]) ).

tff(f38,plain,
    in(sK3,sK0),
    inference(cnf_transformation,[],[f30]) ).

tff(f106,plain,
    $less(2,$sum(2,sK2)),
    inference(evaluation,[],[f105]) ).

tff(f105,plain,
    $less(2,$sum($sum(1,sK2),1)),
    inference(unit_resulting_resolution,[],[f89,f18]) ).

tff(f89,plain,
    ~ $less($sum(1,sK2),2),
    inference(evaluation,[],[f88]) ).

tff(f88,plain,
    ~ $less($sum(1,sK2),$sum(1,1)),
    inference(unit_resulting_resolution,[],[f85,f20]) ).

tff(f85,plain,
    $less(1,$sum(1,sK2)),
    inference(forward_demodulation,[],[f84,f9]) ).

tff(f84,plain,
    $less(1,$sum(sK2,1)),
    inference(unit_resulting_resolution,[],[f82,f18]) ).

tff(f82,plain,
    ~ $less(sK2,1),
    inference(evaluation,[],[f74]) ).

tff(f74,plain,
    ~ $less(sK2,$sum(0,1)),
    inference(unit_resulting_resolution,[],[f52,f20]) ).

tff(f52,plain,
    $less(0,sK2),
    inference(unit_resulting_resolution,[],[f36,f35]) ).

tff(f36,plain,
    in(sK2,sK1),
    inference(cnf_transformation,[],[f30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : DAT026_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36  % Computer : n021.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   : Thu Aug 24 14:17:10 EDT 2023
% 0.14/0.37  % CPUTime    : 
% 0.14/0.37  This is a TF0_THM_EQU_ARI problem
% 0.14/0.37  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.APCKrO65Jd/Vampire---4.8_2922
% 0.14/0.37  % (3032)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43  % (3037)lrs+1010_2:1_amm=off:bs=on:bsr=on:canc=force:fsd=off:fsr=off:gs=on:gsaa=full_model:gsem=on:nm=0:nwc=1.3:sas=z3:sac=on:tha=off:thi=overlap:tgt=ground:uwa=ground:stl=60_408 on Vampire---4 for (408ds/0Mi)
% 0.23/0.43  % (3039)lrs-1010_3_av=off:br=off:drc=off:er=known:fsd=off:fde=unused:nm=4:nwc=3.0:sp=scramble:urr=on:stl=180_280 on Vampire---4 for (280ds/0Mi)
% 0.23/0.43  % (3034)dis-1010_2:3_canc=force:fsd=off:fde=unused:gs=on:gsem=on:nm=0:nwc=1.3:sas=z3:tha=off:thf=on:uwa=ground_572 on Vampire---4 for (572ds/0Mi)
% 0.23/0.43  % (3038)ott+10_1024_av=off:bd=preordered:br=off:ep=RSTC:fsr=off:fde=none:nm=2:urr=on_318 on Vampire---4 for (318ds/0Mi)
% 0.23/0.43  % (3033)lrs+2_32_add=large:amm=off:bd=off:bs=unit_only:drc=off:flr=on:fsd=off:fde=none:nm=0:nwc=1.1:sos=theory:sp=reverse_arity:tgt=ground:stl=180_1034 on Vampire---4 for (1034ds/0Mi)
% 0.23/0.43  % (3035)dis-10_20_canc=force:fsd=off:gs=on:gsem=off:nm=0:sas=z3:sac=on:tha=off:thi=strong:tgt=ground_476 on Vampire---4 for (476ds/0Mi)
% 0.23/0.43  % (3036)dis-11_10:1_canc=force:fsd=off:nwc=1.5:sas=z3:tha=off:uwa=all_472 on Vampire---4 for (472ds/0Mi)
% 0.23/0.44  % (3039)First to succeed.
% 0.23/0.44  % (3039)Refutation found. Thanks to Tanya!
% 0.23/0.44  % SZS status Theorem for Vampire---4
% 0.23/0.44  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.44  % (3039)------------------------------
% 0.23/0.44  % (3039)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.44  % (3039)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.44  % (3039)Termination reason: Refutation
% 0.23/0.44  
% 0.23/0.44  % (3039)Memory used [KB]: 1279
% 0.23/0.44  % (3039)Time elapsed: 0.013 s
% 0.23/0.44  % (3039)------------------------------
% 0.23/0.44  % (3039)------------------------------
% 0.23/0.44  % (3032)Success in time 0.072 s
% 0.23/0.44  % Vampire---4.8 exiting
%------------------------------------------------------------------------------