TSTP Solution File: DAT028_1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : DAT028_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n006.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 31 16:03:56 EDT 2022

% Result   : Theorem 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   51 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :  133 (   4 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  140 (  49   ~;  34   |;  36   &)
%                                         (   2 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :  160 (  58 atm;   3 fun;  47 num;  52 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   68 (  44   !;  24   ?;  68   :)

% 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_7,type,
    sK0: collection ).

tff(func_def_8,type,
    sK1: collection ).

tff(func_def_9,type,
    sK2: $int ).

tff(func_def_10,type,
    sK3: $int > $int ).

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

tff(f113,plain,
    $false,
    inference(avatar_sat_refutation,[],[f45,f64,f112]) ).

tff(f112,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f111]) ).

tff(f111,plain,
    ( $false
    | ~ spl4_1 ),
    inference(subsumption_resolution,[],[f110,f77]) ).

tff(f77,plain,
    ~ $less(sK3(sK2),1),
    inference(evaluation,[],[f76]) ).

tff(f76,plain,
    ~ $less(sK3(sK2),$sum(0,1)),
    inference(resolution,[],[f73,f20]) ).

tff(f20,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_166,[]) ).

tff(f73,plain,
    $less(0,sK3(sK2)),
    inference(resolution,[],[f51,f29]) ).

tff(f29,plain,
    ! [X5: $int] :
      ( ~ in(X5,sK0)
      | $less(0,X5) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f28,plain,
    ( in(sK2,sK1)
    & ~ $less(1,sK2)
    & ! [X3: $int] :
        ( ~ in(X3,sK1)
        | ( in(sK3(X3),sK0)
          & $less(sK3(X3),X3) ) )
    & ! [X5: $int] :
        ( ~ in(X5,sK0)
        | $less(0,X5) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f24,f27,f26,f25]) ).

tff(f25,plain,
    ( ? [X0: collection,X1: collection] :
        ( ? [X2: $int] :
            ( in(X2,X1)
            & ~ $less(1,X2) )
        & ! [X3: $int] :
            ( ~ in(X3,X1)
            | ? [X4: $int] :
                ( in(X4,X0)
                & $less(X4,X3) ) )
        & ! [X5: $int] :
            ( ~ in(X5,X0)
            | $less(0,X5) ) )
   => ( ? [X2: $int] :
          ( in(X2,sK1)
          & ~ $less(1,X2) )
      & ! [X3: $int] :
          ( ~ in(X3,sK1)
          | ? [X4: $int] :
              ( in(X4,sK0)
              & $less(X4,X3) ) )
      & ! [X5: $int] :
          ( ~ in(X5,sK0)
          | $less(0,X5) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f26,plain,
    ( ? [X2: $int] :
        ( in(X2,sK1)
        & ~ $less(1,X2) )
   => ( in(sK2,sK1)
      & ~ $less(1,sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f27,plain,
    ! [X3: $int] :
      ( ? [X4: $int] :
          ( in(X4,sK0)
          & $less(X4,X3) )
     => ( in(sK3(X3),sK0)
        & $less(sK3(X3),X3) ) ),
    introduced(choice_axiom,[]) ).

tff(f24,plain,
    ? [X0: collection,X1: collection] :
      ( ? [X2: $int] :
          ( in(X2,X1)
          & ~ $less(1,X2) )
      & ! [X3: $int] :
          ( ~ in(X3,X1)
          | ? [X4: $int] :
              ( in(X4,X0)
              & $less(X4,X3) ) )
      & ! [X5: $int] :
          ( ~ in(X5,X0)
          | $less(0,X5) ) ),
    inference(rectify,[],[f23]) ).

tff(f23,plain,
    ? [X0: collection,X1: collection] :
      ( ? [X5: $int] :
          ( in(X5,X1)
          & ~ $less(1,X5) )
      & ! [X2: $int] :
          ( ~ in(X2,X1)
          | ? [X3: $int] :
              ( in(X3,X0)
              & $less(X3,X2) ) )
      & ! [X4: $int] :
          ( ~ in(X4,X0)
          | $less(0,X4) ) ),
    inference(flattening,[],[f22]) ).

tff(f22,plain,
    ? [X0: collection,X1: collection] :
      ( ? [X5: $int] :
          ( in(X5,X1)
          & ~ $less(1,X5) )
      & ! [X2: $int] :
          ( ~ in(X2,X1)
          | ? [X3: $int] :
              ( in(X3,X0)
              & $less(X3,X2) ) )
      & ! [X4: $int] :
          ( ~ in(X4,X0)
          | $less(0,X4) ) ),
    inference(ennf_transformation,[],[f21]) ).

tff(f21,plain,
    ~ ! [X0: collection,X1: collection] :
        ( ( ! [X2: $int] :
              ( in(X2,X1)
             => ? [X3: $int] :
                  ( in(X3,X0)
                  & $less(X3,X2) ) )
          & ! [X4: $int] :
              ( in(X4,X0)
             => $less(0,X4) ) )
       => ! [X5: $int] :
            ( in(X5,X1)
           => $less(1,X5) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,plain,
    ~ ! [X1: collection,X0: collection] :
        ( ( ! [X3: $int] :
              ( in(X3,X0)
             => ? [X4: $int] :
                  ( $less(X4,X3)
                  & in(X4,X1) ) )
          & ! [X2: $int] :
              ( in(X2,X1)
             => $less(0,X2) ) )
       => ! [X5: $int] :
            ( in(X5,X0)
           => $less(1,X5) ) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X1: collection,X0: collection] :
        ( ( ! [X3: $int] :
              ( in(X3,X0)
             => ? [X4: $int] :
                  ( $greater(X3,X4)
                  & in(X4,X1) ) )
          & ! [X2: $int] :
              ( in(X2,X1)
             => $greater(X2,0) ) )
       => ! [X5: $int] :
            ( in(X5,X0)
           => $greater(X5,1) ) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X1: collection,X0: collection] :
      ( ( ! [X3: $int] :
            ( in(X3,X0)
           => ? [X4: $int] :
                ( $greater(X3,X4)
                & in(X4,X1) ) )
        & ! [X2: $int] :
            ( in(X2,X1)
           => $greater(X2,0) ) )
     => ! [X5: $int] :
          ( in(X5,X0)
         => $greater(X5,1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f51,plain,
    in(sK3(sK2),sK0),
    inference(resolution,[],[f31,f33]) ).

tff(f33,plain,
    in(sK2,sK1),
    inference(cnf_transformation,[],[f28]) ).

tff(f31,plain,
    ! [X3: $int] :
      ( ~ in(X3,sK1)
      | in(sK3(X3),sK0) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f110,plain,
    ( $less(sK3(sK2),1)
    | ~ spl4_1 ),
    inference(resolution,[],[f66,f48]) ).

tff(f48,plain,
    $less(sK3(sK2),sK2),
    inference(resolution,[],[f30,f33]) ).

tff(f30,plain,
    ! [X3: $int] :
      ( ~ in(X3,sK1)
      | $less(sK3(X3),X3) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f66,plain,
    ( ! [X1: $int] :
        ( ~ $less(X1,sK2)
        | $less(X1,1) )
    | ~ spl4_1 ),
    inference(resolution,[],[f39,f15]) ).

tff(f15,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X2)
      | ~ $less(X0,X1)
      | $less(X0,X2) ),
    introduced(theory_axiom_148,[]) ).

tff(f39,plain,
    ( $less(sK2,1)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f37]) ).

tff(f37,plain,
    ( spl4_1
  <=> $less(sK2,1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

tff(f64,plain,
    ~ spl4_2,
    inference(avatar_contradiction_clause,[],[f63]) ).

tff(f63,plain,
    ( $false
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f62,f50]) ).

tff(f50,plain,
    ( $less(sK3(1),1)
    | ~ spl4_2 ),
    inference(forward_demodulation,[],[f48,f43]) ).

tff(f43,plain,
    ( ( 1 = sK2 )
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f41]) ).

tff(f41,plain,
    ( spl4_2
  <=> ( 1 = sK2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

tff(f62,plain,
    ( ~ $less(sK3(1),1)
    | ~ spl4_2 ),
    inference(evaluation,[],[f61]) ).

tff(f61,plain,
    ( ~ $less(sK3(1),$sum(0,1))
    | ~ spl4_2 ),
    inference(resolution,[],[f58,f20]) ).

tff(f58,plain,
    ( $less(0,sK3(1))
    | ~ spl4_2 ),
    inference(resolution,[],[f53,f29]) ).

tff(f53,plain,
    ( in(sK3(1),sK0)
    | ~ spl4_2 ),
    inference(forward_demodulation,[],[f51,f43]) ).

tff(f45,plain,
    ( spl4_2
    | spl4_1 ),
    inference(avatar_split_clause,[],[f35,f37,f41]) ).

tff(f35,plain,
    ( $less(sK2,1)
    | ( 1 = sK2 ) ),
    inference(resolution,[],[f32,f16]) ).

tff(f16,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_149,[]) ).

tff(f32,plain,
    ~ $less(1,sK2),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : DAT028=1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon Aug 29 20:15:40 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.51  % (1235)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.53  % (1230)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 0.20/0.53  % (1243)lrs+10_1:1_sd=10:sos=all:ss=axioms:st=5.0:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.53  % (1231)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 0.20/0.53  % (1246)dis+2_1:1_av=off:bsr=on:erd=off:s2pl=on:sgt=16:sos=on:sp=frequency:ss=axioms:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 0.20/0.54  % (1238)lrs+22_1:1_amm=sco:fsr=off:gve=force:sos=on:uwa=all:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54  % (1235)First to succeed.
% 0.20/0.54  % (1247)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54  % (1240)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.54  % (1235)Refutation found. Thanks to Tanya!
% 0.20/0.54  % SZS status Theorem for theBenchmark
% 0.20/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (1235)------------------------------
% 0.20/0.54  % (1235)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (1235)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (1235)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (1235)Memory used [KB]: 5500
% 0.20/0.54  % (1235)Time elapsed: 0.126 s
% 0.20/0.54  % (1235)Instructions burned: 3 (million)
% 0.20/0.54  % (1235)------------------------------
% 0.20/0.54  % (1235)------------------------------
% 0.20/0.54  % (1223)Success in time 0.188 s
%------------------------------------------------------------------------------