TSTP Solution File: DAT024_1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : DAT024_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 : n026.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 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   51 (   8 unt;   7 typ;   0 def)
%            Number of atoms       :  125 (   9 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  145 (  64   ~;  34   |;  32   &)
%                                         (   4 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :  132 (  38 atm;   3 fun;  67 num;  24 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    9 (   5 usr;   6 con; 0-2 aty)
%            Number of variables   :   31 (  21   !;  10   ?;  31   :)

% 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: $int ).

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

tff(f186,plain,
    $false,
    inference(avatar_sat_refutation,[],[f105,f119,f161,f167,f185]) ).

tff(f185,plain,
    ~ spl2_8,
    inference(avatar_contradiction_clause,[],[f184]) ).

tff(f184,plain,
    ( $false
    | ~ spl2_8 ),
    inference(subsumption_resolution,[],[f168,f27]) ).

tff(f27,plain,
    ~ in(1,sK0),
    inference(cnf_transformation,[],[f26]) ).

tff(f26,plain,
    ( $less(sK1,2)
    & in(sK1,sK0)
    & ~ in(0,sK0)
    & ! [X2: $int] :
        ( ~ in(X2,sK0)
        | ~ $less(X2,0) )
    & ~ in(1,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f25,f24]) ).

tff(f24,plain,
    ( ? [X0: collection] :
        ( ? [X1: $int] :
            ( $less(X1,2)
            & in(X1,X0) )
        & ~ in(0,X0)
        & ! [X2: $int] :
            ( ~ in(X2,X0)
            | ~ $less(X2,0) )
        & ~ in(1,X0) )
   => ( ? [X1: $int] :
          ( $less(X1,2)
          & in(X1,sK0) )
      & ~ in(0,sK0)
      & ! [X2: $int] :
          ( ~ in(X2,sK0)
          | ~ $less(X2,0) )
      & ~ in(1,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f25,plain,
    ( ? [X1: $int] :
        ( $less(X1,2)
        & in(X1,sK0) )
   => ( $less(sK1,2)
      & in(sK1,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f23,plain,
    ? [X0: collection] :
      ( ? [X1: $int] :
          ( $less(X1,2)
          & in(X1,X0) )
      & ~ in(0,X0)
      & ! [X2: $int] :
          ( ~ in(X2,X0)
          | ~ $less(X2,0) )
      & ~ in(1,X0) ),
    inference(rectify,[],[f22]) ).

tff(f22,plain,
    ? [X0: collection] :
      ( ? [X2: $int] :
          ( $less(X2,2)
          & in(X2,X0) )
      & ~ in(0,X0)
      & ! [X1: $int] :
          ( ~ in(X1,X0)
          | ~ $less(X1,0) )
      & ~ in(1,X0) ),
    inference(flattening,[],[f21]) ).

tff(f21,plain,
    ? [X0: collection] :
      ( ? [X2: $int] :
          ( $less(X2,2)
          & in(X2,X0) )
      & ~ in(0,X0)
      & ! [X1: $int] :
          ( ~ in(X1,X0)
          | ~ $less(X1,0) )
      & ~ in(1,X0) ),
    inference(ennf_transformation,[],[f8]) ).

tff(f8,plain,
    ~ ! [X0: collection] :
        ( ( ~ in(0,X0)
          & ! [X1: $int] :
              ( in(X1,X0)
             => ~ $less(X1,0) )
          & ~ in(1,X0) )
       => ! [X2: $int] :
            ( in(X2,X0)
           => ~ $less(X2,2) ) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X0: collection] :
        ( ( ! [X1: $int] :
              ( in(X1,X0)
             => $greatereq(X1,0) )
          & ~ in(1,X0)
          & ~ in(0,X0) )
       => ! [X2: $int] :
            ( in(X2,X0)
           => $greatereq(X2,2) ) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X0: collection] :
      ( ( ! [X1: $int] :
            ( in(X1,X0)
           => $greatereq(X1,0) )
        & ~ in(1,X0)
        & ~ in(0,X0) )
     => ! [X2: $int] :
          ( in(X2,X0)
         => $greatereq(X2,2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f168,plain,
    ( in(1,sK0)
    | ~ spl2_8 ),
    inference(superposition,[],[f30,f138]) ).

tff(f138,plain,
    ( ( 1 = sK1 )
    | ~ spl2_8 ),
    inference(avatar_component_clause,[],[f136]) ).

tff(f136,plain,
    ( spl2_8
  <=> ( 1 = sK1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).

tff(f30,plain,
    in(sK1,sK0),
    inference(cnf_transformation,[],[f26]) ).

tff(f167,plain,
    ( spl2_8
    | ~ spl2_6
    | spl2_7 ),
    inference(avatar_split_clause,[],[f166,f132,f102,f136]) ).

tff(f102,plain,
    ( spl2_6
  <=> $less(0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

tff(f132,plain,
    ( spl2_7
  <=> $less(1,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

tff(f166,plain,
    ( ( 1 = sK1 )
    | ~ spl2_6
    | spl2_7 ),
    inference(subsumption_resolution,[],[f163,f123]) ).

tff(f123,plain,
    ( ~ $less(sK1,1)
    | ~ spl2_6 ),
    inference(evaluation,[],[f121]) ).

tff(f121,plain,
    ( ~ $less(sK1,$sum(0,1))
    | ~ spl2_6 ),
    inference(resolution,[],[f104,f20]) ).

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

tff(f104,plain,
    ( $less(0,sK1)
    | ~ spl2_6 ),
    inference(avatar_component_clause,[],[f102]) ).

tff(f163,plain,
    ( $less(sK1,1)
    | ( 1 = sK1 )
    | spl2_7 ),
    inference(resolution,[],[f133,f16]) ).

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

tff(f133,plain,
    ( ~ $less(1,sK1)
    | spl2_7 ),
    inference(avatar_component_clause,[],[f132]) ).

tff(f161,plain,
    ~ spl2_7,
    inference(avatar_contradiction_clause,[],[f160]) ).

tff(f160,plain,
    ( $false
    | ~ spl2_7 ),
    inference(subsumption_resolution,[],[f159,f31]) ).

tff(f31,plain,
    $less(sK1,2),
    inference(cnf_transformation,[],[f26]) ).

tff(f159,plain,
    ( ~ $less(sK1,2)
    | ~ spl2_7 ),
    inference(evaluation,[],[f157]) ).

tff(f157,plain,
    ( ~ $less(sK1,$sum(1,1))
    | ~ spl2_7 ),
    inference(resolution,[],[f134,f20]) ).

tff(f134,plain,
    ( $less(1,sK1)
    | ~ spl2_7 ),
    inference(avatar_component_clause,[],[f132]) ).

tff(f119,plain,
    ~ spl2_5,
    inference(avatar_contradiction_clause,[],[f118]) ).

tff(f118,plain,
    ( $false
    | ~ spl2_5 ),
    inference(subsumption_resolution,[],[f106,f29]) ).

tff(f29,plain,
    ~ in(0,sK0),
    inference(cnf_transformation,[],[f26]) ).

tff(f106,plain,
    ( in(0,sK0)
    | ~ spl2_5 ),
    inference(superposition,[],[f30,f100]) ).

tff(f100,plain,
    ( ( 0 = sK1 )
    | ~ spl2_5 ),
    inference(avatar_component_clause,[],[f98]) ).

tff(f98,plain,
    ( spl2_5
  <=> ( 0 = sK1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

tff(f105,plain,
    ( spl2_5
    | spl2_6 ),
    inference(avatar_split_clause,[],[f96,f102,f98]) ).

tff(f96,plain,
    ( $less(0,sK1)
    | ( 0 = sK1 ) ),
    inference(resolution,[],[f50,f30]) ).

tff(f50,plain,
    ! [X0: $int] :
      ( ~ in(X0,sK0)
      | ( 0 = X0 )
      | $less(0,X0) ),
    inference(resolution,[],[f28,f16]) ).

tff(f28,plain,
    ! [X2: $int] :
      ( ~ $less(X2,0)
      | ~ in(X2,sK0) ),
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : DAT024=1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 29 20:30:50 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.20/0.48  % (8972)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)
% 0.20/0.48  % (8964)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.49  % (8951)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.49  % (8964)Instruction limit reached!
% 0.20/0.49  % (8964)------------------------------
% 0.20/0.49  % (8964)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (8964)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (8964)Termination reason: Unknown
% 0.20/0.49  % (8964)Termination phase: Saturation
% 0.20/0.49  
% 0.20/0.49  % (8964)Memory used [KB]: 5500
% 0.20/0.49  % (8964)Time elapsed: 0.075 s
% 0.20/0.49  % (8964)Instructions burned: 3 (million)
% 0.20/0.49  % (8964)------------------------------
% 0.20/0.49  % (8964)------------------------------
% 0.20/0.49  % (8967)lrs+10_1:1_ss=axioms:st=5.0:tha=off:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.49  % (8967)Refutation not found, incomplete strategy% (8967)------------------------------
% 0.20/0.49  % (8967)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (8972)First to succeed.
% 0.20/0.49  % (8967)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (8967)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.49  
% 0.20/0.49  % (8967)Memory used [KB]: 5500
% 0.20/0.49  % (8967)Time elapsed: 0.076 s
% 0.20/0.49  % (8967)Instructions burned: 2 (million)
% 0.20/0.49  % (8967)------------------------------
% 0.20/0.49  % (8967)------------------------------
% 0.20/0.49  % (8972)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (8972)------------------------------
% 0.20/0.49  % (8972)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (8972)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (8972)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (8972)Memory used [KB]: 5500
% 0.20/0.49  % (8972)Time elapsed: 0.081 s
% 0.20/0.49  % (8972)Instructions burned: 6 (million)
% 0.20/0.49  % (8972)------------------------------
% 0.20/0.49  % (8972)------------------------------
% 0.20/0.49  % (8947)Success in time 0.151 s
%------------------------------------------------------------------------------