TSTP Solution File: NUM410+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n009.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 17:59:22 EDT 2022

% Result   : Theorem 0.18s 0.49s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   30 (  11 unt;   0 def)
%            Number of atoms       :  100 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  111 (  41   ~;  34   |;  23   &)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   27 (  24   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f254,plain,
    $false,
    inference(subsumption_resolution,[],[f250,f199]) ).

fof(f199,plain,
    ~ transfinite_sequence_of(sK11,relation_rng(sK11)),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ( relation(sK11)
    & ~ transfinite_sequence_of(sK11,relation_rng(sK11))
    & function(sK11)
    & ordinal(relation_dom(sK11)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f83,f125]) ).

fof(f125,plain,
    ( ? [X0] :
        ( relation(X0)
        & ~ transfinite_sequence_of(X0,relation_rng(X0))
        & function(X0)
        & ordinal(relation_dom(X0)) )
   => ( relation(sK11)
      & ~ transfinite_sequence_of(sK11,relation_rng(sK11))
      & function(sK11)
      & ordinal(relation_dom(sK11)) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ? [X0] :
      ( relation(X0)
      & ~ transfinite_sequence_of(X0,relation_rng(X0))
      & function(X0)
      & ordinal(relation_dom(X0)) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ? [X0] :
      ( ~ transfinite_sequence_of(X0,relation_rng(X0))
      & ordinal(relation_dom(X0))
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ( ordinal(relation_dom(X0))
         => transfinite_sequence_of(X0,relation_rng(X0)) ) ),
    inference(negated_conjecture,[],[f40]) ).

fof(f40,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( ordinal(relation_dom(X0))
       => transfinite_sequence_of(X0,relation_rng(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_ordinal1) ).

fof(f250,plain,
    transfinite_sequence_of(sK11,relation_rng(sK11)),
    inference(unit_resulting_resolution,[],[f200,f198,f194,f243,f141]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( transfinite_sequence_of(X0,X1)
      | ~ relation(X0)
      | ~ subset(relation_rng(X0),X1)
      | ~ function(X0)
      | ~ transfinite_sequence(X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ( ( transfinite_sequence_of(X0,X1)
          | ~ subset(relation_rng(X0),X1) )
        & ( subset(relation_rng(X0),X1)
          | ~ transfinite_sequence_of(X0,X1) ) )
      | ~ transfinite_sequence(X0) ),
    inference(rectify,[],[f94]) ).

fof(f94,plain,
    ! [X1,X0] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ( ( transfinite_sequence_of(X1,X0)
          | ~ subset(relation_rng(X1),X0) )
        & ( subset(relation_rng(X1),X0)
          | ~ transfinite_sequence_of(X1,X0) ) )
      | ~ transfinite_sequence(X1) ),
    inference(nnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X1,X0] :
      ( ~ relation(X1)
      | ~ function(X1)
      | ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) )
      | ~ transfinite_sequence(X1) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X1,X0] :
      ( ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) )
      | ~ relation(X1)
      | ~ transfinite_sequence(X1)
      | ~ function(X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0] :
      ( ( relation(X1)
        & transfinite_sequence(X1)
        & function(X1) )
     => ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).

fof(f243,plain,
    transfinite_sequence(sK11),
    inference(subsumption_resolution,[],[f242,f198]) ).

fof(f242,plain,
    ( transfinite_sequence(sK11)
    | ~ function(sK11) ),
    inference(subsumption_resolution,[],[f230,f197]) ).

fof(f197,plain,
    ordinal(relation_dom(sK11)),
    inference(cnf_transformation,[],[f126]) ).

fof(f230,plain,
    ( ~ ordinal(relation_dom(sK11))
    | ~ function(sK11)
    | transfinite_sequence(sK11) ),
    inference(resolution,[],[f200,f155]) ).

fof(f155,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ ordinal(relation_dom(X0))
      | transfinite_sequence(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ function(X0)
      | ( ( ordinal(relation_dom(X0))
          | ~ transfinite_sequence(X0) )
        & ( transfinite_sequence(X0)
          | ~ ordinal(relation_dom(X0)) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ~ function(X0)
      | ( ordinal(relation_dom(X0))
      <=> transfinite_sequence(X0) )
      | ~ relation(X0) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( ( ordinal(relation_dom(X0))
      <=> transfinite_sequence(X0) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ( relation(X0)
        & function(X0) )
     => ( ordinal(relation_dom(X0))
      <=> transfinite_sequence(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).

fof(f194,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f48]) ).

fof(f48,plain,
    ! [X1] : subset(X1,X1),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X1,X0] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f198,plain,
    function(sK11),
    inference(cnf_transformation,[],[f126]) ).

fof(f200,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f126]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n009.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   : Tue Aug 30 06:26:05 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.45  % (9689)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.47  % (9712)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.18/0.47  % (9689)Refutation not found, incomplete strategy% (9689)------------------------------
% 0.18/0.47  % (9689)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.47  % (9689)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.47  % (9689)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.47  
% 0.18/0.47  % (9689)Memory used [KB]: 6012
% 0.18/0.47  % (9689)Time elapsed: 0.092 s
% 0.18/0.47  % (9689)Instructions burned: 3 (million)
% 0.18/0.47  % (9689)------------------------------
% 0.18/0.47  % (9689)------------------------------
% 0.18/0.47  % (9707)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.18/0.48  % (9704)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.18/0.48  % (9692)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.48  % (9697)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.48  % (9692)First to succeed.
% 0.18/0.49  % (9692)Refutation found. Thanks to Tanya!
% 0.18/0.49  % SZS status Theorem for theBenchmark
% 0.18/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49  % (9692)------------------------------
% 0.18/0.49  % (9692)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49  % (9692)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49  % (9692)Termination reason: Refutation
% 0.18/0.49  
% 0.18/0.49  % (9692)Memory used [KB]: 6012
% 0.18/0.49  % (9692)Time elapsed: 0.009 s
% 0.18/0.49  % (9692)Instructions burned: 3 (million)
% 0.18/0.49  % (9692)------------------------------
% 0.18/0.49  % (9692)------------------------------
% 0.18/0.49  % (9684)Success in time 0.144 s
%------------------------------------------------------------------------------