TSTP Solution File: GRA002+4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n022.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 : Sun May 5 05:43:17 EDT 2024
% Result : Theorem 0.56s 0.74s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 10 unt; 0 def)
% Number of atoms : 145 ( 21 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 156 ( 59 ~; 44 |; 30 &)
% ( 7 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 100 ( 90 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f109,plain,
$false,
inference(avatar_sat_refutation,[],[f74,f75,f85,f94,f108]) ).
fof(f108,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f107]) ).
fof(f107,plain,
( $false
| ~ spl5_3 ),
inference(resolution,[],[f80,f76]) ).
fof(f76,plain,
path(sK1,sK2,sK0),
inference(resolution,[],[f48,f57]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f43,f44]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
=> ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X2,X9] :
( shortest_path(X1,X2,X9)
<=> ( ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) )
& X1 != X2
& path(X1,X2,X9) ) ),
file('/export/starexec/sandbox/tmp/tmp.W3XKsOxIcG/Vampire---4.8_28846',shortest_path_defn) ).
fof(f48,plain,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( ~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph))
& shortest_path(sK1,sK2,sK0)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f28,f35]) ).
fof(f35,plain,
( ? [X0,X1,X2] :
( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
& shortest_path(X1,X2,X0) )
=> ( ~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph))
& shortest_path(sK1,sK2,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ? [X0,X1,X2] :
( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
& shortest_path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/tmp/tmp.W3XKsOxIcG/Vampire---4.8_28846',maximal_path_length) ).
fof(f80,plain,
( ! [X0,X1] : ~ path(X0,X1,sK0)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f79,plain,
( spl5_3
<=> ! [X0,X1] : ~ path(X0,X1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f94,plain,
( ~ spl5_2
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f93]) ).
fof(f93,plain,
( $false
| ~ spl5_2
| spl5_4 ),
inference(resolution,[],[f91,f48]) ).
fof(f91,plain,
( ! [X0,X1] : ~ shortest_path(X0,X1,sK0)
| ~ spl5_2
| spl5_4 ),
inference(resolution,[],[f88,f84]) ).
fof(f84,plain,
( ~ less_or_equal(number_of_in(sequential_pairs,sK0),number_of_in(triangles,graph))
| spl5_4 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f82,plain,
( spl5_4
<=> less_or_equal(number_of_in(sequential_pairs,sK0),number_of_in(triangles,graph)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f88,plain,
( ! [X2,X0,X1] :
( less_or_equal(number_of_in(sequential_pairs,X0),number_of_in(triangles,graph))
| ~ shortest_path(X1,X2,X0) )
| ~ spl5_2 ),
inference(superposition,[],[f62,f73]) ).
fof(f73,plain,
( ! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f72,plain,
( spl5_2
<=> ! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f62,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X10,X11] : less_or_equal(number_of_in(X10,X11),number_of_in(X10,graph)),
file('/export/starexec/sandbox/tmp/tmp.W3XKsOxIcG/Vampire---4.8_28846',graph_has_them_all) ).
fof(f85,plain,
( spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f77,f82,f79]) ).
fof(f77,plain,
! [X0,X1] :
( ~ less_or_equal(number_of_in(sequential_pairs,sK0),number_of_in(triangles,graph))
| ~ path(X0,X1,sK0) ),
inference(superposition,[],[f49,f56]) ).
fof(f56,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X1,X2,X3] :
( path(X1,X2,X3)
=> number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
file('/export/starexec/sandbox/tmp/tmp.W3XKsOxIcG/Vampire---4.8_28846',path_length_sequential_pairs) ).
fof(f49,plain,
~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f36]) ).
fof(f75,plain,
spl5_1,
inference(avatar_split_clause,[],[f47,f68]) ).
fof(f68,plain,
( spl5_1
<=> complete ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f47,plain,
complete,
inference(cnf_transformation,[],[f36]) ).
fof(f74,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f46,f72,f68]) ).
fof(f46,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0)
| ~ complete ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
( ! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0) )
| ~ complete ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.W3XKsOxIcG/Vampire---4.8_28846',triangles_and_sequential_pairs) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 18:25:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.W3XKsOxIcG/Vampire---4.8_28846
% 0.56/0.74 % (28963)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)
% 0.56/0.74 % (28956)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)
% 0.56/0.74 % (28963)Refutation not found, incomplete strategy% (28963)------------------------------
% 0.56/0.74 % (28963)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74 % (28963)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74
% 0.56/0.74 % (28963)Memory used [KB]: 1040
% 0.56/0.74 % (28963)Time elapsed: 0.002 s
% 0.56/0.74 % (28963)Instructions burned: 3 (million)
% 0.56/0.74 % (28958)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.56/0.74 % (28959)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)
% 0.56/0.74 % (28957)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)
% 0.56/0.74 % (28961)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)
% 0.56/0.74 % (28960)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)
% 0.56/0.74 % (28962)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)
% 0.56/0.74 % (28963)------------------------------
% 0.56/0.74 % (28963)------------------------------
% 0.56/0.74 % (28959)Refutation not found, incomplete strategy% (28959)------------------------------
% 0.56/0.74 % (28959)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74 % (28959)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74
% 0.56/0.74 % (28956)Refutation not found, incomplete strategy% (28956)------------------------------
% 0.56/0.74 % (28956)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74 % (28956)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74
% 0.56/0.74 % (28956)Memory used [KB]: 1056
% 0.56/0.74 % (28956)Time elapsed: 0.004 s
% 0.56/0.74 % (28956)Instructions burned: 3 (million)
% 0.56/0.74 % (28959)Memory used [KB]: 1047
% 0.56/0.74 % (28959)Time elapsed: 0.004 s
% 0.56/0.74 % (28959)Instructions burned: 3 (million)
% 0.56/0.74 % (28961)First to succeed.
% 0.56/0.74 % (28956)------------------------------
% 0.56/0.74 % (28956)------------------------------
% 0.56/0.74 % (28959)------------------------------
% 0.56/0.74 % (28959)------------------------------
% 0.56/0.74 % (28964)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)
% 0.56/0.74 % (28961)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28955"
% 0.56/0.74 % (28964)Also succeeded, but the first one will report.
% 0.56/0.74 % (28961)Refutation found. Thanks to Tanya!
% 0.56/0.74 % SZS status Theorem for Vampire---4
% 0.56/0.74 % SZS output start Proof for Vampire---4
% See solution above
% 0.56/0.75 % (28961)------------------------------
% 0.56/0.75 % (28961)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75 % (28961)Termination reason: Refutation
% 0.56/0.75
% 0.56/0.75 % (28961)Memory used [KB]: 1069
% 0.56/0.75 % (28961)Time elapsed: 0.005 s
% 0.56/0.75 % (28961)Instructions burned: 5 (million)
% 0.56/0.75 % (28955)Success in time 0.38 s
% 0.56/0.75 % Vampire---4.8 exiting
%------------------------------------------------------------------------------