TSTP Solution File: GRA010+2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRA010+2 : 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 : n024.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 05:43:20 EDT 2024
% Result : Theorem 0.54s 0.73s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 4 unt; 0 def)
% Number of atoms : 178 ( 22 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 208 ( 79 ~; 65 |; 43 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 91 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f159,plain,
$false,
inference(avatar_sat_refutation,[],[f113,f118,f123,f127,f149,f158]) ).
fof(f158,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f157]) ).
fof(f157,plain,
( $false
| ~ spl8_1 ),
inference(resolution,[],[f108,f62]) ).
fof(f62,plain,
path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
( number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0)
& ! [X3,X4] :
( triangle(X3,X4,sK3(X3,X4))
| ~ sequential(X3,X4)
| ~ on_path(X4,sK0)
| ~ on_path(X3,sK0) )
& path(sK1,sK2,sK0)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f33,f44,f43]) ).
fof(f43,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
& path(X1,X2,X0) )
=> ( number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0)
& ! [X4,X3] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,sK0)
| ~ on_path(X3,sK0) )
& path(sK1,sK2,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
=> triangle(X3,X4,sK3(X3,X4)) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
& path(X1,X2,X0) )
& complete ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
& path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
~ ( complete
=> ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
( complete
=> ! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.cYWXFOnjNC/Vampire---4.8_29356',complete_means_sequential_pairs_and_triangles) ).
fof(f108,plain,
( ! [X0,X1] : ~ path(X0,X1,sK0)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f107,plain,
( spl8_1
<=> ! [X0,X1] : ~ path(X0,X1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f149,plain,
( ~ spl8_4
| ~ spl8_2
| ~ spl8_3
| ~ spl8_5 ),
inference(avatar_split_clause,[],[f148,f125,f115,f110,f120]) ).
fof(f120,plain,
( spl8_4
<=> sequential(sK6(sK0),sK7(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f110,plain,
( spl8_2
<=> on_path(sK6(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f115,plain,
( spl8_3
<=> on_path(sK7(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f125,plain,
( spl8_5
<=> ! [X0] : ~ triangle(sK6(sK0),sK7(sK0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f148,plain,
( ~ sequential(sK6(sK0),sK7(sK0))
| ~ spl8_2
| ~ spl8_3
| ~ spl8_5 ),
inference(subsumption_resolution,[],[f147,f112]) ).
fof(f112,plain,
( on_path(sK6(sK0),sK0)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f147,plain,
( ~ sequential(sK6(sK0),sK7(sK0))
| ~ on_path(sK6(sK0),sK0)
| ~ spl8_3
| ~ spl8_5 ),
inference(subsumption_resolution,[],[f142,f117]) ).
fof(f117,plain,
( on_path(sK7(sK0),sK0)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f142,plain,
( ~ sequential(sK6(sK0),sK7(sK0))
| ~ on_path(sK7(sK0),sK0)
| ~ on_path(sK6(sK0),sK0)
| ~ spl8_5 ),
inference(resolution,[],[f63,f126]) ).
fof(f126,plain,
( ! [X0] : ~ triangle(sK6(sK0),sK7(sK0),X0)
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f63,plain,
! [X3,X4] :
( triangle(X3,X4,sK3(X3,X4))
| ~ sequential(X3,X4)
| ~ on_path(X4,sK0)
| ~ on_path(X3,sK0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f127,plain,
( spl8_1
| spl8_5 ),
inference(avatar_split_clause,[],[f102,f125,f107]) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ triangle(sK6(sK0),sK7(sK0),X0)
| ~ path(X1,X2,sK0) ),
inference(trivial_inequality_removal,[],[f101]) ).
fof(f101,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| ~ triangle(sK6(sK0),sK7(sK0),X0)
| ~ path(X1,X2,sK0) ),
inference(superposition,[],[f64,f93]) ).
fof(f93,plain,
! [X2,X0,X1,X5] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ triangle(sK6(X0),sK7(X0),X5)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
& sequential(sK6(X0),sK7(X0))
& on_path(sK7(X0),X0)
& on_path(sK6(X0),X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f40,f59]) ).
fof(f59,plain,
! [X0] :
( ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
& sequential(sK6(X0),sK7(X0))
& on_path(sK7(X0),X0)
& on_path(sK6(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
file('/export/starexec/sandbox/tmp/tmp.cYWXFOnjNC/Vampire---4.8_29356',sequential_pairs_and_triangles) ).
fof(f64,plain,
number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0),
inference(cnf_transformation,[],[f45]) ).
fof(f123,plain,
( spl8_1
| spl8_4 ),
inference(avatar_split_clause,[],[f103,f120,f107]) ).
fof(f103,plain,
! [X0,X1] :
( sequential(sK6(sK0),sK7(sK0))
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| sequential(sK6(sK0),sK7(sK0))
| ~ path(X0,X1,sK0) ),
inference(superposition,[],[f64,f92]) ).
fof(f92,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| sequential(sK6(X0),sK7(X0))
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f118,plain,
( spl8_1
| spl8_3 ),
inference(avatar_split_clause,[],[f104,f115,f107]) ).
fof(f104,plain,
! [X0,X1] :
( on_path(sK7(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| on_path(sK7(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(superposition,[],[f64,f91]) ).
fof(f91,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK7(X0),X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f113,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f105,f110,f107]) ).
fof(f105,plain,
! [X0,X1] :
( on_path(sK6(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| on_path(sK6(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(superposition,[],[f64,f90]) ).
fof(f90,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK6(X0),X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA010+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.14 % 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
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 18:21:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.35 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.cYWXFOnjNC/Vampire---4.8_29356
% 0.54/0.73 % (29469)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)
% 0.54/0.73 % (29464)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)
% 0.54/0.73 % (29466)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.54/0.73 % (29468)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)
% 0.54/0.73 % (29469)First to succeed.
% 0.54/0.73 % (29469)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-29463"
% 0.54/0.73 % (29469)Refutation found. Thanks to Tanya!
% 0.54/0.73 % SZS status Theorem for Vampire---4
% 0.54/0.73 % SZS output start Proof for Vampire---4
% See solution above
% 0.54/0.73 % (29469)------------------------------
% 0.54/0.73 % (29469)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.54/0.73 % (29469)Termination reason: Refutation
% 0.54/0.73
% 0.54/0.73 % (29469)Memory used [KB]: 1104
% 0.54/0.73 % (29469)Time elapsed: 0.004 s
% 0.54/0.73 % (29469)Instructions burned: 6 (million)
% 0.54/0.73 % (29463)Success in time 0.376 s
% 0.54/0.73 % Vampire---4.8 exiting
%------------------------------------------------------------------------------