TSTP Solution File: GRA002+4 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n013.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 16:13:31 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 136 ( 25 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 144 ( 53 ~; 38 |; 32 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 98 ( 85 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f294,plain,
$false,
inference(avatar_sat_refutation,[],[f227,f252,f293]) ).
fof(f293,plain,
~ spl37_2,
inference(avatar_contradiction_clause,[],[f292]) ).
fof(f292,plain,
( $false
| ~ spl37_2 ),
inference(subsumption_resolution,[],[f291,f284]) ).
fof(f284,plain,
( less_or_equal(number_of_in(sequential_pairs,sK3),number_of_in(triangles,graph))
| ~ spl37_2 ),
inference(superposition,[],[f143,f283]) ).
fof(f283,plain,
( number_of_in(sequential_pairs,sK3) = number_of_in(triangles,sK3)
| ~ spl37_2 ),
inference(resolution,[],[f226,f127]) ).
fof(f127,plain,
shortest_path(sK5,sK4,sK3),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
( shortest_path(sK5,sK4,sK3)
& ~ less_or_equal(minus(length_of(sK3),n1),number_of_in(triangles,graph))
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f78,f79]) ).
fof(f79,plain,
( ? [X0,X1,X2] :
( shortest_path(X2,X1,X0)
& ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) )
=> ( shortest_path(sK5,sK4,sK3)
& ~ less_or_equal(minus(length_of(sK3),n1),number_of_in(triangles,graph)) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ? [X0,X1,X2] :
( shortest_path(X2,X1,X0)
& ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) )
& complete ),
inference(rectify,[],[f62]) ).
fof(f62,plain,
( ? [X0,X2,X1] :
( shortest_path(X1,X2,X0)
& ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) )
& complete ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,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/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f226,plain,
( ! [X2,X0,X1] :
( ~ shortest_path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
| ~ spl37_2 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f225,plain,
( spl37_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,[spl37_2])]) ).
fof(f143,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f37]) ).
fof(f37,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/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f291,plain,
~ less_or_equal(number_of_in(sequential_pairs,sK3),number_of_in(triangles,graph)),
inference(backward_demodulation,[],[f126,f290]) ).
fof(f290,plain,
number_of_in(sequential_pairs,sK3) = minus(length_of(sK3),n1),
inference(resolution,[],[f124,f256]) ).
fof(f256,plain,
path(sK5,sK4,sK3),
inference(resolution,[],[f106,f127]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| ( ~ less_or_equal(length_of(X2),length_of(sK0(X0,X1,X2)))
& path(X0,X1,sK0(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 )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f66,f67]) ).
fof(f67,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(sK0(X0,X1,X2)))
& path(X0,X1,sK0(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ 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 )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f65]) ).
fof(f65,plain,
! [X0,X2,X1] :
( ( shortest_path(X0,X2,X1)
| ~ path(X0,X2,X1)
| ? [X3] :
( ~ less_or_equal(length_of(X1),length_of(X3))
& path(X0,X2,X3) )
| X0 = X2 )
& ( ( path(X0,X2,X1)
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X0,X2,X3) )
& X0 != X2 )
| ~ shortest_path(X0,X2,X1) ) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X2,X1] :
( ( shortest_path(X0,X2,X1)
| ~ path(X0,X2,X1)
| ? [X3] :
( ~ less_or_equal(length_of(X1),length_of(X3))
& path(X0,X2,X3) )
| X0 = X2 )
& ( ( path(X0,X2,X1)
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X0,X2,X3) )
& X0 != X2 )
| ~ shortest_path(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X2,X1] :
( shortest_path(X0,X2,X1)
<=> ( path(X0,X2,X1)
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X0,X2,X3) )
& X0 != X2 ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1,X0,X2] :
( shortest_path(X0,X2,X1)
<=> ( ! [X3] :
( path(X0,X2,X3)
=> less_or_equal(length_of(X1),length_of(X3)) )
& X0 != X2
& path(X0,X2,X1) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X9,X2] :
( ( ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) )
& X1 != X2
& path(X1,X2,X9) )
<=> shortest_path(X1,X2,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = minus(length_of(X0),n1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = minus(length_of(X0),n1) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X0,X2,X1] :
( ~ path(X2,X1,X0)
| number_of_in(sequential_pairs,X0) = minus(length_of(X0),n1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X1,X2,X0] :
( path(X2,X1,X0)
=> number_of_in(sequential_pairs,X0) = minus(length_of(X0),n1) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3,X2,X1] :
( path(X1,X2,X3)
=> number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(f126,plain,
~ less_or_equal(minus(length_of(sK3),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f80]) ).
fof(f252,plain,
spl37_1,
inference(avatar_split_clause,[],[f125,f221]) ).
fof(f221,plain,
( spl37_1
<=> complete ),
introduced(avatar_definition,[new_symbols(naming,[spl37_1])]) ).
fof(f125,plain,
complete,
inference(cnf_transformation,[],[f80]) ).
fof(f227,plain,
( ~ spl37_1
| spl37_2 ),
inference(avatar_split_clause,[],[f121,f225,f221]) ).
fof(f121,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ complete
| ~ shortest_path(X1,X2,X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( ~ complete
| ! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0) ) ),
inference(rectify,[],[f50]) ).
fof(f50,plain,
( ~ complete
| ! [X2,X0,X1] :
( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ shortest_path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
( complete
=> ! [X1,X0,X2] :
( shortest_path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
( complete
=> ! [X1,X2,X3] :
( shortest_path(X1,X2,X3)
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n013.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 21:57:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47 % (12706)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.48 % (12698)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.48 % (12706)First to succeed.
% 0.19/0.48 % (12714)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.48 % (12698)Instruction limit reached!
% 0.19/0.48 % (12698)------------------------------
% 0.19/0.48 % (12698)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48 % (12698)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48 % (12698)Termination reason: Unknown
% 0.19/0.48 % (12698)Termination phase: Naming
% 0.19/0.48
% 0.19/0.48 % (12698)Memory used [KB]: 895
% 0.19/0.48 % (12698)Time elapsed: 0.003 s
% 0.19/0.48 % (12698)Instructions burned: 2 (million)
% 0.19/0.48 % (12698)------------------------------
% 0.19/0.48 % (12698)------------------------------
% 0.19/0.49 % (12693)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.49 % (12706)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (12706)------------------------------
% 0.19/0.49 % (12706)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (12706)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (12706)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (12706)Memory used [KB]: 5628
% 0.19/0.49 % (12706)Time elapsed: 0.095 s
% 0.19/0.49 % (12706)Instructions burned: 8 (million)
% 0.19/0.49 % (12706)------------------------------
% 0.19/0.49 % (12706)------------------------------
% 0.19/0.49 % (12684)Success in time 0.144 s
%------------------------------------------------------------------------------