TSTP Solution File: GRA009+2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRA009+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 : n015.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 0.61s 0.79s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 22
% Syntax : Number of formulae : 155 ( 27 unt; 0 def)
% Number of atoms : 508 ( 119 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 602 ( 249 ~; 228 |; 77 &)
% ( 20 <=>; 24 =>; 0 <=; 4 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 8 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 248 ( 227 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f694,plain,
$false,
inference(avatar_sat_refutation,[],[f219,f402,f596,f655,f664,f687,f693]) ).
fof(f693,plain,
( ~ spl28_1
| ~ spl28_2 ),
inference(avatar_contradiction_clause,[],[f692]) ).
fof(f692,plain,
( $false
| ~ spl28_1
| ~ spl28_2 ),
inference(subsumption_resolution,[],[f691,f132]) ).
fof(f132,plain,
head_of(sK3) != tail_of(sK3),
inference(unit_resulting_resolution,[],[f121,f69]) ).
fof(f69,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox/tmp/tmp.yOx5i78WOu/Vampire---4.8_12409',no_loops) ).
fof(f121,plain,
edge(sK3),
inference(unit_resulting_resolution,[],[f45,f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X6,X7] :
( sequential(X6,X7)
<=> ( head_of(X6) = tail_of(X7)
& X6 != X7
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox/tmp/tmp.yOx5i78WOu/Vampire---4.8_12409',sequential_defn) ).
fof(f45,plain,
sequential(sK3,sK4),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
( ? [X0,X1,X2] :
( ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
& shortest_path(X1,X2,X0) )
& complete ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
( ? [X0,X1,X2] :
( ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
& shortest_path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) ) ) ),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yOx5i78WOu/Vampire---4.8_12409',complete_means_path_means_stuff_means_triangles) ).
fof(f691,plain,
( head_of(sK3) = tail_of(sK3)
| ~ spl28_1
| ~ spl28_2 ),
inference(forward_demodulation,[],[f213,f218]) ).
fof(f218,plain,
( sK3 = sK4
| ~ spl28_2 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f216,plain,
( spl28_2
<=> sK3 = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl28_2])]) ).
fof(f213,plain,
( tail_of(sK3) = head_of(sK4)
| ~ spl28_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f212,plain,
( spl28_1
<=> tail_of(sK3) = head_of(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_1])]) ).
fof(f687,plain,
( spl28_1
| ~ spl28_17 ),
inference(avatar_contradiction_clause,[],[f686]) ).
fof(f686,plain,
( $false
| spl28_1
| ~ spl28_17 ),
inference(subsumption_resolution,[],[f685,f141]) ).
fof(f141,plain,
head_of(sK3) != head_of(sK4),
inference(forward_demodulation,[],[f136,f123]) ).
fof(f123,plain,
head_of(sK3) = tail_of(sK4),
inference(unit_resulting_resolution,[],[f45,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f136,plain,
tail_of(sK4) != head_of(sK4),
inference(unit_resulting_resolution,[],[f122,f69]) ).
fof(f122,plain,
edge(sK4),
inference(unit_resulting_resolution,[],[f45,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f685,plain,
( head_of(sK3) = head_of(sK4)
| spl28_1
| ~ spl28_17 ),
inference(subsumption_resolution,[],[f684,f48]) ).
fof(f48,plain,
complete,
inference(cnf_transformation,[],[f30]) ).
fof(f684,plain,
( ~ complete
| head_of(sK3) = head_of(sK4)
| spl28_1
| ~ spl28_17 ),
inference(subsumption_resolution,[],[f683,f214]) ).
fof(f214,plain,
( tail_of(sK3) != head_of(sK4)
| spl28_1 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f683,plain,
( tail_of(sK3) = head_of(sK4)
| ~ complete
| head_of(sK3) = head_of(sK4)
| ~ spl28_17 ),
inference(subsumption_resolution,[],[f682,f134]) ).
fof(f134,plain,
vertex(tail_of(sK3)),
inference(unit_resulting_resolution,[],[f121,f71]) ).
fof(f71,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ( vertex(tail_of(X0))
& vertex(head_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.yOx5i78WOu/Vampire---4.8_12409',edge_ends_are_vertices) ).
fof(f682,plain,
( ~ vertex(tail_of(sK3))
| tail_of(sK3) = head_of(sK4)
| ~ complete
| head_of(sK3) = head_of(sK4)
| ~ spl28_17 ),
inference(subsumption_resolution,[],[f681,f137]) ).
fof(f137,plain,
vertex(head_of(sK4)),
inference(unit_resulting_resolution,[],[f122,f70]) ).
fof(f70,plain,
! [X0] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f681,plain,
( ~ vertex(head_of(sK4))
| ~ vertex(tail_of(sK3))
| tail_of(sK3) = head_of(sK4)
| ~ complete
| head_of(sK3) = head_of(sK4)
| ~ spl28_17 ),
inference(subsumption_resolution,[],[f675,f225]) ).
fof(f225,plain,
! [X0] : ~ sP6(sK3,tail_of(sK3),X0),
inference(unit_resulting_resolution,[],[f132,f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ sP6(X2,X1,X0)
| head_of(X2) = X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
( ! [X0,X1] :
( ? [X2] :
( ( ( tail_of(X2) = X1
& head_of(X2) = X0 )
<~> ( tail_of(X2) = X0
& head_of(X2) = X1 ) )
& edge(X2) )
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
| ~ complete ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
( ! [X0,X1] :
( ? [X2] :
( ( ( tail_of(X2) = X1
& head_of(X2) = X0 )
<~> ( tail_of(X2) = X0
& head_of(X2) = X1 ) )
& edge(X2) )
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
| ~ complete ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
( complete
=> ! [X0,X1] :
( ( X0 != X1
& vertex(X1)
& vertex(X0) )
=> ? [X2] :
( ( ( tail_of(X2) = X1
& head_of(X2) = X0 )
<~> ( tail_of(X2) = X0
& head_of(X2) = X1 ) )
& edge(X2) ) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
( complete
=> ! [X1,X2] :
( ( X1 != X2
& vertex(X2)
& vertex(X1) )
=> ? [X0] :
( ( ( tail_of(X0) = X2
& head_of(X0) = X1 )
<~> ( tail_of(X0) = X1
& head_of(X0) = X2 ) )
& edge(X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yOx5i78WOu/Vampire---4.8_12409',complete_properties) ).
fof(f675,plain,
( sP6(sK3,tail_of(sK3),head_of(sK4))
| ~ vertex(head_of(sK4))
| ~ vertex(tail_of(sK3))
| tail_of(sK3) = head_of(sK4)
| ~ complete
| head_of(sK3) = head_of(sK4)
| ~ spl28_17 ),
inference(superposition,[],[f53,f397]) ).
fof(f397,plain,
( sK3 = sK5(head_of(sK4),tail_of(sK3))
| ~ spl28_17 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f395,plain,
( spl28_17
<=> sK3 = sK5(head_of(sK4),tail_of(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_17])]) ).
fof(f53,plain,
! [X0,X1] :
( sP6(sK5(X0,X1),X1,X0)
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete
| head_of(sK5(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f664,plain,
( ~ spl28_15
| ~ spl28_16 ),
inference(avatar_contradiction_clause,[],[f663]) ).
fof(f663,plain,
( $false
| ~ spl28_15
| ~ spl28_16 ),
inference(subsumption_resolution,[],[f662,f141]) ).
fof(f662,plain,
( head_of(sK3) = head_of(sK4)
| ~ spl28_15
| ~ spl28_16 ),
inference(forward_demodulation,[],[f661,f123]) ).
fof(f661,plain,
( tail_of(sK4) = head_of(sK4)
| ~ spl28_15
| ~ spl28_16 ),
inference(forward_demodulation,[],[f388,f393]) ).
fof(f393,plain,
( sK4 = sK5(head_of(sK4),tail_of(sK3))
| ~ spl28_16 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f391,plain,
( spl28_16
<=> sK4 = sK5(head_of(sK4),tail_of(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_16])]) ).
fof(f388,plain,
( head_of(sK4) = tail_of(sK5(head_of(sK4),tail_of(sK3)))
| ~ spl28_15 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f387,plain,
( spl28_15
<=> head_of(sK4) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_15])]) ).
fof(f655,plain,
( spl28_1
| spl28_15 ),
inference(avatar_contradiction_clause,[],[f654]) ).
fof(f654,plain,
( $false
| spl28_1
| spl28_15 ),
inference(subsumption_resolution,[],[f645,f642]) ).
fof(f642,plain,
( tail_of(sK3) = tail_of(sK5(head_of(sK4),tail_of(sK3)))
| spl28_1
| spl28_15 ),
inference(unit_resulting_resolution,[],[f48,f137,f134,f214,f601,f54]) ).
fof(f54,plain,
! [X0,X1] :
( sP6(sK5(X0,X1),X1,X0)
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete
| tail_of(sK5(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f601,plain,
( ! [X0] : ~ sP6(sK5(head_of(sK4),tail_of(sK3)),X0,head_of(sK4))
| spl28_15 ),
inference(unit_resulting_resolution,[],[f389,f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ sP6(X2,X1,X0)
| tail_of(X2) = X0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f389,plain,
( head_of(sK4) != tail_of(sK5(head_of(sK4),tail_of(sK3)))
| spl28_15 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f645,plain,
( tail_of(sK3) != tail_of(sK5(head_of(sK4),tail_of(sK3)))
| spl28_1
| spl28_15 ),
inference(unit_resulting_resolution,[],[f641,f202]) ).
fof(f202,plain,
! [X0] :
( tail_of(X0) != tail_of(sK3)
| head_of(X0) != head_of(sK4) ),
inference(resolution,[],[f187,f92]) ).
fof(f92,plain,
! [X2,X3,X5] :
( ~ sP13(X3,X2)
| head_of(X5) != head_of(X3)
| tail_of(X2) != tail_of(X5) ),
inference(general_splitting,[],[f90,f91_D]) ).
fof(f91,plain,
! [X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ sP12(X4)
| sP13(X3,X2) ),
inference(cnf_transformation,[],[f91_D]) ).
fof(f91_D,plain,
! [X2,X3] :
( ! [X4] :
( ~ precedes(X2,X3,X4)
| ~ sP12(X4) )
<=> ~ sP13(X3,X2) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP13])]) ).
fof(f90,plain,
! [X2,X3,X4,X5] :
( ~ precedes(X2,X3,X4)
| tail_of(X2) != tail_of(X5)
| head_of(X5) != head_of(X3)
| ~ sP12(X4) ),
inference(general_splitting,[],[f88,f89_D]) ).
fof(f89,plain,
! [X1,X4] :
( ~ sP11(X4,X1)
| sP12(X4) ),
inference(cnf_transformation,[],[f89_D]) ).
fof(f89_D,plain,
! [X4] :
( ! [X1] : ~ sP11(X4,X1)
<=> ~ sP12(X4) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP12])]) ).
fof(f88,plain,
! [X2,X3,X1,X4,X5] :
( ~ precedes(X2,X3,X4)
| tail_of(X2) != tail_of(X5)
| head_of(X5) != head_of(X3)
| ~ sP11(X4,X1) ),
inference(general_splitting,[],[f61,f87_D]) ).
fof(f87,plain,
! [X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| sP11(X4,X1) ),
inference(cnf_transformation,[],[f87_D]) ).
fof(f87_D,plain,
! [X1,X4] :
( ! [X0] : ~ shortest_path(X0,X1,X4)
<=> ~ sP11(X4,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP11])]) ).
fof(f61,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| tail_of(X2) != tail_of(X5)
| head_of(X5) != head_of(X3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X5) != head_of(X3)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X5) != head_of(X3)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X2) = tail_of(X5) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( ~ precedes(X7,X6,X3)
& ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yOx5i78WOu/Vampire---4.8_12409',shortest_path_properties) ).
fof(f187,plain,
sP13(sK4,sK3),
inference(unit_resulting_resolution,[],[f151,f180,f91]) ).
fof(f180,plain,
precedes(sK3,sK4,sK0),
inference(unit_resulting_resolution,[],[f45,f43,f44,f178,f116]) ).
fof(f116,plain,
! [X3,X0,X4] :
( precedes(X3,X4,X0)
| ~ on_path(X4,X0)
| ~ sequential(X3,X4)
| ~ on_path(X3,X0)
| ~ sP25(X0) ),
inference(general_splitting,[],[f114,f115_D]) ).
fof(f115,plain,
! [X0,X1] :
( ~ sP24(X0,X1)
| sP25(X0) ),
inference(cnf_transformation,[],[f115_D]) ).
fof(f115_D,plain,
! [X0] :
( ! [X1] : ~ sP24(X0,X1)
<=> ~ sP25(X0) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP25])]) ).
fof(f114,plain,
! [X3,X0,X1,X4] :
( ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| ~ sequential(X3,X4)
| precedes(X3,X4,X0)
| ~ sP24(X0,X1) ),
inference(general_splitting,[],[f78,f113_D]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| sP24(X0,X1) ),
inference(cnf_transformation,[],[f113_D]) ).
fof(f113_D,plain,
! [X1,X0] :
( ! [X2] : ~ path(X1,X2,X0)
<=> ~ sP24(X0,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP24])]) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| ~ sequential(X3,X4)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
=> precedes(X3,X4,X0) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( ( ( ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) )
| sequential(X6,X7) )
& on_path(X7,X3)
& on_path(X6,X3) )
=> precedes(X6,X7,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.yOx5i78WOu/Vampire---4.8_12409',precedes_defn) ).
fof(f178,plain,
sP25(sK0),
inference(unit_resulting_resolution,[],[f159,f115]) ).
fof(f159,plain,
sP24(sK0,sK1),
inference(unit_resulting_resolution,[],[f143,f113]) ).
fof(f143,plain,
path(sK1,sK2,sK0),
inference(unit_resulting_resolution,[],[f47,f66]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,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,[],[f24]) ).
fof(f24,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.yOx5i78WOu/Vampire---4.8_12409',shortest_path_defn) ).
fof(f47,plain,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f30]) ).
fof(f44,plain,
on_path(sK4,sK0),
inference(cnf_transformation,[],[f30]) ).
fof(f43,plain,
on_path(sK3,sK0),
inference(cnf_transformation,[],[f30]) ).
fof(f151,plain,
sP12(sK0),
inference(unit_resulting_resolution,[],[f145,f89]) ).
fof(f145,plain,
sP11(sK0,sK2),
inference(unit_resulting_resolution,[],[f47,f87]) ).
fof(f641,plain,
( head_of(sK4) = head_of(sK5(head_of(sK4),tail_of(sK3)))
| spl28_1
| spl28_15 ),
inference(unit_resulting_resolution,[],[f48,f137,f134,f214,f601,f53]) ).
fof(f596,plain,
( spl28_1
| spl28_18 ),
inference(avatar_contradiction_clause,[],[f595]) ).
fof(f595,plain,
( $false
| spl28_1
| spl28_18 ),
inference(subsumption_resolution,[],[f586,f561]) ).
fof(f561,plain,
( tail_of(sK3) = tail_of(sK5(head_of(sK4),tail_of(sK3)))
| spl28_1
| spl28_18 ),
inference(unit_resulting_resolution,[],[f48,f137,f134,f214,f505,f54]) ).
fof(f505,plain,
( ! [X0] : ~ sP6(sK5(head_of(sK4),tail_of(sK3)),tail_of(sK3),X0)
| spl28_18 ),
inference(unit_resulting_resolution,[],[f401,f50]) ).
fof(f401,plain,
( tail_of(sK3) != head_of(sK5(head_of(sK4),tail_of(sK3)))
| spl28_18 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f399,plain,
( spl28_18
<=> tail_of(sK3) = head_of(sK5(head_of(sK4),tail_of(sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_18])]) ).
fof(f586,plain,
( tail_of(sK3) != tail_of(sK5(head_of(sK4),tail_of(sK3)))
| spl28_1
| spl28_18 ),
inference(unit_resulting_resolution,[],[f560,f202]) ).
fof(f560,plain,
( head_of(sK4) = head_of(sK5(head_of(sK4),tail_of(sK3)))
| spl28_1
| spl28_18 ),
inference(unit_resulting_resolution,[],[f48,f137,f134,f214,f505,f53]) ).
fof(f402,plain,
( ~ spl28_15
| spl28_16
| spl28_17
| ~ spl28_18
| spl28_1 ),
inference(avatar_split_clause,[],[f329,f212,f399,f395,f391,f387]) ).
fof(f329,plain,
( tail_of(sK3) != head_of(sK5(head_of(sK4),tail_of(sK3)))
| sK3 = sK5(head_of(sK4),tail_of(sK3))
| sK4 = sK5(head_of(sK4),tail_of(sK3))
| head_of(sK4) != tail_of(sK5(head_of(sK4),tail_of(sK3)))
| spl28_1 ),
inference(resolution,[],[f307,f237]) ).
fof(f237,plain,
( edge(sK5(head_of(sK4),tail_of(sK3)))
| spl28_1 ),
inference(unit_resulting_resolution,[],[f48,f137,f134,f214,f55]) ).
fof(f55,plain,
! [X0,X1] :
( edge(sK5(X0,X1))
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| ~ complete ),
inference(cnf_transformation,[],[f32]) ).
fof(f307,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(sK3)
| sK3 = X0
| sK4 = X0
| tail_of(X0) != head_of(sK4) ),
inference(subsumption_resolution,[],[f306,f122]) ).
fof(f306,plain,
! [X0] :
( sK3 = X0
| head_of(X0) != tail_of(sK3)
| ~ edge(X0)
| sK4 = X0
| tail_of(X0) != head_of(sK4)
| ~ edge(sK4) ),
inference(resolution,[],[f205,f60]) ).
fof(f60,plain,
! [X0,X1] :
( sequential(X0,X1)
| ~ edge(X1)
| X0 = X1
| head_of(X0) != tail_of(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f205,plain,
! [X0] :
( ~ sequential(sK4,X0)
| sK3 = X0
| head_of(X0) != tail_of(sK3) ),
inference(subsumption_resolution,[],[f204,f57]) ).
fof(f204,plain,
! [X0] :
( ~ sequential(sK4,X0)
| sK3 = X0
| head_of(X0) != tail_of(sK3)
| ~ edge(X0) ),
inference(subsumption_resolution,[],[f203,f121]) ).
fof(f203,plain,
! [X0] :
( ~ sequential(sK4,X0)
| ~ edge(sK3)
| sK3 = X0
| head_of(X0) != tail_of(sK3)
| ~ edge(X0) ),
inference(resolution,[],[f131,f60]) ).
fof(f131,plain,
! [X0] :
( ~ sequential(X0,sK3)
| ~ sequential(sK4,X0) ),
inference(subsumption_resolution,[],[f130,f57]) ).
fof(f130,plain,
! [X0] :
( ~ edge(X0)
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK3) ),
inference(subsumption_resolution,[],[f129,f121]) ).
fof(f129,plain,
! [X0] :
( ~ edge(X0)
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK3)
| ~ edge(sK3) ),
inference(subsumption_resolution,[],[f128,f45]) ).
fof(f128,plain,
! [X0] :
( ~ edge(X0)
| ~ sequential(sK3,sK4)
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK3)
| ~ edge(sK3) ),
inference(subsumption_resolution,[],[f127,f122]) ).
fof(f127,plain,
! [X0] :
( ~ edge(sK4)
| ~ edge(X0)
| ~ sequential(sK3,sK4)
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK3)
| ~ edge(sK3) ),
inference(resolution,[],[f46,f68]) ).
fof(f68,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ edge(X1)
| ~ edge(X2)
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X6,X7,X8] :
( triangle(X6,X7,X8)
<=> ( sequential(X8,X6)
& sequential(X7,X8)
& sequential(X6,X7)
& edge(X8)
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox/tmp/tmp.yOx5i78WOu/Vampire---4.8_12409',triangle_defn) ).
fof(f46,plain,
! [X5] : ~ triangle(sK3,sK4,X5),
inference(cnf_transformation,[],[f30]) ).
fof(f219,plain,
( ~ spl28_1
| spl28_2 ),
inference(avatar_split_clause,[],[f210,f216,f212]) ).
fof(f210,plain,
( sK3 = sK4
| tail_of(sK3) != head_of(sK4) ),
inference(subsumption_resolution,[],[f209,f122]) ).
fof(f209,plain,
( sK3 = sK4
| tail_of(sK3) != head_of(sK4)
| ~ edge(sK4) ),
inference(subsumption_resolution,[],[f208,f121]) ).
fof(f208,plain,
( ~ edge(sK3)
| sK3 = sK4
| tail_of(sK3) != head_of(sK4)
| ~ edge(sK4) ),
inference(resolution,[],[f206,f60]) ).
fof(f206,plain,
~ sequential(sK4,sK3),
inference(unit_resulting_resolution,[],[f178,f44,f43,f186,f116]) ).
fof(f186,plain,
~ precedes(sK4,sK3,sK0),
inference(unit_resulting_resolution,[],[f150,f180,f83]) ).
fof(f83,plain,
! [X2,X3,X4] :
( ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4)
| sP9(X4,X3) ),
inference(cnf_transformation,[],[f83_D]) ).
fof(f83_D,plain,
! [X3,X4] :
( ! [X2] :
( ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4) )
<=> ~ sP9(X4,X3) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).
fof(f150,plain,
! [X0] : ~ sP9(sK0,X0),
inference(unit_resulting_resolution,[],[f144,f85]) ).
fof(f85,plain,
! [X3,X4] :
( ~ sP9(X4,X3)
| sP10(X4) ),
inference(cnf_transformation,[],[f85_D]) ).
fof(f85_D,plain,
! [X4] :
( ! [X3] : ~ sP9(X4,X3)
<=> ~ sP10(X4) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP10])]) ).
fof(f144,plain,
~ sP10(sK0),
inference(unit_resulting_resolution,[],[f47,f86]) ).
fof(f86,plain,
! [X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ sP10(X4) ),
inference(general_splitting,[],[f84,f85_D]) ).
fof(f84,plain,
! [X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ sP9(X4,X3) ),
inference(general_splitting,[],[f62,f83_D]) ).
fof(f62,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRA009+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.10/0.11 % 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
% 0.11/0.31 % Computer : n015.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 18:21:38 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 This is a FOF_THM_RFO_SEQ problem
% 0.11/0.32 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.yOx5i78WOu/Vampire---4.8_12409
% 0.55/0.77 % (12521)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 (2995ds/34Mi)
% 0.55/0.77 % (12520)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.55/0.77 % (12517)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 (2995ds/34Mi)
% 0.55/0.77 % (12519)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.55/0.77 % (12518)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 (2995ds/51Mi)
% 0.55/0.77 % (12523)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 (2995ds/83Mi)
% 0.55/0.77 % (12522)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.55/0.77 % (12524)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 (2995ds/56Mi)
% 0.55/0.77 % (12522)Refutation not found, incomplete strategy% (12522)------------------------------
% 0.55/0.77 % (12522)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.77 % (12522)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.77
% 0.55/0.77 % (12522)Memory used [KB]: 1050
% 0.55/0.77 % (12522)Time elapsed: 0.003 s
% 0.55/0.77 % (12522)Instructions burned: 3 (million)
% 0.55/0.77 % (12524)Refutation not found, incomplete strategy% (12524)------------------------------
% 0.55/0.77 % (12524)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.77 % (12524)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.77
% 0.55/0.77 % (12524)Memory used [KB]: 1052
% 0.55/0.77 % (12522)------------------------------
% 0.55/0.77 % (12522)------------------------------
% 0.55/0.77 % (12524)Time elapsed: 0.003 s
% 0.55/0.77 % (12524)Instructions burned: 3 (million)
% 0.55/0.77 % (12524)------------------------------
% 0.55/0.77 % (12524)------------------------------
% 0.55/0.77 % (12520)Refutation not found, incomplete strategy% (12520)------------------------------
% 0.55/0.77 % (12520)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.77 % (12520)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.77
% 0.55/0.77 % (12520)Memory used [KB]: 1046
% 0.55/0.77 % (12520)Time elapsed: 0.003 s
% 0.55/0.77 % (12520)Instructions burned: 3 (million)
% 0.55/0.78 % (12520)------------------------------
% 0.55/0.78 % (12520)------------------------------
% 0.55/0.78 % (12525)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 (2995ds/55Mi)
% 0.55/0.78 % (12526)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.61/0.78 % (12527)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.61/0.78 % (12525)Refutation not found, incomplete strategy% (12525)------------------------------
% 0.61/0.78 % (12525)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.78 % (12525)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.78
% 0.61/0.78 % (12525)Memory used [KB]: 1070
% 0.61/0.78 % (12525)Time elapsed: 0.003 s
% 0.61/0.78 % (12525)Instructions burned: 4 (million)
% 0.61/0.78 % (12525)------------------------------
% 0.61/0.78 % (12525)------------------------------
% 0.61/0.78 % (12528)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.61/0.79 % (12523)First to succeed.
% 0.61/0.79 % (12521)Instruction limit reached!
% 0.61/0.79 % (12521)------------------------------
% 0.61/0.79 % (12521)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.79 % (12521)Termination reason: Unknown
% 0.61/0.79 % (12521)Termination phase: Saturation
% 0.61/0.79
% 0.61/0.79 % (12521)Memory used [KB]: 1366
% 0.61/0.79 % (12521)Time elapsed: 0.018 s
% 0.61/0.79 % (12521)Instructions burned: 35 (million)
% 0.61/0.79 % (12521)------------------------------
% 0.61/0.79 % (12521)------------------------------
% 0.61/0.79 % (12523)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12516"
% 0.61/0.79 % (12517)Instruction limit reached!
% 0.61/0.79 % (12517)------------------------------
% 0.61/0.79 % (12517)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.79 % (12517)Termination reason: Unknown
% 0.61/0.79 % (12517)Termination phase: Saturation
% 0.61/0.79
% 0.61/0.79 % (12517)Memory used [KB]: 1706
% 0.61/0.79 % (12517)Time elapsed: 0.020 s
% 0.61/0.79 % (12517)Instructions burned: 35 (million)
% 0.61/0.79 % (12517)------------------------------
% 0.61/0.79 % (12517)------------------------------
% 0.61/0.79 % (12523)Refutation found. Thanks to Tanya!
% 0.61/0.79 % SZS status Theorem for Vampire---4
% 0.61/0.79 % SZS output start Proof for Vampire---4
% See solution above
% 0.61/0.79 % (12523)------------------------------
% 0.61/0.79 % (12523)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.79 % (12523)Termination reason: Refutation
% 0.61/0.79
% 0.61/0.79 % (12523)Memory used [KB]: 1365
% 0.61/0.79 % (12523)Time elapsed: 0.019 s
% 0.61/0.79 % (12523)Instructions burned: 39 (million)
% 0.61/0.79 % (12516)Success in time 0.463 s
% 0.61/0.79 % Vampire---4.8 exiting
%------------------------------------------------------------------------------