TSTP Solution File: GRA004+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : GRA004+1 : 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_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 16:13:20 EDT 2022
% Result : Theorem 1.58s 0.56s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 92 ( 13 unt; 0 def)
% Number of atoms : 408 ( 109 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 488 ( 172 ~; 151 |; 131 &)
% ( 9 <=>; 22 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 256 ( 212 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f308,plain,
$false,
inference(avatar_sat_refutation,[],[f173,f181,f246,f279,f304]) ).
fof(f304,plain,
( ~ spl13_1
| ~ spl13_4 ),
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f303,plain,
( $false
| ~ spl13_1
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f296,f245]) ).
fof(f245,plain,
( head_of(sK4) = head_of(sK5)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f243,plain,
( spl13_4
<=> head_of(sK4) = head_of(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f296,plain,
( head_of(sK4) != head_of(sK5)
| ~ spl13_1 ),
inference(unit_resulting_resolution,[],[f102,f105,f164,f97]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ shortest_path(X1,X3,X2)
| ~ precedes(X4,X0,X2)
| tail_of(X5) != tail_of(X4)
| head_of(X0) != head_of(X5) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X0,X4,X2)
& ! [X5] :
( tail_of(X5) != tail_of(X4)
| head_of(X0) != head_of(X5) ) )
| ~ shortest_path(X1,X3,X2)
| ~ precedes(X4,X0,X2) ),
inference(rectify,[],[f43]) ).
fof(f43,plain,
! [X3,X2,X4,X1,X0] :
( ( ~ precedes(X3,X0,X4)
& ! [X5] :
( tail_of(X0) != tail_of(X5)
| head_of(X3) != head_of(X5) ) )
| ~ shortest_path(X2,X1,X4)
| ~ precedes(X0,X3,X4) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
! [X0,X3,X4,X2,X1] :
( ( ~ precedes(X3,X0,X4)
& ! [X5] :
( tail_of(X0) != tail_of(X5)
| head_of(X3) != head_of(X5) ) )
| ~ shortest_path(X2,X1,X4)
| ~ precedes(X0,X3,X4) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X3,X4,X2,X1] :
( ( shortest_path(X2,X1,X4)
& precedes(X0,X3,X4) )
=> ( ~ ? [X5] :
( tail_of(X0) = tail_of(X5)
& head_of(X3) = head_of(X5) )
& ~ precedes(X3,X0,X4) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X6,X2,X1,X7,X3] :
( ( shortest_path(X1,X2,X3)
& precedes(X6,X7,X3) )
=> ( ~ precedes(X7,X6,X3)
& ~ ? [X8] :
( tail_of(X8) = tail_of(X6)
& head_of(X8) = head_of(X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).
fof(f164,plain,
( tail_of(sK5) = tail_of(sK2)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f162,plain,
( spl13_1
<=> tail_of(sK5) = tail_of(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f105,plain,
precedes(sK2,sK4,sK1),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( precedes(sK2,sK4,sK1)
& ( head_of(sK4) = tail_of(sK2)
| ( head_of(sK4) = head_of(sK5)
& tail_of(sK5) = tail_of(sK2) )
| head_of(sK4) = head_of(sK2) )
& shortest_path(sK0,sK3,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f63,f65,f64]) ).
fof(f64,plain,
( ? [X0,X1,X2,X3,X4] :
( precedes(X2,X4,X1)
& ( head_of(X4) = tail_of(X2)
| ? [X5] :
( head_of(X4) = head_of(X5)
& tail_of(X5) = tail_of(X2) )
| head_of(X4) = head_of(X2) )
& shortest_path(X0,X3,X1) )
=> ( precedes(sK2,sK4,sK1)
& ( head_of(sK4) = tail_of(sK2)
| ? [X5] :
( head_of(sK4) = head_of(X5)
& tail_of(X5) = tail_of(sK2) )
| head_of(sK4) = head_of(sK2) )
& shortest_path(sK0,sK3,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
( ? [X5] :
( head_of(sK4) = head_of(X5)
& tail_of(X5) = tail_of(sK2) )
=> ( head_of(sK4) = head_of(sK5)
& tail_of(sK5) = tail_of(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
? [X0,X1,X2,X3,X4] :
( precedes(X2,X4,X1)
& ( head_of(X4) = tail_of(X2)
| ? [X5] :
( head_of(X4) = head_of(X5)
& tail_of(X5) = tail_of(X2) )
| head_of(X4) = head_of(X2) )
& shortest_path(X0,X3,X1) ),
inference(rectify,[],[f51]) ).
fof(f51,plain,
? [X3,X1,X4,X0,X2] :
( precedes(X4,X2,X1)
& ( tail_of(X4) = head_of(X2)
| ? [X5] :
( head_of(X2) = head_of(X5)
& tail_of(X5) = tail_of(X4) )
| head_of(X4) = head_of(X2) )
& shortest_path(X3,X0,X1) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
? [X3,X0,X4,X2,X1] :
( ( tail_of(X4) = head_of(X2)
| ? [X5] :
( head_of(X2) = head_of(X5)
& tail_of(X5) = tail_of(X4) )
| head_of(X4) = head_of(X2) )
& precedes(X4,X2,X1)
& shortest_path(X3,X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X3,X0,X4,X2,X1] :
( ( precedes(X4,X2,X1)
& shortest_path(X3,X0,X1) )
=> ( head_of(X4) != head_of(X2)
& tail_of(X4) != head_of(X2)
& ~ ? [X5] :
( head_of(X2) = head_of(X5)
& tail_of(X5) = tail_of(X4) ) ) ),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X2,X3,X7,X1,X6] :
( ( shortest_path(X1,X2,X3)
& precedes(X6,X7,X3) )
=> ( ~ ? [X8] :
( tail_of(X8) = tail_of(X6)
& head_of(X8) = head_of(X7) )
& head_of(X6) != head_of(X7)
& tail_of(X6) != head_of(X7) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X2,X3,X7,X1,X6] :
( ( shortest_path(X1,X2,X3)
& precedes(X6,X7,X3) )
=> ( ~ ? [X8] :
( tail_of(X8) = tail_of(X6)
& head_of(X8) = head_of(X7) )
& head_of(X6) != head_of(X7)
& tail_of(X6) != head_of(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties_lemma) ).
fof(f102,plain,
shortest_path(sK0,sK3,sK1),
inference(cnf_transformation,[],[f66]) ).
fof(f279,plain,
~ spl13_3,
inference(avatar_contradiction_clause,[],[f278]) ).
fof(f278,plain,
( $false
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f258,f240]) ).
fof(f240,plain,
head_of(sK2) != tail_of(sK2),
inference(resolution,[],[f234,f113]) ).
fof(f113,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,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/benchmark/theBenchmark.p',no_loops) ).
fof(f234,plain,
edge(sK2),
inference(unit_resulting_resolution,[],[f149,f190,f101]) ).
fof(f101,plain,
! [X2,X3,X0,X1] :
( ~ path(X2,X1,X3)
| edge(X0)
| ~ on_path(X0,X3) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ( edge(X0)
& in_path(tail_of(X0),X3)
& in_path(head_of(X0),X3) )
| ~ path(X2,X1,X3)
| ~ on_path(X0,X3) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X1,X2,X3,X0] :
( ( edge(X1)
& in_path(tail_of(X1),X0)
& in_path(head_of(X1),X0) )
| ~ path(X3,X2,X0)
| ~ on_path(X1,X0) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X3,X1,X0,X2] :
( ( edge(X1)
& in_path(tail_of(X1),X0)
& in_path(head_of(X1),X0) )
| ~ path(X3,X2,X0)
| ~ on_path(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X3,X1,X0,X2] :
( ( path(X3,X2,X0)
& on_path(X1,X0) )
=> ( edge(X1)
& in_path(tail_of(X1),X0)
& in_path(head_of(X1),X0) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X3,X0,X2,X1] :
( ( on_path(X0,X3)
& path(X1,X2,X3) )
=> ( in_path(tail_of(X0),X3)
& in_path(head_of(X0),X3)
& edge(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',on_path_properties) ).
fof(f190,plain,
on_path(sK2,sK1),
inference(unit_resulting_resolution,[],[f105,f149,f112]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2)
| on_path(X3,X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| ! [X3,X4] :
( ( on_path(X3,X2)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X2) )
| ~ sequential(X3,X4) )
& ( ( sequential(X3,sK6(X2,X3,X4))
& precedes(sK6(X2,X3,X4),X4,X2) )
| sequential(X3,X4) )
& on_path(X4,X2) )
| ~ precedes(X3,X4,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f70,f71]) ).
fof(f71,plain,
! [X2,X3,X4] :
( ? [X6] :
( sequential(X3,X6)
& precedes(X6,X4,X2) )
=> ( sequential(X3,sK6(X2,X3,X4))
& precedes(sK6(X2,X3,X4),X4,X2) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| ! [X3,X4] :
( ( on_path(X3,X2)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X2) )
| ~ sequential(X3,X4) )
& ( ? [X6] :
( sequential(X3,X6)
& precedes(X6,X4,X2) )
| sequential(X3,X4) )
& on_path(X4,X2) )
| ~ precedes(X3,X4,X2) ) ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
! [X2,X1,X0] :
( ~ path(X2,X1,X0)
| ! [X3,X4] :
( ( on_path(X3,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) )
| sequential(X3,X4) )
& on_path(X4,X0) )
| ~ precedes(X3,X4,X0) ) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X2,X1,X0] :
( ~ path(X2,X1,X0)
| ! [X3,X4] :
( ( on_path(X3,X0)
& ( ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) )
| sequential(X3,X4) )
& on_path(X4,X0) )
| ~ precedes(X3,X4,X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X2,X1,X0] :
( ~ path(X2,X1,X0)
| ! [X3,X4] :
( ( on_path(X3,X0)
& ( sequential(X3,X4)
<~> ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) )
& on_path(X4,X0) )
| ~ precedes(X3,X4,X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X1,X0,X2] :
( path(X2,X1,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( on_path(X3,X0)
& ( sequential(X3,X4)
<~> ? [X5] :
( sequential(X3,X5)
& precedes(X5,X4,X0) ) )
& on_path(X4,X0) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X3,X2,X1] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( precedes(X6,X7,X3)
=> ( ( sequential(X6,X7)
<~> ? [X8] :
( sequential(X6,X8)
& precedes(X8,X7,X3) ) )
& on_path(X7,X3)
& on_path(X6,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
fof(f149,plain,
path(sK0,sK3,sK1),
inference(unit_resulting_resolution,[],[f102,f117]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ shortest_path(X1,X0,X2)
| path(X1,X0,X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X1,X0,X3) )
& path(X1,X0,X2) )
| ~ shortest_path(X1,X0,X2) )
& ( shortest_path(X1,X0,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK7(X0,X1,X2)))
& path(X1,X0,sK7(X0,X1,X2)) )
| ~ path(X1,X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f76,f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ less_or_equal(length_of(X2),length_of(X4))
& path(X1,X0,X4) )
=> ( ~ less_or_equal(length_of(X2),length_of(sK7(X0,X1,X2)))
& path(X1,X0,sK7(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X1,X0,X3) )
& path(X1,X0,X2) )
| ~ shortest_path(X1,X0,X2) )
& ( shortest_path(X1,X0,X2)
| X0 = X1
| ? [X4] :
( ~ less_or_equal(length_of(X2),length_of(X4))
& path(X1,X0,X4) )
| ~ path(X1,X0,X2) ) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0,X2,X1] :
( ( ( X0 != X2
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X2,X0,X3) )
& path(X2,X0,X1) )
| ~ shortest_path(X2,X0,X1) )
& ( shortest_path(X2,X0,X1)
| X0 = X2
| ? [X3] :
( ~ less_or_equal(length_of(X1),length_of(X3))
& path(X2,X0,X3) )
| ~ path(X2,X0,X1) ) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X2,X1] :
( ( ( X0 != X2
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X2,X0,X3) )
& path(X2,X0,X1) )
| ~ shortest_path(X2,X0,X1) )
& ( shortest_path(X2,X0,X1)
| X0 = X2
| ? [X3] :
( ~ less_or_equal(length_of(X1),length_of(X3))
& path(X2,X0,X3) )
| ~ path(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X2,X1] :
( ( X0 != X2
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X2,X0,X3) )
& path(X2,X0,X1) )
<=> shortest_path(X2,X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X2,X1] :
( ( X0 != X2
& path(X2,X0,X1)
& ! [X3] :
( path(X2,X0,X3)
=> less_or_equal(length_of(X1),length_of(X3)) ) )
<=> shortest_path(X2,X0,X1) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X2,X9,X1] :
( ( ! [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/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f258,plain,
( head_of(sK2) = tail_of(sK2)
| ~ spl13_3 ),
inference(backward_demodulation,[],[f172,f251]) ).
fof(f251,plain,
( sK2 = sK4
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f250,f172]) ).
fof(f250,plain,
( head_of(sK4) != tail_of(sK2)
| sK2 = sK4 ),
inference(subsumption_resolution,[],[f249,f227]) ).
fof(f227,plain,
edge(sK4),
inference(unit_resulting_resolution,[],[f149,f189,f101]) ).
fof(f189,plain,
on_path(sK4,sK1),
inference(unit_resulting_resolution,[],[f105,f149,f108]) ).
fof(f108,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2)
| on_path(X4,X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f249,plain,
( ~ edge(sK4)
| sK2 = sK4
| head_of(sK4) != tail_of(sK2) ),
inference(subsumption_resolution,[],[f248,f234]) ).
fof(f248,plain,
( ~ edge(sK2)
| sK2 = sK4
| ~ edge(sK4)
| head_of(sK4) != tail_of(sK2) ),
inference(resolution,[],[f235,f127]) ).
fof(f127,plain,
! [X0,X1] :
( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| ~ edge(X0)
| X0 = X1
| ~ edge(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| X0 = X1
| head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1) )
& ( ( X0 != X1
& head_of(X0) = tail_of(X1)
& edge(X0)
& edge(X1) )
| ~ sequential(X0,X1) ) ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
! [X1,X0] :
( ( sequential(X1,X0)
| X0 = X1
| tail_of(X0) != head_of(X1)
| ~ edge(X1)
| ~ edge(X0) )
& ( ( X0 != X1
& tail_of(X0) = head_of(X1)
& edge(X1)
& edge(X0) )
| ~ sequential(X1,X0) ) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X1,X0] :
( ( sequential(X1,X0)
| X0 = X1
| tail_of(X0) != head_of(X1)
| ~ edge(X1)
| ~ edge(X0) )
& ( ( X0 != X1
& tail_of(X0) = head_of(X1)
& edge(X1)
& edge(X0) )
| ~ sequential(X1,X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X1,X0] :
( sequential(X1,X0)
<=> ( X0 != X1
& tail_of(X0) = head_of(X1)
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X7,X6] :
( sequential(X6,X7)
<=> ( head_of(X6) = tail_of(X7)
& X6 != X7
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).
fof(f235,plain,
~ sequential(sK4,sK2),
inference(unit_resulting_resolution,[],[f149,f189,f155,f190,f107]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4] :
( precedes(X4,X3,X2)
| ~ sequential(X4,X3)
| ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| ~ on_path(X4,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| ! [X3,X4] :
( ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| ( ~ sequential(X4,X3)
& ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X2) ) )
| precedes(X4,X3,X2) ) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ path(X2,X0,X1)
| ! [X3,X4] :
( ~ on_path(X4,X1)
| ~ on_path(X3,X1)
| ( ~ sequential(X4,X3)
& ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X1) ) )
| precedes(X4,X3,X1) ) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X1,X2,X0] :
( ! [X4,X3] :
( precedes(X4,X3,X1)
| ~ on_path(X4,X1)
| ~ on_path(X3,X1)
| ( ~ sequential(X4,X3)
& ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X1) ) ) )
| ~ path(X2,X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X1,X2,X0] :
( path(X2,X0,X1)
=> ! [X4,X3] :
( ( on_path(X4,X1)
& on_path(X3,X1)
& ( ? [X5] :
( sequential(X4,X5)
& precedes(X5,X3,X1) )
| sequential(X4,X3) ) )
=> precedes(X4,X3,X1) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X2,X3,X1] :
( path(X1,X2,X3)
=> ! [X7,X6] :
( ( ( ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) )
| sequential(X6,X7) )
& on_path(X6,X3)
& on_path(X7,X3) )
=> precedes(X6,X7,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).
fof(f155,plain,
~ precedes(sK4,sK2,sK1),
inference(unit_resulting_resolution,[],[f102,f105,f98]) ).
fof(f98,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X1,X3,X2)
| ~ precedes(X0,X4,X2)
| ~ precedes(X4,X0,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f172,plain,
( head_of(sK4) = tail_of(sK2)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f170,plain,
( spl13_3
<=> head_of(sK4) = tail_of(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f246,plain,
( spl13_4
| spl13_3
| spl13_2 ),
inference(avatar_split_clause,[],[f104,f166,f170,f243]) ).
fof(f166,plain,
( spl13_2
<=> head_of(sK4) = head_of(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f104,plain,
( head_of(sK4) = head_of(sK2)
| head_of(sK4) = tail_of(sK2)
| head_of(sK4) = head_of(sK5) ),
inference(cnf_transformation,[],[f66]) ).
fof(f181,plain,
~ spl13_2,
inference(avatar_contradiction_clause,[],[f180]) ).
fof(f180,plain,
( $false
| ~ spl13_2 ),
inference(trivial_inequality_removal,[],[f174]) ).
fof(f174,plain,
( tail_of(sK2) != tail_of(sK2)
| ~ spl13_2 ),
inference(unit_resulting_resolution,[],[f102,f105,f168,f97]) ).
fof(f168,plain,
( head_of(sK4) = head_of(sK2)
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f173,plain,
( spl13_1
| spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f103,f170,f166,f162]) ).
fof(f103,plain,
( head_of(sK4) = tail_of(sK2)
| head_of(sK4) = head_of(sK2)
| tail_of(sK5) = tail_of(sK2) ),
inference(cnf_transformation,[],[f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA004+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 21:58:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.51 % (4332)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.52 % (4345)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (4354)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)
% 0.19/0.52 % (4352)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.52 % (4346)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.52 % (4335)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52 % (4333)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.53 % (4351)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)
% 0.19/0.53 % (4336)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)
% 0.19/0.53 % (4343)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.53 % (4346)Instruction limit reached!
% 0.19/0.53 % (4346)------------------------------
% 0.19/0.53 % (4346)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (4346)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (4346)Termination reason: Unknown
% 0.19/0.53 % (4346)Termination phase: Clausification
% 0.19/0.53
% 0.19/0.53 % (4346)Memory used [KB]: 1535
% 0.19/0.53 % (4346)Time elapsed: 0.003 s
% 0.19/0.53 % (4346)Instructions burned: 3 (million)
% 0.19/0.53 % (4346)------------------------------
% 0.19/0.53 % (4346)------------------------------
% 0.19/0.53 % (4334)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.53 % (4339)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)
% 0.19/0.53 % (4337)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.53 % (4338)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.53 % (4348)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53 % (4355)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.53 % (4334)Instruction limit reached!
% 0.19/0.53 % (4334)------------------------------
% 0.19/0.53 % (4334)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (4334)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (4334)Termination reason: Unknown
% 0.19/0.53 % (4334)Termination phase: Property scanning
% 0.19/0.53
% 0.19/0.53 % (4338)Refutation not found, incomplete strategy% (4338)------------------------------
% 0.19/0.53 % (4338)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (4334)Memory used [KB]: 1535
% 0.19/0.53 % (4334)Time elapsed: 0.004 s
% 0.19/0.53 % (4334)Instructions burned: 3 (million)
% 0.19/0.54 % (4334)------------------------------
% 0.19/0.54 % (4334)------------------------------
% 0.19/0.54 % (4336)Refutation not found, incomplete strategy% (4336)------------------------------
% 0.19/0.54 % (4336)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (4336)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (4336)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.54
% 0.19/0.54 % (4336)Memory used [KB]: 6012
% 0.19/0.54 % (4336)Time elapsed: 0.133 s
% 0.19/0.54 % (4336)Instructions burned: 2 (million)
% 0.19/0.54 % (4336)------------------------------
% 0.19/0.54 % (4336)------------------------------
% 0.19/0.54 % (4353)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.54 % (4359)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)
% 0.19/0.54 % (4360)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.54 % (4338)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (4338)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.54
% 0.19/0.54 % (4338)Memory used [KB]: 6012
% 0.19/0.54 % (4338)Time elapsed: 0.094 s
% 0.19/0.54 % (4338)Instructions burned: 3 (million)
% 0.19/0.54 % (4338)------------------------------
% 0.19/0.54 % (4338)------------------------------
% 0.19/0.54 % (4347)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.54 % (4349)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.54 % (4350)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.54 % (4350)Instruction limit reached!
% 0.19/0.54 % (4350)------------------------------
% 0.19/0.54 % (4350)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (4350)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (4350)Termination reason: Unknown
% 0.19/0.54 % (4350)Termination phase: Preprocessing 3
% 0.19/0.54
% 0.19/0.54 % (4350)Memory used [KB]: 1407
% 0.19/0.54 % (4350)Time elapsed: 0.002 s
% 0.19/0.54 % (4350)Instructions burned: 2 (million)
% 0.19/0.54 % (4350)------------------------------
% 0.19/0.54 % (4350)------------------------------
% 0.19/0.54 % (4353)First to succeed.
% 0.19/0.54 % (4356)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.54 % (4340)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.54 % (4358)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.55 % (4344)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)
% 0.19/0.55 % (4361)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.55 % (4342)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.55 % (4333)Instruction limit reached!
% 0.19/0.55 % (4333)------------------------------
% 0.19/0.55 % (4333)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55 % (4333)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55 % (4333)Termination reason: Unknown
% 0.19/0.55 % (4333)Termination phase: Saturation
% 0.19/0.55
% 0.19/0.55 % (4333)Memory used [KB]: 6268
% 0.19/0.55 % (4333)Time elapsed: 0.154 s
% 0.19/0.55 % (4333)Instructions burned: 13 (million)
% 0.19/0.55 % (4333)------------------------------
% 0.19/0.55 % (4333)------------------------------
% 0.19/0.55 % (4343)Instruction limit reached!
% 0.19/0.55 % (4343)------------------------------
% 0.19/0.55 % (4343)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55 % (4343)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55 % (4343)Termination reason: Unknown
% 0.19/0.55 % (4343)Termination phase: Saturation
% 0.19/0.55
% 0.19/0.55 % (4343)Memory used [KB]: 6140
% 0.19/0.55 % (4343)Time elapsed: 0.160 s
% 0.19/0.55 % (4343)Instructions burned: 8 (million)
% 0.19/0.55 % (4343)------------------------------
% 0.19/0.55 % (4343)------------------------------
% 0.19/0.55 % (4341)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.55 % (4357)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 1.58/0.55 % (4337)Instruction limit reached!
% 1.58/0.55 % (4337)------------------------------
% 1.58/0.55 % (4337)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.55 % (4337)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.58/0.55 % (4337)Termination reason: Unknown
% 1.58/0.55 % (4337)Termination phase: Saturation
% 1.58/0.55
% 1.58/0.55 % (4337)Memory used [KB]: 1663
% 1.58/0.55 % (4337)Time elapsed: 0.139 s
% 1.58/0.55 % (4337)Instructions burned: 16 (million)
% 1.58/0.55 % (4337)------------------------------
% 1.58/0.55 % (4337)------------------------------
% 1.58/0.56 % (4351)Instruction limit reached!
% 1.58/0.56 % (4351)------------------------------
% 1.58/0.56 % (4351)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.56 % (4353)Refutation found. Thanks to Tanya!
% 1.58/0.56 % SZS status Theorem for theBenchmark
% 1.58/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.58/0.56 % (4353)------------------------------
% 1.58/0.56 % (4353)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.56 % (4353)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.58/0.56 % (4353)Termination reason: Refutation
% 1.58/0.56
% 1.58/0.56 % (4353)Memory used [KB]: 6268
% 1.58/0.56 % (4353)Time elapsed: 0.153 s
% 1.58/0.56 % (4353)Instructions burned: 11 (million)
% 1.58/0.56 % (4353)------------------------------
% 1.58/0.56 % (4353)------------------------------
% 1.58/0.56 % (4331)Success in time 0.207 s
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