TSTP Solution File: GRA009+1 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : GRA009+1 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 : Mon Jun 24 06:36:13 EDT 2024
% Result : Theorem 9.98s 3.14s
% Output : Refutation 9.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 47
% Syntax : Number of formulae : 140 ( 27 unt; 29 typ; 0 def)
% Number of atoms : 452 ( 122 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1395 ( 146 ~; 115 |; 134 &; 938 @)
% ( 3 <=>; 54 =>; 2 <=; 3 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 14 con; 0-3 aty)
% Number of variables : 298 ( 0 ^ 273 !; 25 ?; 298 :)
% Comments :
%------------------------------------------------------------------------------
thf(complete_type,type,
complete: $o ).
thf(shortest_path_type,type,
shortest_path: $i > $i > $i > $o ).
thf(on_path_type,type,
on_path: $i > $i > $o ).
thf(sequential_type,type,
sequential: $i > $i > $o ).
thf(triangle_type,type,
triangle: $i > $i > $i > $o ).
thf(path_type,type,
path: $i > $i > $i > $o ).
thf(vertex_type,type,
vertex: $i > $o ).
thf(edge_type,type,
edge: $i > $o ).
thf(tail_of_type,type,
tail_of: $i > $i ).
thf(head_of_type,type,
head_of: $i > $i ).
thf(path_cons_type,type,
path_cons: $i > $i > $i ).
thf(empty_type,type,
empty: $i ).
thf(number_of_in_type,type,
number_of_in: $i > $i > $i ).
thf(sequential_pairs_type,type,
sequential_pairs: $i ).
thf(minus_type,type,
minus: $i > $i > $i ).
thf(length_of_type,type,
length_of: $i > $i ).
thf(n1_type,type,
n1: $i ).
thf(less_or_equal_type,type,
less_or_equal: $i > $i > $o ).
thf(graph_type,type,
graph: $i ).
thf(edges_type,type,
edges: $i ).
thf(precedes_type,type,
precedes: $i > $i > $i > $o ).
thf(in_path_type,type,
in_path: $i > $i > $o ).
thf(triangles_type,type,
triangles: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk9_type,type,
sk9: $i > $i > $i > $i ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( sequential @ A @ B )
<=> ( ( edge @ A )
& ( edge @ B )
& ( A != B )
& ( ( head_of @ A )
= ( tail_of @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( sequential @ A @ B )
=> ( ( edge @ A )
& ( edge @ B )
& ( A != B )
& ( ( head_of @ A )
= ( tail_of @ B ) ) ) )
& ( ( ( edge @ A )
& ( edge @ B )
& ( A != B )
& ( ( head_of @ A )
= ( tail_of @ B ) ) )
=> ( sequential @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( path @ B @ C @ A )
& ! [D: $i,E: $i] :
( ( ( on_path @ D @ A )
& ( on_path @ E @ A )
& ( sequential @ D @ E ) )
=> ? [F: $i] : ( triangle @ D @ E @ F ) ) )
=> ( ( number_of_in @ sequential_pairs @ A )
= ( number_of_in @ triangles @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
thf(141,plain,
! [A: $i,B: $i,C: $i] :
( ( ( path @ B @ C @ A )
& ! [D: $i,E: $i] :
( ( ( on_path @ D @ A )
& ( on_path @ E @ A )
& ( sequential @ D @ E ) )
=> ? [F: $i] : ( triangle @ D @ E @ F ) ) )
=> ( ( number_of_in @ sequential_pairs @ A )
= ( number_of_in @ triangles @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ E )
& ( precedes @ C @ D @ E ) )
=> ( ~ ? [F: $i] :
( ( ( tail_of @ F )
= ( tail_of @ C ) )
& ( ( head_of @ F )
= ( head_of @ D ) ) )
& ~ ( precedes @ D @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).
thf(77,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ E )
& ( precedes @ C @ D @ E ) )
=> ( ~ ? [F: $i] :
( ( ( tail_of @ F )
= ( tail_of @ C ) )
& ( ( head_of @ F )
= ( head_of @ D ) ) )
& ~ ( precedes @ D @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(78,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( shortest_path @ A @ B @ E )
| ~ ( precedes @ C @ D @ E )
| ( ( tail_of @ F )
!= ( tail_of @ C ) )
| ( ( head_of @ F )
!= ( head_of @ D ) ) ),
inference(cnf,[status(esa)],[77]) ).
thf(80,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( tail_of @ F )
!= ( tail_of @ C ) )
| ( ( head_of @ F )
!= ( head_of @ D ) )
| ~ ( shortest_path @ A @ B @ E )
| ~ ( precedes @ C @ D @ E ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( path @ A @ B @ C )
<= ( ( vertex @ A )
& ( vertex @ B )
& ? [D: $i] :
( ( edge @ D )
& ( A
= ( tail_of @ D ) )
& ( ( ( B
= ( head_of @ D ) )
& ( C
= ( path_cons @ D @ empty ) ) )
| ? [E: $i] :
( ( path @ ( head_of @ D ) @ B @ E )
& ( C
= ( path_cons @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_defn) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( path @ A @ B @ C )
| ~ ( ( vertex @ A )
& ( vertex @ B )
& ? [D: $i] :
( ( edge @ D )
& ( A
= ( tail_of @ D ) )
& ( ( ( B
= ( head_of @ D ) )
& ( C
= ( path_cons @ D @ empty ) ) )
| ? [E: $i] :
( ( path @ ( head_of @ D ) @ B @ E )
& ( C
= ( path_cons @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( path @ A @ B @ C )
| ~ ( vertex @ A )
| ~ ( vertex @ B )
| ~ ( edge @ D )
| ( A
!= ( tail_of @ D ) )
| ( B
!= ( head_of @ D ) )
| ( C
!= ( path_cons @ D @ empty ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tail_of @ D ) )
| ( B
!= ( head_of @ D ) )
| ( C
!= ( path_cons @ D @ empty ) )
| ( path @ A @ B @ C )
| ~ ( vertex @ A )
| ~ ( vertex @ B )
| ~ ( edge @ D ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(31,plain,
! [A: $i] :
( ( path @ ( tail_of @ A ) @ ( head_of @ A ) @ ( path_cons @ A @ empty ) )
| ~ ( vertex @ ( tail_of @ A ) )
| ~ ( vertex @ ( head_of @ A ) )
| ~ ( edge @ A ) ),
inference(simp,[status(thm)],[30]) ).
thf(1,conjecture,
( complete
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ C )
& ( on_path @ D @ C )
& ( on_path @ E @ C )
& ( sequential @ D @ E ) )
=> ? [F: $i] : ( triangle @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_path_and_stuff_means_triangles) ).
thf(2,negated_conjecture,
~ ( complete
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ C )
& ( on_path @ D @ C )
& ( on_path @ E @ C )
& ( sequential @ D @ E ) )
=> ? [F: $i] : ( triangle @ D @ E @ F ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ( complete
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ C )
& ( on_path @ D @ C )
& ( on_path @ E @ C )
& ( sequential @ D @ E ) )
=> ? [F: $i] : ( triangle @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,plain,
sequential @ sk4 @ sk5,
inference(cnf,[status(esa)],[20]) ).
thf(66,plain,
( ! [A: $i,B: $i] :
( ( sequential @ A @ B )
=> ( ( edge @ A )
& ( edge @ B )
& ( A != B )
& ( ( head_of @ A )
= ( tail_of @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ( edge @ A )
& ( edge @ B )
& ( A != B )
& ( ( head_of @ A )
= ( tail_of @ B ) ) )
=> ( sequential @ A @ B ) ) ),
inference(miniscope,[status(thm)],[65]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( sequential @ A @ B )
| ( edge @ A ) ),
inference(cnf,[status(esa)],[66]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( edge @ A )
| ( ( sequential @ sk4 @ sk5 )
!= ( sequential @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,68]) ).
thf(386,plain,
edge @ sk4,
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( path @ A @ B @ C )
=> ( ( number_of_in @ sequential_pairs @ C )
= ( minus @ ( length_of @ C ) @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( path @ A @ B @ C )
=> ( ( number_of_in @ sequential_pairs @ C )
= ( minus @ ( length_of @ C ) @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( path @ A @ B @ C )
| ( ( number_of_in @ sequential_pairs @ C )
= ( minus @ ( length_of @ C ) @ n1 ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( minus @ ( length_of @ C ) @ n1 )
= ( number_of_in @ sequential_pairs @ C ) )
| ~ ( path @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( path @ B @ C @ A )
=> ! [D: $i,E: $i] :
( ( precedes @ D @ E @ A )
=> ( ( on_path @ D @ A )
& ( on_path @ E @ A )
& ( ( sequential @ D @ E )
<~> ? [F: $i] :
( ( sequential @ D @ F )
& ( precedes @ F @ E @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
thf(122,plain,
! [A: $i,B: $i,C: $i] :
( ( path @ B @ C @ A )
=> ! [D: $i,E: $i] :
( ( precedes @ D @ E @ A )
=> ( ( on_path @ D @ A )
& ( on_path @ E @ A )
& ~ ( ( ( sequential @ D @ E )
=> ? [F: $i] :
( ( sequential @ D @ F )
& ( precedes @ F @ E @ A ) ) )
& ( ( sequential @ D @ E )
| ~ ? [F: $i] :
( ( sequential @ D @ F )
& ( precedes @ F @ E @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [A: $i] :
( ( edge @ A )
=> ( ( vertex @ ( head_of @ A ) )
& ( vertex @ ( tail_of @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
thf(59,plain,
! [A: $i] :
( ( edge @ A )
=> ( ( vertex @ ( head_of @ A ) )
& ( vertex @ ( tail_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(60,plain,
! [A: $i] :
( ~ ( edge @ A )
| ( vertex @ ( head_of @ A ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(391,plain,
! [A: $i] :
( ( vertex @ ( head_of @ A ) )
| ( ( edge @ sk4 )
!= ( edge @ A ) ) ),
inference(paramod_ordered,[status(thm)],[386,60]) ).
thf(392,plain,
vertex @ ( head_of @ sk4 ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( sk4 ))]]) ).
thf(413,plain,
! [A: $i] :
( ( path @ ( tail_of @ A ) @ ( head_of @ A ) @ ( path_cons @ A @ empty ) )
| ~ ( vertex @ ( tail_of @ A ) )
| ~ ( edge @ A )
| ( ( vertex @ ( head_of @ sk4 ) )
!= ( vertex @ ( head_of @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[392,31]) ).
thf(414,plain,
( ( path @ ( tail_of @ sk4 ) @ ( head_of @ sk4 ) @ ( path_cons @ sk4 @ empty ) )
| ~ ( vertex @ ( tail_of @ sk4 ) )
| ~ ( edge @ sk4 ) ),
inference(pattern_uni,[status(thm)],[413:[bind(A,$thf( sk4 ))]]) ).
thf(61,plain,
! [A: $i] :
( ~ ( edge @ A )
| ( vertex @ ( tail_of @ A ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(395,plain,
! [A: $i] :
( ( vertex @ ( tail_of @ A ) )
| ( ( edge @ sk4 )
!= ( edge @ A ) ) ),
inference(paramod_ordered,[status(thm)],[386,61]) ).
thf(396,plain,
vertex @ ( tail_of @ sk4 ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( sk4 ))]]) ).
thf(714,plain,
( ( path @ ( tail_of @ sk4 ) @ ( head_of @ sk4 ) @ ( path_cons @ sk4 @ empty ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[414,386,396]) ).
thf(715,plain,
path @ ( tail_of @ sk4 ) @ ( head_of @ sk4 ) @ ( path_cons @ sk4 @ empty ),
inference(simp,[status(thm)],[714]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( sequential @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[66]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( sequential @ A @ B ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(73,plain,
! [A: $i] :
~ ( sequential @ A @ A ),
inference(simp,[status(thm)],[72]) ).
thf(151,plain,
! [A: $i] :
( ( sequential @ sk4 @ sk5 )
!= ( sequential @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[23,73]) ).
thf(152,plain,
! [A: $i] :
( ( sk4 != A )
| ( sk5 != A ) ),
inference(simp,[status(thm)],[151]) ).
thf(153,plain,
sk5 != sk4,
inference(simp,[status(thm)],[152]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( path @ A @ B @ C )
=> ( ( vertex @ A )
& ( vertex @ B )
& ? [D: $i] :
( ( edge @ D )
& ( A
= ( tail_of @ D ) )
& ( ( ( B
= ( head_of @ D ) )
& ( C
= ( path_cons @ D @ empty ) ) )
<~> ? [E: $i] :
( ( path @ ( head_of @ D ) @ B @ E )
& ( C
= ( path_cons @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_properties) ).
thf(42,plain,
! [A: $i,B: $i,C: $i] :
( ( path @ A @ B @ C )
=> ( ( vertex @ A )
& ( vertex @ B )
& ? [D: $i] :
( ( edge @ D )
& ( A
= ( tail_of @ D ) )
& ~ ( ( ( ( B
= ( head_of @ D ) )
& ( C
= ( path_cons @ D @ empty ) ) )
=> ? [E: $i] :
( ( path @ ( head_of @ D ) @ B @ E )
& ( C
= ( path_cons @ D @ E ) ) ) )
& ( ( ( B
= ( head_of @ D ) )
& ( C
= ( path_cons @ D @ empty ) ) )
| ~ ? [E: $i] :
( ( path @ ( head_of @ D ) @ B @ E )
& ( C
= ( path_cons @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,plain,
on_path @ sk4 @ sk3,
inference(cnf,[status(esa)],[20]) ).
thf(5,axiom,
! [A: $i,B: $i] : ( less_or_equal @ ( number_of_in @ A @ B ) @ ( number_of_in @ A @ graph ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
thf(37,plain,
! [A: $i,B: $i] : ( less_or_equal @ ( number_of_in @ A @ B ) @ ( number_of_in @ A @ graph ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
shortest_path @ sk1 @ sk2 @ sk3,
inference(cnf,[status(esa)],[20]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( shortest_path @ A @ B @ C )
<=> ( ( path @ A @ B @ C )
& ( A != B )
& ! [D: $i] :
( ( path @ A @ B @ D )
=> ( less_or_equal @ ( length_of @ C ) @ ( length_of @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
thf(81,plain,
! [A: $i,B: $i,C: $i] :
( ( ( shortest_path @ A @ B @ C )
=> ( ( path @ A @ B @ C )
& ( A != B )
& ! [D: $i] :
( ( path @ A @ B @ D )
=> ( less_or_equal @ ( length_of @ C ) @ ( length_of @ D ) ) ) ) )
& ( ( ( path @ A @ B @ C )
& ( A != B )
& ! [D: $i] :
( ( path @ A @ B @ D )
=> ( less_or_equal @ ( length_of @ C ) @ ( length_of @ D ) ) ) )
=> ( shortest_path @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(82,plain,
( ! [A: $i,B: $i,C: $i] :
( ( shortest_path @ A @ B @ C )
=> ( ( path @ A @ B @ C )
& ( A != B )
& ! [D: $i] :
( ( path @ A @ B @ D )
=> ( less_or_equal @ ( length_of @ C ) @ ( length_of @ D ) ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( path @ A @ B @ C )
& ( A != B )
& ! [D: $i] :
( ( path @ A @ B @ D )
=> ( less_or_equal @ ( length_of @ C ) @ ( length_of @ D ) ) ) )
=> ( shortest_path @ A @ B @ C ) ) ),
inference(miniscope,[status(thm)],[81]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( path @ A @ B @ C )
| ( A = B )
| ( path @ A @ B @ ( sk9 @ C @ B @ A ) )
| ( shortest_path @ A @ B @ C ) ),
inference(cnf,[status(esa)],[82]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( path @ A @ B @ C )
| ( path @ A @ B @ ( sk9 @ C @ B @ A ) )
| ( shortest_path @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( path @ A @ B @ C )
| ( path @ A @ B @ ( sk9 @ C @ B @ A ) )
| ( shortest_path @ A @ B @ C ) ),
inference(simp,[status(thm)],[92]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( shortest_path @ A @ B @ C )
| ( A != B ) ),
inference(cnf,[status(esa)],[82]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( shortest_path @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(89,plain,
! [B: $i,A: $i] :
~ ( shortest_path @ A @ A @ B ),
inference(simp,[status(thm)],[88]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( sequential @ A @ B )
| ( edge @ B ) ),
inference(cnf,[status(esa)],[66]) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( edge @ B )
| ( ( sequential @ sk4 @ sk5 )
!= ( sequential @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,70]) ).
thf(920,plain,
edge @ sk5,
inference(pattern_uni,[status(thm)],[919:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( path @ A @ B @ C )
& ( in_path @ D @ C ) )
=> ( ( vertex @ D )
& ? [E: $i] :
( ( on_path @ E @ C )
& ( ( D
= ( head_of @ E ) )
| ( D
= ( tail_of @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_path_properties) ).
thf(102,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( path @ A @ B @ C )
& ( in_path @ D @ C ) )
=> ( ( vertex @ D )
& ? [E: $i] :
( ( on_path @ E @ C )
& ( ( D
= ( head_of @ E ) )
| ( D
= ( tail_of @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(79,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( shortest_path @ A @ B @ E )
| ~ ( precedes @ C @ D @ E )
| ~ ( precedes @ D @ C @ E ) ),
inference(cnf,[status(esa)],[77]) ).
thf(167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( precedes @ C @ D @ E )
| ~ ( precedes @ D @ C @ E )
| ( ( shortest_path @ sk1 @ sk2 @ sk3 )
!= ( shortest_path @ A @ B @ E ) ) ),
inference(paramod_ordered,[status(thm)],[25,79]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ~ ( precedes @ A @ B @ sk3 )
| ~ ( precedes @ B @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( sk3 ))]]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( precedes @ A @ B @ sk3 )
| ~ ( precedes @ B @ A @ sk3 ) ),
inference(simp,[status(thm)],[168]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ~ ( precedes @ A @ B @ sk3 )
| ( ( precedes @ B @ A @ sk3 )
!= ( precedes @ A @ B @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[171]) ).
thf(344,plain,
! [A: $i] :
~ ( precedes @ A @ A @ sk3 ),
inference(pattern_uni,[status(thm)],[343:[bind(A,$thf( B ))]]) ).
thf(349,plain,
! [A: $i] :
~ ( precedes @ A @ A @ sk3 ),
inference(simp,[status(thm)],[344]) ).
thf(38,plain,
! [B: $i,A: $i] : ( less_or_equal @ ( number_of_in @ A @ B ) @ ( number_of_in @ A @ graph ) ),
inference(cnf,[status(esa)],[37]) ).
thf(21,plain,
complete,
inference(cnf,[status(esa)],[20]) ).
thf(29,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( path @ A @ B @ C )
| ~ ( vertex @ A )
| ~ ( vertex @ B )
| ~ ( edge @ D )
| ( A
!= ( tail_of @ D ) )
| ~ ( path @ ( head_of @ D ) @ B @ E )
| ( C
!= ( path_cons @ D @ E ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(32,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tail_of @ D ) )
| ( C
!= ( path_cons @ D @ E ) )
| ( path @ A @ B @ C )
| ~ ( vertex @ A )
| ~ ( vertex @ B )
| ~ ( edge @ D )
| ~ ( path @ ( head_of @ D ) @ B @ E ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( path @ ( tail_of @ B ) @ A @ ( path_cons @ B @ C ) )
| ~ ( vertex @ ( tail_of @ B ) )
| ~ ( vertex @ A )
| ~ ( edge @ B )
| ~ ( path @ ( head_of @ B ) @ A @ C ) ),
inference(simp,[status(thm)],[32]) ).
thf(9,axiom,
! [A: $i] :
( ( edge @ A )
=> ( ( head_of @ A )
!= ( tail_of @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
thf(62,plain,
! [A: $i] :
( ( edge @ A )
=> ( ( head_of @ A )
!= ( tail_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(63,plain,
! [A: $i] :
( ~ ( edge @ A )
| ( ( head_of @ A )
!= ( tail_of @ A ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [A: $i] :
( ( ( head_of @ A )
!= ( tail_of @ A ) )
| ~ ( edge @ A ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(937,plain,
! [A: $i] :
( ( ( head_of @ A )
!= ( tail_of @ A ) )
| ( ( edge @ sk5 )
!= ( edge @ A ) ) ),
inference(paramod_ordered,[status(thm)],[920,64]) ).
thf(938,plain,
( ( head_of @ sk5 )
!= ( tail_of @ sk5 ) ),
inference(pattern_uni,[status(thm)],[937:[bind(A,$thf( sk5 ))]]) ).
thf(181,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( path @ A @ B @ C )
| ( shortest_path @ A @ B @ C )
| ( D = E )
| ( path @ D @ E @ ( sk9 @ F @ E @ D ) )
| ( shortest_path @ D @ E @ F )
| ( ( path @ A @ B @ ( sk9 @ C @ B @ A ) )
!= ( path @ D @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[93,93]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( path @ C @ B @ A )
| ( shortest_path @ C @ B @ A )
| ( C = B )
| ( path @ C @ B @ ( sk9 @ ( sk9 @ A @ B @ C ) @ B @ C ) )
| ( shortest_path @ C @ B @ ( sk9 @ A @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( I )),bind(E,$thf( H )),bind(F,$thf( sk9 @ G @ H @ I ))]]) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( path @ C @ B @ A )
| ( shortest_path @ C @ B @ A )
| ( path @ C @ B @ ( sk9 @ ( sk9 @ A @ B @ C ) @ B @ C ) )
| ( shortest_path @ C @ B @ ( sk9 @ A @ B @ C ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( shortest_path @ sk1 @ sk2 @ sk3 )
!= ( shortest_path @ A @ A @ B ) ),
inference(paramod_ordered,[status(thm)],[25,89]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( sk1 != A )
| ( sk2 != A )
| ( sk3 != B ) ),
inference(simp,[status(thm)],[159]) ).
thf(161,plain,
sk2 != sk1,
inference(simp,[status(thm)],[160]) ).
thf(818,plain,
! [C: $i,B: $i,A: $i] :
( ( ( minus @ ( length_of @ C ) @ n1 )
= ( number_of_in @ sequential_pairs @ C ) )
| ( ( path @ ( tail_of @ sk4 ) @ ( head_of @ sk4 ) @ ( path_cons @ sk4 @ empty ) )
!= ( path @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[715,36]) ).
thf(819,plain,
( ( minus @ ( length_of @ ( path_cons @ sk4 @ empty ) ) @ n1 )
= ( number_of_in @ sequential_pairs @ ( path_cons @ sk4 @ empty ) ) ),
inference(pattern_uni,[status(thm)],[818:[bind(A,$thf( tail_of @ sk4 )),bind(B,$thf( head_of @ sk4 )),bind(C,$thf( path_cons @ sk4 @ empty ))]]) ).
thf(22,plain,
! [A: $i] :
~ ( triangle @ sk4 @ sk5 @ A ),
inference(cnf,[status(esa)],[20]) ).
thf(169,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( shortest_path @ A @ B @ E )
| ~ ( precedes @ C @ D @ E )
| ( ( precedes @ D @ C @ E )
!= ( precedes @ C @ D @ E ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[79]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( shortest_path @ A @ B @ D )
| ~ ( precedes @ C @ C @ D ) ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( shortest_path @ A @ B @ D )
| ~ ( precedes @ C @ C @ D ) ),
inference(simp,[status(thm)],[170]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( path @ A @ B @ C )
=> ( ( length_of @ C )
= ( number_of_in @ edges @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_defn) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( path @ A @ B @ C )
=> ( ( length_of @ C )
= ( number_of_in @ edges @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( path @ A @ B @ C )
& ( on_path @ D @ C ) )
=> ( ( edge @ D )
& ( in_path @ ( head_of @ D ) @ C )
& ( in_path @ ( tail_of @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',on_path_properties) ).
thf(98,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( path @ A @ B @ C )
& ( on_path @ D @ C ) )
=> ( ( edge @ D )
& ( in_path @ ( head_of @ D ) @ C )
& ( in_path @ ( tail_of @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(26,plain,
on_path @ sk5 @ sk3,
inference(cnf,[status(esa)],[20]) ).
thf(16,axiom,
( complete
=> ! [A: $i,B: $i] :
( ( ( vertex @ A )
& ( vertex @ B )
& ( A != B ) )
=> ? [C: $i] :
( ( edge @ C )
& ( ( ( A
= ( head_of @ C ) )
& ( B
= ( tail_of @ C ) ) )
<~> ( ( B
= ( head_of @ C ) )
& ( A
= ( tail_of @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_properties) ).
thf(107,plain,
( complete
=> ! [A: $i,B: $i] :
( ( ( vertex @ A )
& ( vertex @ B )
& ( A != B ) )
=> ? [C: $i] :
( ( edge @ C )
& ~ ( ( ( ( A
= ( head_of @ C ) )
& ( B
= ( tail_of @ C ) ) )
=> ( ( B
= ( head_of @ C ) )
& ( A
= ( tail_of @ C ) ) ) )
& ( ( ( A
= ( head_of @ C ) )
& ( B
= ( tail_of @ C ) ) )
| ~ ( ( B
= ( head_of @ C ) )
& ( A
= ( tail_of @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(399,plain,
! [A: $i] :
( ( ( head_of @ A )
!= ( tail_of @ A ) )
| ( ( edge @ sk4 )
!= ( edge @ A ) ) ),
inference(paramod_ordered,[status(thm)],[386,64]) ).
thf(400,plain,
( ( head_of @ sk4 )
!= ( tail_of @ sk4 ) ),
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( sk4 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( path @ B @ C @ A )
=> ! [D: $i,E: $i] :
( ( precedes @ D @ E @ A )
<= ( ( on_path @ D @ A )
& ( on_path @ E @ A )
& ( ( sequential @ D @ E )
| ? [F: $i] :
( ( sequential @ D @ F )
& ( precedes @ F @ E @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).
thf(94,plain,
! [A: $i,B: $i,C: $i] :
( ( path @ B @ C @ A )
=> ! [D: $i,E: $i] :
( ( precedes @ D @ E @ A )
| ~ ( ( on_path @ D @ A )
& ( on_path @ E @ A )
& ( ( sequential @ D @ E )
| ? [F: $i] :
( ( sequential @ D @ F )
& ( precedes @ F @ E @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(927,plain,
! [A: $i] :
( ( vertex @ ( tail_of @ A ) )
| ( ( edge @ sk5 )
!= ( edge @ A ) ) ),
inference(paramod_ordered,[status(thm)],[920,61]) ).
thf(928,plain,
vertex @ ( tail_of @ sk5 ),
inference(pattern_uni,[status(thm)],[927:[bind(A,$thf( sk5 ))]]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( triangle @ A @ B @ C )
<=> ( ( edge @ A )
& ( edge @ B )
& ( edge @ C )
& ( sequential @ A @ B )
& ( sequential @ B @ C )
& ( sequential @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
thf(131,plain,
! [A: $i,B: $i,C: $i] :
( ( ( triangle @ A @ B @ C )
=> ( ( edge @ A )
& ( edge @ B )
& ( edge @ C )
& ( sequential @ A @ B )
& ( sequential @ B @ C )
& ( sequential @ C @ A ) ) )
& ( ( ( edge @ A )
& ( edge @ B )
& ( edge @ C )
& ( sequential @ A @ B )
& ( sequential @ B @ C )
& ( sequential @ C @ A ) )
=> ( triangle @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1440,plain,
$false,
inference(e,[status(thm)],[65,141,77,80,31,386,36,122,715,153,42,24,37,25,20,93,61,396,89,920,60,102,349,38,392,70,21,33,73,938,298,34,161,64,819,22,59,27,172,81,39,98,26,171,23,107,79,400,94,928,131,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA009+1 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.10/0.30 % Computer : n002.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Jun 18 15:02:55 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.84/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.97 % [INFO] Parsing done (130ms).
% 1.22/0.98 % [INFO] Running in sequential loop mode.
% 1.86/1.21 % [INFO] eprover registered as external prover.
% 1.86/1.21 % [INFO] Scanning for conjecture ...
% 1.93/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 2.19/1.34 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.43/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.43/1.39 % [INFO] Type checking passed.
% 2.43/1.40 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 9.98/3.14 % External prover 'e' found a proof!
% 9.98/3.14 % [INFO] Killing All external provers ...
% 9.98/3.14 % Time passed: 2656ms (effective reasoning time: 2157ms)
% 9.98/3.14 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.98/3.14 % Axioms used in derivation (17): path_defn, sequential_defn, graph_has_them_all, path_properties, sequential_pairs_and_triangles, edge_ends_are_vertices, no_loops, length_defn, triangle_defn, complete_properties, shortest_path_defn, in_path_properties, precedes_properties, on_path_properties, path_length_sequential_pairs, shortest_path_properties, precedes_defn
% 9.98/3.14 % No. of inferences in proof: 111
% 9.98/3.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2656 ms resp. 2157 ms w/o parsing
% 9.98/3.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.98/3.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------