TSTP Solution File: GRA007+2 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : GRA007+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 27.36s 6.55s
% Output : Refutation 27.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 50
% Syntax : Number of formulae : 139 ( 16 unt; 31 typ; 0 def)
% Number of atoms : 467 ( 129 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1560 ( 131 ~; 116 |; 157 &;1086 @)
% ( 3 <=>; 62 =>; 2 <=; 3 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 14 con; 0-3 aty)
% Number of variables : 315 ( 0 ^ 283 !; 32 ?; 315 :)
% Comments :
%------------------------------------------------------------------------------
thf(complete_type,type,
complete: $o ).
thf(shortest_path_type,type,
shortest_path: $i > $i > $i > $o ).
thf(precedes_type,type,
precedes: $i > $i > $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_type,type,
path: $i > $i > $i > $o ).
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(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(triangles_type,type,
triangles: $i ).
thf(vertex_type,type,
vertex: $i > $o ).
thf(path_cons_type,type,
path_cons: $i > $i > $i ).
thf(empty_type,type,
empty: $i ).
thf(in_path_type,type,
in_path: $i > $i > $o ).
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(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk14_type,type,
sk14: $i > $i > $i > $i ).
thf(15,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(116,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)],[15]) ).
thf(8,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(58,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)],[8]) ).
thf(60,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)],[58]) ).
thf(1,conjecture,
( complete
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ E )
& ( precedes @ C @ D @ E ) )
=> ? [F: $i] :
( ( edge @ F )
& ( ( tail_of @ F )
= ( head_of @ D ) )
& ( ( head_of @ F )
= ( tail_of @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
thf(2,negated_conjecture,
~ ( complete
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ E )
& ( precedes @ C @ D @ E ) )
=> ? [F: $i] :
( ( edge @ F )
& ( ( tail_of @ F )
= ( head_of @ D ) )
& ( ( head_of @ F )
= ( tail_of @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ( complete
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ E )
& ( precedes @ C @ D @ E ) )
=> ? [F: $i] :
( ( edge @ F )
& ( ( tail_of @ F )
= ( head_of @ D ) )
& ( ( head_of @ F )
= ( tail_of @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
~ ( complete
=> ! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( shortest_path @ A @ B @ E )
& ( precedes @ C @ D @ E ) )
=> ? [E: $i] :
( ( edge @ E )
& ( ( tail_of @ E )
= ( head_of @ D ) )
& ( ( head_of @ E )
= ( tail_of @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(25,plain,
shortest_path @ sk1 @ sk2 @ sk5,
inference(cnf,[status(esa)],[22]) ).
thf(501,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( precedes @ C @ D @ E )
| ~ ( precedes @ D @ C @ E )
| ( ( shortest_path @ sk1 @ sk2 @ sk5 )
!= ( shortest_path @ A @ B @ E ) ) ),
inference(paramod_ordered,[status(thm)],[25,60]) ).
thf(502,plain,
! [B: $i,A: $i] :
( ~ ( precedes @ A @ B @ sk5 )
| ~ ( precedes @ B @ A @ sk5 ) ),
inference(pattern_uni,[status(thm)],[501:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( sk5 ))]]) ).
thf(505,plain,
! [B: $i,A: $i] :
( ~ ( precedes @ A @ B @ sk5 )
| ~ ( precedes @ B @ A @ sk5 ) ),
inference(simp,[status(thm)],[502]) ).
thf(708,plain,
! [B: $i,A: $i] :
( ~ ( precedes @ A @ B @ sk5 )
| ( ( precedes @ B @ A @ sk5 )
!= ( precedes @ A @ B @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[505]) ).
thf(709,plain,
! [A: $i] :
~ ( precedes @ A @ A @ sk5 ),
inference(pattern_uni,[status(thm)],[708:[bind(A,$thf( B ))]]) ).
thf(710,plain,
! [A: $i] :
~ ( precedes @ A @ A @ sk5 ),
inference(simp,[status(thm)],[709]) ).
thf(18,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(128,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)],[18]) ).
thf(23,plain,
! [A: $i] :
( ~ ( edge @ A )
| ( ( tail_of @ A )
!= ( head_of @ sk4 ) )
| ( ( head_of @ A )
!= ( tail_of @ sk3 ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(27,plain,
! [A: $i] :
( ( ( tail_of @ A )
!= ( head_of @ sk4 ) )
| ( ( head_of @ A )
!= ( tail_of @ sk3 ) )
| ~ ( edge @ A ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(14,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(103,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)],[14]) ).
thf(104,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)],[103]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( path @ A @ B @ C )
| ( A = B )
| ( path @ A @ B @ ( sk14 @ C @ B @ A ) )
| ( shortest_path @ A @ B @ C ) ),
inference(cnf,[status(esa)],[104]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( path @ A @ B @ C )
| ( path @ A @ B @ ( sk14 @ C @ B @ A ) )
| ( shortest_path @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( path @ A @ B @ C )
| ( path @ A @ B @ ( sk14 @ C @ B @ A ) )
| ( shortest_path @ A @ B @ C ) ),
inference(simp,[status(thm)],[112]) ).
thf(19,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(143,plain,
! [A: $i] :
( ( edge @ A )
=> ( ( vertex @ ( head_of @ A ) )
& ( vertex @ ( tail_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(145,plain,
! [A: $i] :
( ~ ( edge @ A )
| ( vertex @ ( tail_of @ A ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(10,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(79,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)],[10]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( shortest_path @ A @ B @ C )
| ( A != B ) ),
inference(cnf,[status(esa)],[104]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( shortest_path @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(115,plain,
! [B: $i,A: $i] :
~ ( shortest_path @ A @ A @ B ),
inference(simp,[status(thm)],[114]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( shortest_path @ sk1 @ sk2 @ sk5 )
!= ( shortest_path @ A @ A @ B ) ),
inference(paramod_ordered,[status(thm)],[25,115]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( sk1 != A )
| ( sk2 != A )
| ( sk5 != B ) ),
inference(simp,[status(thm)],[156]) ).
thf(158,plain,
sk2 != sk1,
inference(simp,[status(thm)],[157]) ).
thf(304,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( path @ A @ B @ C )
| ( path @ A @ B @ ( sk14 @ C @ B @ A ) )
| ( shortest_path @ A @ B @ C )
| ( B != sk1 )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[113,158]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ~ ( path @ sk2 @ A @ B )
| ( path @ sk2 @ A @ ( sk14 @ B @ A @ sk2 ) )
| ( shortest_path @ sk2 @ A @ B )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[304:[bind(A,$thf( sk2 ))]]) ).
thf(337,plain,
! [A: $i] :
( ~ ( path @ sk2 @ sk1 @ A )
| ( path @ sk2 @ sk1 @ ( sk14 @ A @ sk1 @ sk2 ) )
| ( shortest_path @ sk2 @ sk1 @ A ) ),
inference(simp,[status(thm)],[305]) ).
thf(16,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(120,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)],[16]) ).
thf(6,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(36,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)],[6]) ).
thf(37,plain,
! [A: $i] :
( ( ? [B: $i,C: $i] : ( path @ B @ C @ A )
& ! [B: $i,C: $i] :
( ( ( on_path @ B @ A )
& ( on_path @ C @ A )
& ( sequential @ B @ C ) )
=> ? [D: $i] : ( triangle @ B @ C @ D ) ) )
=> ( ( number_of_in @ sequential_pairs @ A )
= ( number_of_in @ triangles @ A ) ) ),
inference(miniscope,[status(thm)],[36]) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( path @ B @ C @ A )
| ~ ( triangle @ ( sk6 @ A ) @ ( sk7 @ A ) @ D )
| ( ( number_of_in @ sequential_pairs @ A )
= ( number_of_in @ triangles @ A ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( number_of_in @ triangles @ A )
= ( number_of_in @ sequential_pairs @ A ) )
| ~ ( path @ B @ C @ A )
| ~ ( triangle @ ( sk6 @ A ) @ ( sk7 @ A ) @ D ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(24,plain,
precedes @ sk3 @ sk4 @ sk5,
inference(cnf,[status(esa)],[22]) ).
thf(7,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(46,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)],[7]) ).
thf(47,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)],[46]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( sequential @ A @ B )
| ( edge @ B ) ),
inference(cnf,[status(esa)],[47]) ).
thf(432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( path @ A @ B @ C )
| ( shortest_path @ A @ B @ C )
| ( path @ sk2 @ sk1 @ ( sk14 @ D @ sk1 @ sk2 ) )
| ( shortest_path @ sk2 @ sk1 @ D )
| ( ( path @ A @ B @ ( sk14 @ C @ B @ A ) )
!= ( path @ sk2 @ sk1 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[113,337]) ).
thf(433,plain,
! [A: $i] :
( ( sk2 = sk1 )
| ~ ( path @ sk2 @ sk1 @ A )
| ( shortest_path @ sk2 @ sk1 @ A )
| ( path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ A @ sk1 @ sk2 ) @ sk1 @ sk2 ) )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ A @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[432:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( E )),bind(D,$thf( sk14 @ E @ sk1 @ sk2 ))]]) ).
thf(446,plain,
! [A: $i] :
( ( sk2 = sk1 )
| ~ ( path @ sk2 @ sk1 @ A )
| ( shortest_path @ sk2 @ sk1 @ A )
| ( path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ A @ sk1 @ sk2 ) @ sk1 @ sk2 ) )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ A @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[433]) ).
thf(536,plain,
! [A: $i] :
( ~ ( path @ sk2 @ sk1 @ A )
| ( shortest_path @ sk2 @ sk1 @ A )
| ( path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ A @ sk1 @ sk2 ) @ sk1 @ sk2 ) )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ A @ sk1 @ sk2 ) ) ),
inference(simplifyReflect,[status(thm)],[446,158]) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( path @ A @ B @ C )
| ( shortest_path @ A @ B @ C )
| ( shortest_path @ sk2 @ sk1 @ D )
| ( path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ D @ sk1 @ sk2 ) @ sk1 @ sk2 ) )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ D @ sk1 @ sk2 ) )
| ( ( path @ A @ B @ ( sk14 @ C @ B @ A ) )
!= ( path @ sk2 @ sk1 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[113,536]) ).
thf(580,plain,
! [A: $i] :
( ( sk2 = sk1 )
| ~ ( path @ sk2 @ sk1 @ A )
| ( shortest_path @ sk2 @ sk1 @ A )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ A @ sk1 @ sk2 ) )
| ( path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ ( sk14 @ A @ sk1 @ sk2 ) @ sk1 @ sk2 ) @ sk1 @ sk2 ) )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ A @ sk1 @ sk2 ) @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[579:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( E )),bind(D,$thf( sk14 @ E @ sk1 @ sk2 ))]]) ).
thf(597,plain,
! [A: $i] :
( ( sk2 = sk1 )
| ~ ( path @ sk2 @ sk1 @ A )
| ( shortest_path @ sk2 @ sk1 @ A )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ A @ sk1 @ sk2 ) )
| ( path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ ( sk14 @ A @ sk1 @ sk2 ) @ sk1 @ sk2 ) @ sk1 @ sk2 ) )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ A @ sk1 @ sk2 ) @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[580]) ).
thf(724,plain,
! [A: $i] :
( ~ ( path @ sk2 @ sk1 @ A )
| ( shortest_path @ sk2 @ sk1 @ A )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ A @ sk1 @ sk2 ) )
| ( path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ ( sk14 @ A @ sk1 @ sk2 ) @ sk1 @ sk2 ) @ sk1 @ sk2 ) )
| ( shortest_path @ sk2 @ sk1 @ ( sk14 @ ( sk14 @ A @ sk1 @ sk2 ) @ sk1 @ sk2 ) ) ),
inference(simplifyReflect,[status(thm)],[597,158]) ).
thf(12,axiom,
! [A: $i] :
( ( edge @ A )
=> ( ( head_of @ A )
!= ( tail_of @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
thf(93,plain,
! [A: $i] :
( ( edge @ A )
=> ( ( head_of @ A )
!= ( tail_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(159,plain,
! [A: $i] :
( ( ( tail_of @ A )
!= ( head_of @ sk4 ) )
| ~ ( edge @ A )
| ( ( head_of @ A )
!= ( head_of @ sk4 ) )
| ( ( tail_of @ sk3 )
!= ( tail_of @ A ) ) ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(161,plain,
! [A: $i] :
( ( ( tail_of @ A )
!= ( head_of @ sk4 ) )
| ~ ( edge @ A )
| ( ( head_of @ A )
!= ( head_of @ sk4 ) )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[159]) ).
thf(164,plain,
( ( ( head_of @ sk4 )
!= ( tail_of @ sk3 ) )
| ~ ( edge @ sk3 )
| ( ( head_of @ sk4 )
!= ( head_of @ sk3 ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(11,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(84,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)],[11]) ).
thf(3,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(28,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)],[3]) ).
thf(5,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(33,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)],[5]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ E )
& ( precedes @ C @ D @ E ) )
=> ~ ? [F: $i] :
( ( edge @ F )
& ( ( tail_of @ F )
= ( tail_of @ C ) )
& ( ( head_of @ F )
= ( head_of @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_short_cut_edge) ).
thf(124,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( shortest_path @ A @ B @ E )
& ( precedes @ C @ D @ E ) )
=> ~ ? [F: $i] :
( ( edge @ F )
& ( ( tail_of @ F )
= ( tail_of @ C ) )
& ( ( head_of @ F )
= ( head_of @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,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(96,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)],[13]) ).
thf(4,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(31,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)],[4]) ).
thf(32,plain,
! [B: $i,A: $i] : ( less_or_equal @ ( number_of_in @ A @ B ) @ ( number_of_in @ A @ graph ) ),
inference(cnf,[status(esa)],[31]) ).
thf(9,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(62,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)],[9]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( path @ A @ B @ C )
| ( vertex @ A ) ),
inference(cnf,[status(esa)],[62]) ).
thf(20,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(146,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)],[20]) ).
thf(147,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 ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( edge @ A )
& ( edge @ B )
& ( edge @ C )
& ( sequential @ A @ B )
& ( sequential @ B @ C )
& ( sequential @ C @ A ) )
=> ( triangle @ A @ B @ C ) ) ),
inference(miniscope,[status(thm)],[146]) ).
thf(149,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( triangle @ A @ B @ C )
| ( edge @ B ) ),
inference(cnf,[status(esa)],[147]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( path @ A @ B @ C )
| ( vertex @ B ) ),
inference(cnf,[status(esa)],[62]) ).
thf(144,plain,
! [A: $i] :
( ~ ( edge @ A )
| ( vertex @ ( head_of @ A ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( path @ A @ B @ C )
| ( ( length_of @ C )
= ( number_of_in @ edges @ C ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( ( number_of_in @ edges @ C )
= ( length_of @ C ) )
| ~ ( path @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(497,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( shortest_path @ A @ B @ E )
| ~ ( precedes @ D @ C @ E )
| ( ( precedes @ sk3 @ sk4 @ sk5 )
!= ( precedes @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[24,60]) ).
thf(498,plain,
! [B: $i,A: $i] :
( ~ ( shortest_path @ A @ B @ sk5 )
| ~ ( precedes @ sk4 @ sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[497:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk3 )),bind(D,$thf( sk4 )),bind(E,$thf( sk5 ))]]) ).
thf(524,plain,
! [B: $i,A: $i] :
( ~ ( precedes @ sk4 @ sk3 @ sk5 )
| ( ( shortest_path @ sk1 @ sk2 @ sk5 )
!= ( shortest_path @ A @ B @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[25,498]) ).
thf(525,plain,
~ ( precedes @ sk4 @ sk3 @ sk5 ),
inference(pattern_uni,[status(thm)],[524:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( triangle @ A @ B @ C )
| ( edge @ C ) ),
inference(cnf,[status(esa)],[147]) ).
thf(94,plain,
! [A: $i] :
( ~ ( edge @ A )
| ( ( head_of @ A )
!= ( tail_of @ A ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(95,plain,
! [A: $i] :
( ( ( head_of @ A )
!= ( tail_of @ A ) )
| ~ ( edge @ A ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( sequential @ A @ B )
| ( edge @ A ) ),
inference(cnf,[status(esa)],[47]) ).
thf(26,plain,
complete,
inference(cnf,[status(esa)],[22]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( sequential @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[47]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( sequential @ A @ B ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(55,plain,
! [A: $i] :
~ ( sequential @ A @ A ),
inference(simp,[status(thm)],[54]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( triangle @ A @ B @ C )
| ( edge @ A ) ),
inference(cnf,[status(esa)],[147]) ).
thf(29,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)],[28]) ).
thf(30,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)],[29]) ).
thf(636,plain,
( ( precedes @ sk4 @ sk3 @ sk5 )
!= ( precedes @ sk3 @ sk4 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[24,525]) ).
thf(637,plain,
( ( sk4 != sk3 )
| ( sk4 != sk3 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[636]) ).
thf(644,plain,
sk4 != sk3,
inference(simp,[status(thm)],[637]) ).
thf(4924,plain,
$false,
inference(e,[status(thm)],[116,60,710,128,27,113,103,145,143,79,337,115,120,42,24,25,52,724,46,93,164,84,28,21,33,124,96,32,64,149,71,144,505,35,525,150,95,50,31,26,158,55,58,536,151,36,146,30,644,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRA007+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.10/0.11 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Jun 18 21:18:10 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.78/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.01 % [INFO] Parsing done (165ms).
% 1.25/1.02 % [INFO] Running in sequential loop mode.
% 1.60/1.30 % [INFO] eprover registered as external prover.
% 1.60/1.30 % [INFO] Scanning for conjecture ...
% 1.90/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 1.90/1.46 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.24/1.54 % [INFO] Problem is first-order (TPTP FOF).
% 2.24/1.55 % [INFO] Type checking passed.
% 2.24/1.55 % [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 ...
% 27.36/6.55 % External prover 'e' found a proof!
% 27.36/6.55 % [INFO] Killing All external provers ...
% 27.36/6.55 % Time passed: 6081ms (effective reasoning time: 5522ms)
% 27.36/6.55 % 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)>
% 27.36/6.55 % Axioms used in derivation (18): path_defn, sequential_defn, graph_has_them_all, path_properties, sequential_pairs_and_triangles, edge_ends_are_vertices, no_loops, no_short_cut_edge, 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
% 27.36/6.55 % No. of inferences in proof: 108
% 27.36/6.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6081 ms resp. 5522 ms w/o parsing
% 27.38/6.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.38/6.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------