TSTP Solution File: GRA010+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 : Fri May 19 11:12:46 EDT 2023
% Result : Theorem 4.39s 2.19s
% Output : Refutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 41
% Syntax : Number of formulae : 61 ( 3 unt; 23 typ; 0 def)
% Number of atoms : 230 ( 61 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 681 ( 24 ~; 11 |; 122 &; 465 @)
% ( 3 <=>; 51 =>; 2 <=; 3 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 8 con; 0-3 aty)
% Number of variables : 151 ( 0 ^; 126 !; 25 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
thf(complete_type,type,
complete: $o ).
thf(path_type,type,
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(number_of_in_type,type,
number_of_in: $i > $i > $i ).
thf(sequential_pairs_type,type,
sequential_pairs: $i ).
thf(triangles_type,type,
triangles: $i ).
thf(shortest_path_type,type,
shortest_path: $i > $i > $i > $o ).
thf(precedes_type,type,
precedes: $i > $i > $i > $o ).
thf(tail_of_type,type,
tail_of: $i > $i ).
thf(head_of_type,type,
head_of: $i > $i ).
thf(edge_type,type,
edge: $i > $o ).
thf(vertex_type,type,
vertex: $i > $o ).
thf(less_or_equal_type,type,
less_or_equal: $i > $i > $o ).
thf(graph_type,type,
graph: $i ).
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(length_of_type,type,
length_of: $i > $i ).
thf(minus_type,type,
minus: $i > $i > $i ).
thf(n1_type,type,
n1: $i ).
thf(edges_type,type,
edges: $i ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
thf(101,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)],[14]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( sequential @ A @ B )
<=> ( ( edge @ A )
& ( edge @ B )
& ( A != B )
& ( ( head_of @ A )
= ( tail_of @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_defn) ).
thf(37,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)],[6]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',on_path_properties) ).
thf(97,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)],[13]) ).
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/sandbox2/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(10,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/sandbox2/benchmark/theBenchmark.p',path_defn) ).
thf(73,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)],[10]) ).
thf(5,axiom,
! [A: $i] :
( ( edge @ A )
=> ( ( head_of @ A )
!= ( tail_of @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_loops) ).
thf(34,plain,
! [A: $i] :
( ( edge @ A )
=> ( ( head_of @ A )
!= ( tail_of @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',shortest_path_properties) ).
thf(27,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)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( less_or_equal @ ( number_of_in @ A @ B ) @ ( number_of_in @ A @ graph ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
thf(49,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)],[7]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).
thf(80,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)],[11]) ).
thf(4,axiom,
! [A: $i] :
( ( edge @ A )
=> ( ( vertex @ ( head_of @ A ) )
& ( vertex @ ( tail_of @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
thf(31,plain,
! [A: $i] :
( ( edge @ A )
=> ( ( vertex @ ( head_of @ A ) )
& ( vertex @ ( tail_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( path @ A @ B @ C )
=> ( ( length_of @ C )
= ( number_of_in @ edges @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',length_defn) ).
thf(104,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)],[15]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',path_properties) ).
thf(51,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)],[8]) ).
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/sandbox2/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(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/sandbox2/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(1,conjecture,
( complete
=> ! [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/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
thf(2,negated_conjecture,
~ ( complete
=> ! [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(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ( complete
=> ! [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)],[2]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',precedes_defn) ).
thf(93,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)],[12]) ).
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/sandbox2/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(9,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/sandbox2/benchmark/theBenchmark.p',in_path_properties) ).
thf(68,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)],[9]) ).
thf(151,plain,
$false,
inference(e,[status(thm)],[101,37,97,141,73,34,27,49,80,31,104,51,107,122,20,93,131,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.16/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n026.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 20:48:36 EDT 2023
% 0.16/0.36 % CPUTime :
% 1.00/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.04 % [INFO] Parsing done (133ms).
% 1.37/1.05 % [INFO] Running in sequential loop mode.
% 1.80/1.28 % [INFO] eprover registered as external prover.
% 1.80/1.28 % [INFO] cvc4 registered as external prover.
% 1.80/1.28 % [INFO] Scanning for conjecture ...
% 2.07/1.36 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 2.07/1.41 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.42/1.46 % [INFO] Problem is first-order (TPTP FOF).
% 2.42/1.47 % [INFO] Type checking passed.
% 2.42/1.47 % [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 ...
% 4.39/2.19 % External prover 'e' found a proof!
% 4.39/2.19 % [INFO] Killing All external provers ...
% 4.39/2.19 % Time passed: 1653ms (effective reasoning time: 1129ms)
% 4.39/2.19 % 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)>
% 4.39/2.19 % 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
% 4.39/2.19 % No. of inferences in proof: 38
% 4.39/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1653 ms resp. 1129 ms w/o parsing
% 4.64/2.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.64/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------