%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:18:22 AM UTC 2026
% Result : Theorem 8.68s 4.79s
% Output : Refutation 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 61 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 706 ( 19 ~; 6 |; 126 &; 487 @)
% ( 3 <=>; 60 =>; 2 <=; 3 <~>)
% Maximal formula depth : 19 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 8 con; 0-3 aty)
% Number of variables : 163 ( 0 ^; 136 !; 27 ?; 163 :)
% Comments :
%------------------------------------------------------------------------------
thf(complete_decl,type,
complete: $o ).
thf(path_decl,type,
path: $i > $i > $i > $o ).
thf(on_path_decl,type,
on_path: $i > $i > $o ).
thf(sequential_decl,type,
sequential: $i > $i > $o ).
thf(triangle_decl,type,
triangle: $i > $i > $i > $o ).
thf(number_of_in_decl,type,
number_of_in: $i > $i > $i ).
thf(sequential_pairs_decl,type,
sequential_pairs: $i ).
thf(triangles_decl,type,
triangles: $i ).
thf(shortest_path_decl,type,
shortest_path: $i > $i > $i > $o ).
thf(precedes_decl,type,
precedes: $i > $i > $i > $o ).
thf(tail_of_decl,type,
tail_of: $i > $i ).
thf(head_of_decl,type,
head_of: $i > $i ).
thf(edge_decl,type,
edge: $i > $o ).
thf(vertex_decl,type,
vertex: $i > $o ).
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(graph_decl,type,
graph: $i ).
thf(path_cons_decl,type,
path_cons: $i > $i > $i ).
thf(empty_decl,type,
empty: $i ).
thf(in_path_decl,type,
in_path: $i > $i > $o ).
thf(length_of_decl,type,
length_of: $i > $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(n1_decl,type,
n1: $i ).
thf(edges_decl,type,
edges: $i ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ shortest_path ) ) )
<=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ path ) ) )
=> ( D @ length_of @ ( C @ length_of @ less_or_equal ) ) )
& ( A != B )
& ( C @ ( B @ ( A @ path ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
thf(88,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( D @ ( B @ ( A @ path ) ) )
=> ( D @ length_of @ ( C @ length_of @ less_or_equal ) ) )
& ( A != B )
& ( C @ ( B @ ( A @ path ) ) ) )
=> ( C @ ( B @ ( A @ shortest_path ) ) ) )
& ( ( C @ ( B @ ( A @ shortest_path ) ) )
=> ( ! [D: $i] :
( ( D @ ( B @ ( A @ path ) ) )
=> ( D @ length_of @ ( C @ length_of @ less_or_equal ) ) )
& ( A != B )
& ( C @ ( B @ ( A @ path ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ path ) ) )
=> ( ( C @ ( sequential_pairs @ number_of_in ) )
= ( n1 @ ( C @ length_of @ minus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
thf(115,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ path ) ) )
=> ( ( C @ ( sequential_pairs @ number_of_in ) )
= ( n1 @ ( C @ length_of @ minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ path ) ) )
=> ( ? [D: $i] :
( ( ( ( C
= ( empty @ ( D @ path_cons ) ) )
& ( B
= ( D @ head_of ) ) )
<~> ? [E: $i] :
( ( C
= ( E @ ( D @ path_cons ) ) )
& ( E @ ( B @ ( D @ head_of @ path ) ) ) ) )
& ( A
= ( D @ tail_of ) )
& ( D @ edge ) )
& ( B @ vertex )
& ( A @ vertex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_properties) ).
thf(56,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ path ) ) )
=> ( ? [D: $i] :
( ~ ( ( ? [E: $i] :
( ( C
= ( E @ ( D @ path_cons ) ) )
& ( E @ ( B @ ( D @ head_of @ path ) ) ) )
=> ( ( C
= ( empty @ ( D @ path_cons ) ) )
& ( B
= ( D @ head_of ) ) ) )
& ( ( ( C
= ( empty @ ( D @ path_cons ) ) )
& ( B
= ( D @ head_of ) ) )
=> ? [E: $i] :
( ( C
= ( E @ ( D @ path_cons ) ) )
& ( E @ ( B @ ( D @ head_of @ path ) ) ) ) ) )
& ( A
= ( D @ tail_of ) )
& ( D @ edge ) )
& ( B @ vertex )
& ( A @ vertex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ on_path ) )
& ( C @ ( B @ ( A @ path ) ) ) )
=> ( ( C @ ( D @ tail_of @ in_path ) )
& ( C @ ( D @ head_of @ in_path ) )
& ( D @ edge ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',on_path_properties) ).
thf(110,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ on_path ) )
& ( C @ ( B @ ( A @ path ) ) ) )
=> ( ( C @ ( D @ tail_of @ in_path ) )
& ( C @ ( D @ head_of @ in_path ) )
& ( D @ edge ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ ( C @ precedes ) ) )
& ( E @ ( B @ ( A @ shortest_path ) ) ) )
=> ( ~ ( E @ ( C @ ( D @ precedes ) ) )
& ~ ? [F: $i] :
( ( ( F @ head_of )
= ( D @ head_of ) )
& ( ( F @ tail_of )
= ( C @ tail_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).
thf(29,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ ( C @ precedes ) ) )
& ( E @ ( B @ ( A @ shortest_path ) ) ) )
=> ( ~ ( E @ ( C @ ( D @ precedes ) ) )
& ~ ? [F: $i] :
( ( ( F @ head_of )
= ( D @ head_of ) )
& ( ( F @ tail_of )
= ( C @ tail_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
( complete
=> ! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ vertex )
& ( A @ vertex ) )
=> ? [C: $i] :
( ( ( ( B
= ( C @ tail_of ) )
& ( A
= ( C @ head_of ) ) )
<~> ( ( A
= ( C @ tail_of ) )
& ( B
= ( C @ head_of ) ) ) )
& ( C @ edge ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_properties) ).
thf(121,plain,
( complete
=> ! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ vertex )
& ( A @ vertex ) )
=> ? [C: $i] :
( ~ ( ( ( ( A
= ( C @ tail_of ) )
& ( B
= ( C @ head_of ) ) )
=> ( ( B
= ( C @ tail_of ) )
& ( A
= ( C @ head_of ) ) ) )
& ( ( ( B
= ( C @ tail_of ) )
& ( A
= ( C @ head_of ) ) )
=> ( ( A
= ( C @ tail_of ) )
& ( B
= ( C @ head_of ) ) ) ) )
& ( C @ edge ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
( complete
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ sequential ) )
& ( E @ ( D @ ( C @ precedes ) ) )
& ( E @ ( B @ ( A @ shortest_path ) ) ) )
=> ? [F: $i] : ( F @ ( D @ ( C @ triangle ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
thf(102,plain,
( complete
=> ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( C @ sequential ) )
& ( E @ ( D @ ( C @ precedes ) ) )
& ( E @ ( B @ ( A @ shortest_path ) ) ) )
=> ? [F: $i] : ( F @ ( D @ ( C @ triangle ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ sequential ) )
<=> ( ( ( A @ head_of )
= ( B @ tail_of ) )
& ( A != B )
& ( B @ edge )
& ( A @ edge ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( ( ( A @ head_of )
= ( B @ tail_of ) )
& ( A != B )
& ( B @ edge )
& ( A @ edge ) )
=> ( B @ ( A @ sequential ) ) )
& ( ( B @ ( A @ sequential ) )
=> ( ( ( A @ head_of )
= ( B @ tail_of ) )
& ( A != B )
& ( B @ edge )
& ( A @ edge ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ path ) ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ precedes ) ) )
<= ( ( ? [F: $i] :
( ( A @ ( E @ ( F @ precedes ) ) )
& ( F @ ( D @ sequential ) ) )
| ( E @ ( D @ sequential ) ) )
& ( A @ ( E @ on_path ) )
& ( A @ ( D @ on_path ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).
thf(105,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ path ) ) )
=> ! [D: $i,E: $i] :
( ( ( ? [F: $i] :
( ( A @ ( E @ ( F @ precedes ) ) )
& ( F @ ( D @ sequential ) ) )
| ( E @ ( D @ sequential ) ) )
& ( A @ ( E @ on_path ) )
& ( A @ ( D @ on_path ) ) )
=> ( A @ ( E @ ( D @ precedes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ edge )
=> ( ( A @ tail_of @ vertex )
& ( A @ head_of @ vertex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
thf(34,plain,
! [A: $i] :
( ( A @ edge )
=> ( ( A @ tail_of @ vertex )
& ( A @ head_of @ vertex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ path ) ) )
=> ( ( C @ length_of )
= ( C @ ( edges @ number_of_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_defn) ).
thf(118,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ path ) ) )
=> ( ( C @ length_of )
= ( C @ ( edges @ number_of_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( graph @ ( A @ number_of_in ) @ ( B @ ( A @ number_of_in ) @ less_or_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
thf(54,plain,
! [A: $i,B: $i] : ( graph @ ( A @ number_of_in ) @ ( B @ ( A @ number_of_in ) @ less_or_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ path ) ) )
<= ( ? [D: $i] :
( ( ? [E: $i] :
( ( C
= ( E @ ( D @ path_cons ) ) )
& ( E @ ( B @ ( D @ head_of @ path ) ) ) )
| ( ( C
= ( empty @ ( D @ path_cons ) ) )
& ( B
= ( D @ head_of ) ) ) )
& ( A
= ( D @ tail_of ) )
& ( D @ edge ) )
& ( B @ vertex )
& ( A @ vertex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_defn) ).
thf(80,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] :
( ( ? [E: $i] :
( ( C
= ( E @ ( D @ path_cons ) ) )
& ( E @ ( B @ ( D @ head_of @ path ) ) ) )
| ( ( C
= ( empty @ ( D @ path_cons ) ) )
& ( B
= ( D @ head_of ) ) ) )
& ( A
= ( D @ tail_of ) )
& ( D @ edge ) )
& ( B @ vertex )
& ( A @ vertex ) )
=> ( C @ ( B @ ( A @ path ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( E @ ( D @ sequential ) )
& ( A @ ( E @ on_path ) )
& ( A @ ( D @ on_path ) ) )
=> ? [F: $i] : ( F @ ( E @ ( D @ triangle ) ) ) )
& ( A @ ( C @ ( B @ path ) ) ) )
=> ( ( A @ ( sequential_pairs @ number_of_in ) )
= ( A @ ( triangles @ number_of_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
thf(158,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( E @ ( D @ sequential ) )
& ( A @ ( E @ on_path ) )
& ( A @ ( D @ on_path ) ) )
=> ? [F: $i] : ( F @ ( E @ ( D @ triangle ) ) ) )
& ( A @ ( C @ ( B @ path ) ) ) )
=> ( ( A @ ( sequential_pairs @ number_of_in ) )
= ( A @ ( triangles @ number_of_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ triangle ) ) )
<=> ( ( A @ ( C @ sequential ) )
& ( C @ ( B @ sequential ) )
& ( B @ ( A @ sequential ) )
& ( C @ edge )
& ( B @ edge )
& ( A @ edge ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
thf(147,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ sequential ) )
& ( C @ ( B @ sequential ) )
& ( B @ ( A @ sequential ) )
& ( C @ edge )
& ( B @ edge )
& ( A @ edge ) )
=> ( C @ ( B @ ( A @ triangle ) ) ) )
& ( ( C @ ( B @ ( A @ triangle ) ) )
=> ( ( A @ ( C @ sequential ) )
& ( C @ ( B @ sequential ) )
& ( B @ ( A @ sequential ) )
& ( C @ edge )
& ( B @ edge )
& ( A @ edge ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ in_path ) )
& ( C @ ( B @ ( A @ path ) ) ) )
=> ( ? [E: $i] :
( ( ( D
= ( E @ tail_of ) )
| ( D
= ( E @ head_of ) ) )
& ( C @ ( E @ on_path ) ) )
& ( D @ vertex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_path_properties) ).
thf(74,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ in_path ) )
& ( C @ ( B @ ( A @ path ) ) ) )
=> ( ? [E: $i] :
( ( ( D
= ( E @ tail_of ) )
| ( D
= ( E @ head_of ) ) )
& ( C @ ( E @ on_path ) ) )
& ( D @ vertex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ edge )
=> ( ( A @ head_of )
!= ( A @ tail_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
thf(38,plain,
! [A: $i] :
( ( A @ edge )
=> ( ( A @ head_of )
!= ( A @ tail_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
( complete
=> ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( E @ ( D @ sequential ) )
& ( A @ ( E @ on_path ) )
& ( A @ ( D @ on_path ) ) )
=> ? [F: $i] : ( F @ ( E @ ( D @ triangle ) ) ) )
& ( A @ ( C @ ( B @ path ) ) ) )
=> ( ( A @ ( sequential_pairs @ number_of_in ) )
= ( A @ ( triangles @ number_of_in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
thf(2,negated_conjecture,
~ ( complete
=> ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( E @ ( D @ sequential ) )
& ( A @ ( E @ on_path ) )
& ( A @ ( D @ on_path ) ) )
=> ? [F: $i] : ( F @ ( E @ ( D @ triangle ) ) ) )
& ( A @ ( C @ ( B @ path ) ) ) )
=> ( ( A @ ( sequential_pairs @ number_of_in ) )
= ( A @ ( triangles @ number_of_in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ( complete
=> ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( E @ ( D @ sequential ) )
& ( A @ ( E @ on_path ) )
& ( A @ ( D @ on_path ) ) )
=> ? [F: $i] : ( F @ ( E @ ( D @ triangle ) ) ) )
& ( A @ ( C @ ( B @ path ) ) ) )
=> ( ( A @ ( sequential_pairs @ number_of_in ) )
= ( A @ ( triangles @ number_of_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ path ) ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ precedes ) ) )
=> ( ( ( E @ ( D @ sequential ) )
<~> ? [F: $i] :
( ( A @ ( E @ ( F @ precedes ) ) )
& ( F @ ( D @ sequential ) ) ) )
& ( A @ ( E @ on_path ) )
& ( A @ ( D @ on_path ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
thf(137,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ path ) ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ precedes ) ) )
=> ( ~ ( ( ? [F: $i] :
( ( A @ ( E @ ( F @ precedes ) ) )
& ( F @ ( D @ sequential ) ) )
=> ( E @ ( D @ sequential ) ) )
& ( ( E @ ( D @ sequential ) )
=> ? [F: $i] :
( ( A @ ( E @ ( F @ precedes ) ) )
& ( F @ ( D @ sequential ) ) ) ) )
& ( A @ ( E @ on_path ) )
& ( A @ ( D @ on_path ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(171,plain,
$false,
inference(e,[status(thm)],[88,115,56,110,29,121,102,41,105,34,118,54,80,158,147,74,38,21,137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.14 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.25/0.51 % Computer : n020.cluster.edu
% 0.25/0.51 % Model : x86_64 x86_64
% 0.25/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.51 % Memory : 8046.5625MB
% 0.25/0.51 % OS : Linux 6.8.0-71-generic
% 0.25/0.51 % CPULimit : 300
% 0.25/0.51 % WCLimit : 300
% 0.25/0.51 % DateTime : Fri Sep 25 13:49:19 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.25/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.56/1.46 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.36/1.81 % [INFO] Parsing done (346ms).
% 2.36/1.83 % [INFO] Running in sequential loop mode.
% 3.59/2.50 % [INFO] eprover registered as external prover.
% 3.59/2.52 % [INFO] Scanning for conjecture ...
% 3.95/2.71 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 4.12/2.85 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 4.35/2.95 % [INFO] Problem is first-order (TPTP FOF).
% 4.35/2.97 % [INFO] Type checking passed.
% 4.35/2.98 % [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 ...
% 8.68/4.78 % External prover 'e' found a proof!
% 8.68/4.78 % [INFO] Killing All external provers ...
% 8.68/4.78 % Time passed: 4044ms (effective reasoning time: 2937ms)
% 8.68/4.78 % 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)>
% 8.68/4.79 % 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, sequential_is_triangle, 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
% 8.68/4.79 % No. of inferences in proof: 40
% 8.68/4.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4044 ms resp. 2937 ms w/o parsing
% 9.61/4.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.61/4.92 % [INFO] Killing All external provers ...
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