%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO146+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.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 07:12:27 AM UTC 2026
% Result : Theorem 6.80s 4.29s
% Output : Refutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 10 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 367 ( 10 ~; 0 |; 28 &; 286 @)
% ( 9 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 1 con; 0-3 aty)
% Number of variables : 89 ( 0 ^; 83 !; 6 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(connect_decl,type,
connect: $i > $i > $i > $o ).
thf(start_point_decl,type,
start_point: $i > $i > $o ).
thf(ordered_by_decl,type,
ordered_by: $i > $i > $i > $o ).
thf(incident_o_decl,type,
incident_o: $i > $i > $o ).
thf(trajectory_of_decl,type,
trajectory_of: $i > $i ).
thf(finish_point_decl,type,
finish_point: $i > $i > $o ).
thf(once_decl,type,
once: $i > $o ).
thf(at_the_same_time_decl,type,
at_the_same_time: $i > $i > $i ).
thf(at_decl,type,
at: $i > $i > $i ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ finish_point ) )
<=> ( ! [C: $i] :
( ( ( B @ ( C @ incident_o ) )
& ( A != C ) )
=> ( A @ ( C @ ( B @ ordered_by ) ) ) )
& ( B @ ( A @ incident_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finish_point_defn) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( B @ ( C @ incident_o ) )
& ( A != C ) )
=> ( A @ ( C @ ( B @ ordered_by ) ) ) )
& ( B @ ( A @ incident_o ) ) )
=> ( B @ ( A @ finish_point ) ) )
& ( ( B @ ( A @ finish_point ) )
=> ( ! [C: $i] :
( ( ( B @ ( C @ incident_o ) )
& ( A != C ) )
=> ( A @ ( C @ ( B @ ordered_by ) ) ) )
& ( B @ ( A @ incident_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ once )
=> ( A @ ( A @ at_the_same_time ) @ once ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_at_the_same_time) ).
thf(84,plain,
! [A: $i] :
( ( A @ once )
=> ( A @ ( A @ at_the_same_time ) @ once ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ once )
=> ! [B: $i] :
? [C: $i] : ( C @ ( B @ at ) @ ( A @ at_the_same_time ) @ once ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',localization) ).
thf(74,plain,
! [A: $i] :
( ( A @ once )
=> ! [B: $i] :
? [C: $i] : ( C @ ( B @ at ) @ ( A @ at_the_same_time ) @ once ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ at_the_same_time ) @ once )
=> ( ( B @ once )
& ( A @ once ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjunction_at_the_same_time) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ at_the_same_time ) @ once )
=> ( ( B @ once )
& ( A @ once ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ at_the_same_time ) @ at_the_same_time ) @ once )
<=> ( C @ ( B @ at_the_same_time ) @ ( A @ at_the_same_time ) @ once ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assciativity_of_at_the_same_time) ).
thf(92,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ at_the_same_time ) @ ( A @ at_the_same_time ) @ once )
=> ( C @ ( B @ ( A @ at_the_same_time ) @ at_the_same_time ) @ once ) )
& ( ( C @ ( B @ ( A @ at_the_same_time ) @ at_the_same_time ) @ once )
=> ( C @ ( B @ at_the_same_time ) @ ( A @ at_the_same_time ) @ once ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $i] :
? [B: $i] :
( ( A @ trajectory_of )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trajectories_are_oriented_curves) ).
thf(41,plain,
! [A: $i] :
? [B: $i] :
( ( A @ trajectory_of )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ connect ) ) )
<=> ( C @ ( A @ ( B @ connect ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ connect ) ) )
<=> ( C @ ( A @ ( B @ connect ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ( B @ connect ) ) )
=> ( C @ ( B @ ( A @ connect ) ) ) )
& ( ( C @ ( B @ ( A @ connect ) ) )
=> ( C @ ( A @ ( B @ connect ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ start_point ) )
<=> ( ! [C: $i] :
( ( ( B @ ( C @ incident_o ) )
& ( A != C ) )
=> ( C @ ( A @ ( B @ ordered_by ) ) ) )
& ( B @ ( A @ incident_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',start_point_defn) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( B @ ( C @ incident_o ) )
& ( A != C ) )
=> ( C @ ( A @ ( B @ ordered_by ) ) ) )
& ( B @ ( A @ incident_o ) ) )
=> ( B @ ( A @ start_point ) ) )
& ( ( B @ ( A @ start_point ) )
=> ( ! [C: $i] :
( ( ( B @ ( C @ incident_o ) )
& ( A != C ) )
=> ( C @ ( A @ ( B @ ordered_by ) ) ) )
& ( B @ ( A @ incident_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ at_the_same_time ) @ once )
<=> ( A @ ( B @ at_the_same_time ) @ once ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_at_the_same_time) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ at_the_same_time ) @ once )
=> ( B @ ( A @ at_the_same_time ) @ once ) )
& ( ( B @ ( A @ at_the_same_time ) @ once )
=> ( A @ ( B @ at_the_same_time ) @ once ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( D @ ( C @ ( A @ ordered_by ) ) )
<=> ( D @ ( C @ ( B @ ordered_by ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',o6) ).
thf(26,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( D @ ( C @ ( B @ ordered_by ) ) )
=> ( D @ ( C @ ( A @ ordered_by ) ) ) )
& ( ( D @ ( C @ ( A @ ordered_by ) ) )
=> ( D @ ( C @ ( B @ ordered_by ) ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( F @ at ) @ ( C @ ( E @ at ) @ at_the_same_time ) @ once )
& ( B @ ( F @ at ) @ ( A @ ( E @ at ) @ at_the_same_time ) @ once ) )
=> ~ ( ( B @ ( D @ ( F @ trajectory_of @ ordered_by ) ) )
& ( C @ ( A @ ( E @ trajectory_of @ ordered_by ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homogeneous_behaviour) ).
thf(82,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( F @ at ) @ ( C @ ( E @ at ) @ at_the_same_time ) @ once )
& ( B @ ( F @ at ) @ ( A @ ( E @ at ) @ at_the_same_time ) @ once ) )
=> ~ ( ( B @ ( D @ ( F @ trajectory_of @ ordered_by ) ) )
& ( C @ ( A @ ( E @ trajectory_of @ ordered_by ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ start_point ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',o4) ).
thf(24,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ start_point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ordered_by ) ) )
=> ( ( A @ ( C @ incident_o ) )
& ( A @ ( B @ incident_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',o1) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ordered_by ) ) )
=> ( ( A @ ( C @ incident_o ) )
& ( A @ ( B @ incident_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ at ) @ once )
<=> ( A @ trajectory_of @ ( B @ incident_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',at_on_trajectory) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( ( A @ trajectory_of @ ( B @ incident_o ) )
=> ( B @ ( A @ at ) @ once ) )
& ( ( B @ ( A @ at ) @ once )
=> ( A @ trajectory_of @ ( B @ incident_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ connect ) ) )
<=> ( C @ ( B @ at ) @ ( C @ ( A @ at ) @ at_the_same_time ) @ once ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connect_defn) ).
thf(98,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ at ) @ ( C @ ( A @ at ) @ at_the_same_time ) @ once )
=> ( C @ ( B @ ( A @ connect ) ) ) )
& ( ( C @ ( B @ ( A @ connect ) ) )
=> ( C @ ( B @ at ) @ ( C @ ( A @ at ) @ at_the_same_time ) @ once ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(104,plain,
$false,
inference(e,[status(thm)],[57,84,74,70,92,41,17,44,86,26,82,24,37,76,98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO146+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.90 % Computer : n003.cluster.edu
% 0.22/0.90 % Model : x86_64 x86_64
% 0.22/0.90 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.90 % Memory : 8046.5625MB
% 0.22/0.90 % OS : Linux 6.8.0-71-generic
% 0.22/0.90 % CPULimit : 300
% 0.22/0.90 % WCLimit : 300
% 0.22/0.90 % DateTime : Fri Sep 25 12:57:39 UTC 2026
% 0.22/0.91 % CPUTime :
% 0.22/0.91 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.27/1.66 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/2.03 % [INFO] Parsing done (372ms).
% 1.83/2.06 % [INFO] Running in sequential loop mode.
% 3.24/2.65 % [INFO] eprover registered as external prover.
% 3.24/2.67 % [INFO] Scanning for conjecture ...
% 3.61/2.81 % [INFO] Found a conjecture (or negated_conjecture) and 36 axioms. Running axiom selection ...
% 3.81/2.91 % [INFO] Axiom selection finished. Selected 14 axioms (removed 22 axioms).
% 3.81/2.98 % [INFO] Problem is first-order (TPTP FOF).
% 3.81/2.99 % [INFO] Type checking passed.
% 3.81/3.00 % [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 ...
% 6.80/4.29 % External prover 'e' found a proof!
% 6.80/4.29 % [INFO] Killing All external provers ...
% 6.80/4.29 % Time passed: 3150ms (effective reasoning time: 2219ms)
% 6.80/4.29 % 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)>
% 6.80/4.29 % Axioms used in derivation (14): start_point_defn, trajectories_are_oriented_curves, o1, symmetry_of_at_the_same_time, localization, conjunction_at_the_same_time, finish_point_defn, homogeneous_behaviour, o6, at_on_trajectory, o4, assciativity_of_at_the_same_time, idempotence_of_at_the_same_time, connect_defn
% 6.80/4.29 % No. of inferences in proof: 32
% 6.80/4.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3150 ms resp. 2219 ms w/o parsing
% 7.15/4.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.15/4.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------