%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO082+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 : n002.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 07:12:17 AM UTC 2026
% Result : Theorem 5.21s 2.81s
% Output : Refutation 5.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 24 equ; 0 cnn)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 488 ( 12 ~; 22 |; 64 &; 331 @)
% ( 9 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 119 ( 0 ^; 99 !; 20 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(part_of_decl,type,
part_of: $i > $i > $o ).
thf(inner_point_decl,type,
inner_point: $i > $i > $o ).
thf(meet_decl,type,
meet: $i > $i > $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i ).
thf(open_decl,type,
open: $i > $o ).
thf(end_point_decl,type,
end_point: $i > $i > $o ).
thf(incident_c_decl,type,
incident_c: $i > $i > $o ).
thf(closed_decl,type,
closed: $i > $o ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ inner_point ) )
=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ sum ) ) )
& ( D @ ( C @ ( B @ meet ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ inner_point ) )
=> ? [C: $i,D: $i] :
( ( A
= ( D @ ( C @ sum ) ) )
& ( D @ ( C @ ( B @ meet ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ inner_point ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3) ).
thf(33,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ inner_point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( A
= ( C @ ( B @ sum ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ incident_c ) )
<=> ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn) ).
thf(41,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) )
=> ( A @ ( D @ incident_c ) ) )
& ( ( A @ ( D @ incident_c ) )
=> ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) ) ) )
=> ( A
= ( C @ ( B @ sum ) ) ) )
& ( ( A
= ( C @ ( B @ sum ) ) )
=> ! [D: $i] :
( ( ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) )
=> ( A @ ( D @ incident_c ) ) )
& ( ( A @ ( D @ incident_c ) )
=> ( ( C @ ( D @ incident_c ) )
| ( B @ ( D @ incident_c ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ end_point ) )
<=> ( ! [C: $i,D: $i] :
( ( ( D @ ( A @ incident_c ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( D @ part_of ) )
& ( B @ ( C @ part_of ) ) )
=> ( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) )
& ( B @ ( A @ incident_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',end_point_defn) ).
thf(118,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i,D: $i] :
( ( ( D @ ( A @ incident_c ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( D @ part_of ) )
& ( B @ ( C @ part_of ) ) )
=> ( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) )
& ( B @ ( A @ incident_c ) ) )
=> ( B @ ( A @ end_point ) ) )
& ( ( B @ ( A @ end_point ) )
=> ( ! [C: $i,D: $i] :
( ( ( D @ ( A @ incident_c ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( D @ part_of ) )
& ( B @ ( C @ part_of ) ) )
=> ( ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) )
& ( B @ ( A @ incident_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( C @ ( B @ sum ) ) )
& ( C @ ( B @ ( D @ meet ) ) )
& ( A @ closed ) )
=> ! [E: $i] :
( ( B @ ( E @ end_point ) )
=> ( C @ ( B @ ( E @ meet ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c7) ).
thf(113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A
= ( C @ ( B @ sum ) ) )
& ( C @ ( B @ ( D @ meet ) ) )
& ( A @ closed ) )
=> ! [E: $i] :
( ( B @ ( E @ end_point ) )
=> ( C @ ( B @ ( E @ meet ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( B != A )
& ( A @ ( B @ part_of ) ) )
=> ( B @ open ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( ( B != A )
& ( A @ ( B @ part_of ) ) )
=> ( B @ open ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( D @ ( E @ end_point ) )
& ( C @ ( E @ end_point ) )
& ( B @ ( E @ end_point ) ) )
& ( A @ ( D @ part_of ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ part_of ) ) )
=> ( ( B @ ( D @ part_of ) )
| ( D @ ( B @ part_of ) )
| ( B @ ( C @ part_of ) )
| ( C @ ( B @ part_of ) )
| ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2) ).
thf(143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( D @ ( E @ end_point ) )
& ( C @ ( E @ end_point ) )
& ( B @ ( E @ end_point ) ) )
& ( A @ ( D @ part_of ) )
& ( A @ ( C @ part_of ) )
& ( A @ ( B @ part_of ) ) )
=> ( ( B @ ( D @ part_of ) )
| ( D @ ( B @ part_of ) )
| ( B @ ( C @ part_of ) )
| ( C @ ( B @ part_of ) )
| ( C @ ( D @ part_of ) )
| ( D @ ( C @ part_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ inner_point ) )
<=> ( ~ ( B @ ( A @ end_point ) )
& ( B @ ( A @ incident_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_point_defn) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( ( ~ ( B @ ( A @ end_point ) )
& ( B @ ( A @ incident_c ) ) )
=> ( B @ ( A @ inner_point ) ) )
& ( ( B @ ( A @ inner_point ) )
=> ( ~ ( B @ ( A @ end_point ) )
& ( B @ ( A @ incident_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ end_point ) )
=> ? [C: $i] :
( ( B != C )
& ( A @ ( C @ end_point ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c6) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ end_point ) )
=> ? [C: $i] :
( ( B != C )
& ( A @ ( C @ end_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ incident_c ) )
<=> ( B @ ( C @ incident_c ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9) ).
thf(68,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) )
& ( ( A @ ( C @ incident_c ) )
=> ( B @ ( C @ incident_c ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ part_of ) )
<=> ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) )
=> ( A @ ( B @ part_of ) ) )
& ( ( A @ ( B @ part_of ) )
=> ! [C: $i] :
( ( B @ ( C @ incident_c ) )
=> ( A @ ( C @ incident_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ open )
<=> ? [B: $i] : ( A @ ( B @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',open_defn) ).
thf(35,plain,
! [A: $i] :
( ( ? [B: $i] : ( A @ ( B @ end_point ) )
=> ( A @ open ) )
& ( ( A @ open )
=> ? [B: $i] : ( A @ ( B @ end_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( B @ ( A @ ( C @ meet ) ) )
=> ? [C: $i] :
( C
= ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c8) ).
thf(30,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( B @ ( A @ ( C @ meet ) ) )
=> ? [C: $i] :
( C
= ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( A @ ( B @ part_of ) )
& ( B @ ( A @ part_of ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_antisymmetry) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( A @ ( B @ part_of ) )
& ( B @ ( A @ part_of ) ) )
=> ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i] :
( ( ( A @ ( B @ part_of ) )
& ( B @ ( A @ part_of ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ closed )
<=> ~ ? [B: $i] : ( A @ ( B @ end_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closed_defn) ).
thf(107,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( A @ ( B @ end_point ) )
=> ( A @ closed ) )
& ( ( A @ closed )
=> ~ ? [B: $i] : ( A @ ( B @ end_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ end_point ) )
& ( A @ ( C @ end_point ) )
& ( A @ ( B @ end_point ) ) )
=> ( ( C = D )
| ( B = D )
| ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c5) ).
thf(79,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ end_point ) )
& ( A @ ( C @ end_point ) )
& ( A @ ( B @ end_point ) ) )
=> ( ( C = D )
| ( B = D )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ meet ) ) )
<=> ( ! [D: $i] :
( ( ( C @ ( D @ incident_c ) )
& ( B @ ( D @ incident_c ) ) )
=> ( ( C @ ( D @ end_point ) )
& ( B @ ( D @ end_point ) ) ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( A @ incident_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn) ).
thf(94,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( ( C @ ( D @ incident_c ) )
& ( B @ ( D @ incident_c ) ) )
=> ( ( C @ ( D @ end_point ) )
& ( B @ ( D @ end_point ) ) ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( A @ incident_c ) ) )
=> ( C @ ( B @ ( A @ meet ) ) ) )
& ( ( C @ ( B @ ( A @ meet ) ) )
=> ( ! [D: $i] :
( ( ( C @ ( D @ incident_c ) )
& ( B @ ( D @ incident_c ) ) )
=> ( ( C @ ( D @ end_point ) )
& ( B @ ( D @ end_point ) ) ) )
& ( C @ ( A @ incident_c ) )
& ( B @ ( A @ incident_c ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(148,plain,
$false,
inference(e,[status(thm)],[25,33,41,118,113,145,143,87,82,68,135,35,30,19,107,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO082+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % 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
% 0.14/0.39 % Computer : n002.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Fri Sep 25 12:43:20 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.18 % [INFO] Parsing done (193ms).
% 1.28/1.20 % [INFO] Running in sequential loop mode.
% 1.98/1.59 % [INFO] eprover registered as external prover.
% 2.19/1.60 % [INFO] Scanning for conjecture ...
% 2.37/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.37/1.77 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.57/1.82 % [INFO] Problem is first-order (TPTP FOF).
% 2.57/1.83 % [INFO] Type checking passed.
% 2.57/1.84 % [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 ...
% 5.21/2.80 % External prover 'e' found a proof!
% 5.21/2.80 % [INFO] Killing All external provers ...
% 5.21/2.81 % Time passed: 2263ms (effective reasoning time: 1603ms)
% 5.21/2.81 % 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)>
% 5.21/2.81 % Axioms used in derivation (16): end_point_defn, c8, meet_defn, part_of_defn, c9, sum_defn, closed_defn, c7, inner_point_defn, c3, c4, c5, c2, c1, c6, open_defn
% 5.21/2.81 % No. of inferences in proof: 36
% 5.21/2.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2263 ms resp. 1603 ms w/o parsing
% 5.21/2.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.21/2.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------