%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ022-1 : TPTP v9.3.1. Released v1.1.0.
% 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 : n017.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 08:21:07 AM UTC 2026
% Result : Unsatisfiable 3.55s 2.36s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 33
% Syntax : Number of formulae : 67 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 154 ( 14 ~; 12 |; 0 &; 128 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(ocean_decl,type,
ocean: $i > $o ).
thf(atlantic_decl,type,
atlantic: $i ).
thf(indian_decl,type,
indian: $i ).
thf(pacific_decl,type,
pacific: $i ).
thf(southern_decl,type,
southern: $i ).
thf(state_decl,type,
state: $i > $o ).
thf(western_australia_decl,type,
western_australia: $i ).
thf(northern_territory_decl,type,
northern_territory: $i ).
thf(queensland_decl,type,
queensland: $i ).
thf(south_australia_decl,type,
south_australia: $i ).
thf(new_south_wales_decl,type,
new_south_wales: $i ).
thf(victoria_decl,type,
victoria: $i ).
thf(tasmania_decl,type,
tasmania: $i ).
thf(borders_decl,type,
borders: $i > $i > $o ).
thf(32,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ocean )
| ~ ( C @ ( B @ borders ) )
| ~ ( C @ ( A @ borders ) )
| ~ ( B @ ( A @ borders ) )
| ~ ( B @ state )
| ~ ( A @ state ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_borders) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ocean )
| ~ ( C @ ( B @ borders ) )
| ~ ( C @ ( A @ borders ) )
| ~ ( B @ ( A @ borders ) )
| ~ ( B @ state )
| ~ ( A @ state ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(20,negated_conjecture,
victoria @ ( new_south_wales @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nsw_vic) ).
thf(52,plain,
victoria @ ( new_south_wales @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(31,negated_conjecture,
tasmania @ ( pacific @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pacific_tas) ).
thf(61,plain,
tasmania @ ( pacific @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(16,negated_conjecture,
new_south_wales @ ( south_australia @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sa_nsw) ).
thf(60,plain,
new_south_wales @ ( south_australia @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,negated_conjecture,
northern_territory @ state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',northern_territory) ).
thf(38,plain,
northern_territory @ state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,negated_conjecture,
new_south_wales @ ( queensland @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qld_nsw) ).
thf(65,plain,
new_south_wales @ ( queensland @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(29,negated_conjecture,
new_south_wales @ ( pacific @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pacific_nsw) ).
thf(53,plain,
new_south_wales @ ( pacific @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(2,negated_conjecture,
indian @ ocean,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indian) ).
thf(41,plain,
indian @ ocean,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,negated_conjecture,
new_south_wales @ state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',new_south_wales) ).
thf(39,plain,
new_south_wales @ state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,negated_conjecture,
victoria @ state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',victoria) ).
thf(35,plain,
victoria @ state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,negated_conjecture,
queensland @ state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queensland) ).
thf(43,plain,
queensland @ state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,negated_conjecture,
northern_territory @ ( indian @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indian_nt) ).
thf(58,plain,
northern_territory @ ( indian @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,negated_conjecture,
northern_territory @ ( western_australia @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wa_nt) ).
thf(42,plain,
northern_territory @ ( western_australia @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
atlantic @ ocean,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atlantic) ).
thf(37,plain,
atlantic @ ocean,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,negated_conjecture,
tasmania @ state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tasmania) ).
thf(46,plain,
tasmania @ state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,negated_conjecture,
victoria @ ( south_australia @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sa_vic) ).
thf(57,plain,
victoria @ ( south_australia @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,negated_conjecture,
western_australia @ state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',western_australia) ).
thf(34,plain,
western_australia @ state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,negated_conjecture,
queensland @ ( northern_territory @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nt_qld) ).
thf(45,plain,
queensland @ ( northern_territory @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(30,negated_conjecture,
victoria @ ( pacific @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pacific_vic) ).
thf(64,plain,
victoria @ ( pacific @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3,negated_conjecture,
pacific @ ocean,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pacific) ).
thf(44,plain,
pacific @ ocean,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,negated_conjecture,
tasmania @ ( southern @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',southern_tas) ).
thf(59,plain,
tasmania @ ( southern @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(28,negated_conjecture,
queensland @ ( pacific @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pacific_qld) ).
thf(54,plain,
queensland @ ( pacific @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,negated_conjecture,
queensland @ ( south_australia @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sa_qld) ).
thf(49,plain,
queensland @ ( south_australia @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,negated_conjecture,
southern @ ocean,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',southern) ).
thf(48,plain,
southern @ ocean,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,negated_conjecture,
queensland @ ( indian @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indian_qld) ).
thf(63,plain,
queensland @ ( indian @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(24,negated_conjecture,
western_australia @ ( southern @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',southern_wa) ).
thf(50,plain,
western_australia @ ( southern @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ borders ) )
| ~ ( B @ ( A @ borders ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_borders) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ borders ) )
| ~ ( B @ ( A @ borders ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(13,negated_conjecture,
south_australia @ ( western_australia @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wa_sa) ).
thf(40,plain,
south_australia @ ( western_australia @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,negated_conjecture,
western_australia @ ( indian @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indian_wa) ).
thf(55,plain,
western_australia @ ( indian @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,negated_conjecture,
northern_territory @ ( south_australia @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sa_nt) ).
thf(36,plain,
northern_territory @ ( south_australia @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,negated_conjecture,
south_australia @ ( southern @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',southern_sa) ).
thf(51,plain,
south_australia @ ( southern @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(8,negated_conjecture,
south_australia @ state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',south_australia) ).
thf(47,plain,
south_australia @ state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,negated_conjecture,
victoria @ ( southern @ borders ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',southern_vic) ).
thf(62,plain,
victoria @ ( southern @ borders ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(69,plain,
$false,
inference(e,[status(thm)],[56,52,61,60,38,65,53,41,39,35,43,58,42,37,46,57,34,45,64,44,59,54,49,48,63,50,67,40,55,36,51,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ022-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.08 % 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
% 0.15/0.41 % Computer : n017.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 05:00:33 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.19 % [INFO] Parsing done (201ms).
% 1.39/1.21 % [INFO] Running in sequential loop mode.
% 2.04/1.61 % [INFO] eprover registered as external prover.
% 2.04/1.62 % [INFO] Scanning for conjecture ...
% 2.23/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.23/1.79 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.23/1.79 % [INFO] Problem is propositional (TPTP CNF).
% 2.23/1.79 % [INFO] Type checking passed.
% 2.42/1.80 % [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 ...
% 3.55/2.35 % External prover 'e' found a proof!
% 3.55/2.35 % [INFO] Killing All external provers ...
% 3.55/2.36 % Time passed: 1802ms (effective reasoning time: 1141ms)
% 3.55/2.36 % Axioms used in derivation (1): symmetry_of_borders
% 3.55/2.36 % No. of inferences in proof: 67
% 3.55/2.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1802 ms resp. 1141 ms w/o parsing
% 3.85/2.41 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.85/2.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------