%------------------------------------------------------------------------------
% File : Leo-III---1.7.19
% Problem : SYO983_1 : TPTP v9.2.0. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n024.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 : Wed Oct 1 12:47:14 PM UTC 2025
% Result : Theorem 2.74s 1.63s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 6 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 36 ( 2 ~; 0 |; 3 &; 22 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 11 !; 2 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'$world\'_type',type,
'\'$world\'': $tType ).
thf('\'$local_world\'_type',type,
'\'$local_world\'': '\'$world\'' ).
thf('\'$accessible_world\'_type',type,
'\'$accessible_world\'': '\'$world\'' > '\'$world\'' > $o ).
thf('\'$exists_in_world_$i\'_type',type,
'\'$exists_in_world_$i\'': '\'$world\'' > $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( '\'$exists_in_world_$i\'' @ '\'$local_world\'' @ A )
& ( '\'$exists_in_world_$i\'' @ '\'$local_world\'' @ B ) )
=> ( ( A = B )
=> ! [C: '\'$world\''] :
( ( '\'$accessible_world\'' @ '\'$local_world\'' @ C )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',example) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( '\'$exists_in_world_$i\'' @ '\'$local_world\'' @ A )
& ( '\'$exists_in_world_$i\'' @ '\'$local_world\'' @ B ) )
=> ( ( A = B )
=> ! [C: '\'$world\''] :
( ( '\'$accessible_world\'' @ '\'$local_world\'' @ C )
=> ( A = B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i,B: $i] :
( ( ( '\'$exists_in_world_$i\'' @ '\'$local_world\'' @ A )
& ( '\'$exists_in_world_$i\'' @ '\'$local_world\'' @ B ) )
=> ( ( A = B )
=> ! [C: '\'$world\''] :
( ( '\'$accessible_world\'' @ '\'$local_world\'' @ C )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '\'$world\''] :
? [B: $i] : ( '\'$exists_in_world_$i\'' @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$exists_in_world_$i_nonempty') ).
thf(13,plain,
! [A: '\'$world\''] :
? [B: $i] : ( '\'$exists_in_world_$i\'' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,plain,
$false,
inference(e,[status(thm)],[4,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO983_1 : TPTP v9.2.0. Bugfixed v9.2.0.
% 0.03/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Sep 30 16:45:09 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.99/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/1.00 % [INFO] Parsing done (98ms).
% 1.15/1.01 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.35/1.02 %%% First-order input detected, trying modal-logic-to-TFX embedding (redirected from embedding '$$modal' to embedding '$$fomlModel' version 1.3.5) ... Use flag -p FORCE_HIGHERORDER if you want to have THF output instead.
% 1.48/1.09 % [INFO] Running in sequential loop mode.
% 1.77/1.28 % [INFO] eprover registered as external prover.
% 1.77/1.29 % [INFO] Scanning for conjecture ...
% 1.95/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.11/1.36 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.11/1.37 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.11/1.37 % [INFO] Type checking passed.
% 2.11/1.37 % [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 ...
% 2.74/1.63 % External prover 'e' found a proof!
% 2.74/1.63 % [INFO] Killing All external provers ...
% 2.74/1.63 % Time passed: 1083ms (effective reasoning time: 540ms)
% 2.74/1.63 % 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)>
% 2.74/1.63 % Axioms used in derivation (1): $exists_in_world_$i_nonempty
% 2.74/1.63 % No. of inferences in proof: 6
% 2.74/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1083 ms resp. 540 ms w/o parsing
% 2.74/1.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.74/1.66 % [INFO] Killing All external provers ...
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