%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU792^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n010.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 : Wed Sep 30 08:29:19 AM UTC 2026
% Result : Theorem 3.62s 1.92s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 71 ( 17 equ; 0 cnn)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 272 ( 2 ~; 0 |; 0 &; 221 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 46 ( 0 ^; 46 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(binunion_decl,type,
binunion: $i > $i > $i ).
thf(breln1_decl,type,
breln1: $i > $i > $o ).
thf(breln1invset_decl,type,
breln1invset: $i > $i > $i ).
thf(breln1invprop_decl,type,
breln1invprop: $o ).
thf(breln1compset_decl,type,
breln1compset: $i > $i > $i > $i ).
thf(breln1compprop_decl,type,
breln1compprop: $o ).
thf(breln1unionCommutes_decl,type,
breln1unionCommutes: $o ).
thf(woz2Ex_decl,type,
woz2Ex: $o ).
thf(woz2W_decl,type,
woz2W: $o ).
thf(woz2A_decl,type,
woz2A: $o ).
thf(breln1invprop_def,definition,
( breln1invprop
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ( breln1 @ A @ ( breln1invset @ A @ B ) ) ) ) ) ).
thf(breln1compprop_def,definition,
( breln1compprop
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ( breln1 @ A @ ( breln1compset @ A @ B @ C ) ) ) ) ) ) ).
thf(breln1unionCommutes_def,definition,
( breln1unionCommutes
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ( ( binunion @ B @ C )
= ( binunion @ C @ B ) ) ) ) ) ) ).
thf(woz2Ex_def,definition,
( woz2Ex
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ( B
= ( breln1invset @ A @ ( breln1invset @ A @ B ) ) ) ) ) ) ).
thf(woz2W_def,definition,
( woz2W
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ( ( breln1invset @ A @ ( breln1compset @ A @ B @ C ) )
= ( breln1compset @ A @ ( breln1invset @ A @ C ) @ ( breln1invset @ A @ B ) ) ) ) ) ) ) ).
thf(woz2A_def,definition,
( woz2A
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( breln1 @ A @ D )
=> ( ( breln1compset @ A @ ( binunion @ B @ C ) @ D )
= ( binunion @ ( breln1compset @ A @ B @ D ) @ ( breln1compset @ A @ C @ D ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
( breln1invprop
=> ( breln1compprop
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( breln1 @ A @ D )
=> ( ( breln1compset @ A @ ( binunion @ B @ C ) @ D )
= ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ D ) @ ( breln1invset @ A @ C ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ D ) @ ( breln1invset @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2B) ).
thf(2,negated_conjecture,
~ ( breln1invprop
=> ( breln1compprop
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( breln1 @ A @ D )
=> ( ( breln1compset @ A @ ( binunion @ B @ C ) @ D )
= ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ D ) @ ( breln1invset @ A @ C ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ D ) @ ( breln1invset @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ( breln1 @ A @ ( breln1invset @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ( breln1 @ A @ ( breln1compset @ A @ B @ C ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ( ( binunion @ B @ C )
= ( binunion @ C @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ( B
= ( breln1invset @ A @ ( breln1invset @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ( ( breln1invset @ A @ ( breln1compset @ A @ B @ C ) )
= ( breln1compset @ A @ ( breln1invset @ A @ C ) @ ( breln1invset @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( breln1 @ A @ D )
=> ( ( breln1compset @ A @ ( binunion @ B @ C ) @ D )
= ( binunion @ ( breln1compset @ A @ B @ D ) @ ( breln1compset @ A @ C @ D ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( breln1 @ A @ D )
=> ( ( breln1compset @ A @ ( binunion @ B @ C ) @ D )
= ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ D ) @ ( breln1invset @ A @ C ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ D ) @ ( breln1invset @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU792^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:30:18 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 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
% 0.72/0.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.97/0.69 % [INFO] Parsing done (184ms).
% 1.16/0.70 % [INFO] Running in sequential loop mode.
% 1.63/1.09 % [INFO] eprover registered as external prover.
% 1.63/1.09 % [INFO] Scanning for conjecture ...
% 1.97/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.97/1.27 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.97/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 1.97/1.27 % [INFO] Type checking passed.
% 1.97/1.28 % [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 ...
% 3.62/1.92 % External prover 'e' found a proof!
% 3.62/1.92 % [INFO] Killing All external provers ...
% 3.62/1.92 % Time passed: 1656ms (effective reasoning time: 1212ms)
% 3.62/1.92 % 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)>
% 3.62/1.92 % Axioms used in derivation (0):
% 3.62/1.92 % No. of inferences in proof: 4
% 3.62/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1656 ms resp. 1212 ms w/o parsing
% 3.62/1.97 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.62/1.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------