%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU519_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : n004.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 08:39:13 AM UTC 2026
% Result : Theorem 3.85s 7.55s
% Output : Refutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 18 unt; 0 typ; 2 def)
% Number of atoms : 76 ( 12 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 167 ( 18 ~; 10 |; 3 &; 117 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 2 ^; 42 !; 0 ?; 46 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(powersetI_decl,type,
powersetI: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( A @ powerset @ ( emptyset @ in ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ( powersetI
=> ! [A: $i] : ( A @ powerset @ ( emptyset @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( powersetI
=> ! [A: $i] : ( A @ powerset @ ( emptyset @ in ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( emptysetE
=> ( powersetI
=> ! [A: $i] : ( A @ powerset @ ( emptyset @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ~ ( sk1 @ powerset @ ( emptyset @ in ) )
& powersetI
& emptysetE ),
inference(cnf,[status(esa)],[5]) ).
thf(9,plain,
~ ( sk1 @ powerset @ ( emptyset @ in ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(3,axiom,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
=> ( A @ powerset @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(10,plain,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
=> ( A @ powerset @ ( B @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
=> ( A @ powerset @ ( B @ in ) ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(8,plain,
powersetI,
inference(cnfConj,[status(thm)],[6]) ).
thf(41,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
=> ( A @ powerset @ ( B @ in ) ) ),
inference(rewrite,[status(thm)],[11,8]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( ( A @ powerset @ ( B @ in ) )
| ~ ( A @ ( A @ ( B @ sk2 ) @ in ) ) )
& ( ( A @ powerset @ ( B @ in ) )
| ( B @ ( A @ ( B @ sk2 ) @ in ) ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( A @ powerset @ ( B @ in ) )
| ( B @ ( A @ ( B @ sk2 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[42]) ).
thf(4,axiom,
( emptysetE
= ( ! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(12,plain,
( emptysetE
= ( ! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
( emptysetE
= ( ! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(7,plain,
emptysetE,
inference(cnfConj,[status(thm)],[6]) ).
thf(14,plain,
! [A: $i] :
( ( emptyset @ ( A @ in ) )
=> ! [B: $o] : B ),
inference(rewrite,[status(thm)],[13,7]) ).
thf(15,plain,
! [B: $o,A: $i] :
( B
| ~ ( emptyset @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [B: $o,A: $i] :
( ( B
!= ( sk1 @ powerset @ ( emptyset @ in ) ) )
| ~ $true
| ~ ( emptyset @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[15,9]) ).
thf(17,plain,
! [B: $o,A: $i] :
( ( B
!= ( sk1 @ powerset @ ( emptyset @ in ) ) )
| ~ ( emptyset @ ( A @ in ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [A: $i] :
~ ( emptyset @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( A )),bind(B,$thf( sk1 @ powerset @ ( emptyset @ in ) ))]]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk2 ) @ in ) )
!= ( emptyset @ ( C @ in ) ) )
| ~ $true
| ( A @ powerset @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[43,18]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk2 ) @ in ) )
!= ( emptyset @ ( C @ in ) ) )
| ( A @ powerset @ ( B @ in ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(60,plain,
! [A: $i] : ( A @ powerset @ ( emptyset @ in ) ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( E )),bind(B,$thf( emptyset )),bind(C,$thf( E @ ( emptyset @ sk2 ) ))]]) ).
thf(67,plain,
! [A: $i] : ( A @ powerset @ ( emptyset @ in ) ),
inference(simp,[status(thm)],[60]) ).
thf(69,plain,
~ $true,
inference(rewrite,[status(thm)],[9,67]) ).
thf(70,plain,
$false,
inference(simp,[status(thm)],[69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU519_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % 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
% 0.12/5.40 % Computer : n004.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.41 % CPULimit : 300
% 0.12/5.41 % WCLimit : 300
% 0.12/5.41 % DateTime : Sat Sep 26 10:08:29 UTC 2026
% 0.12/5.41 % CPUTime :
% 0.12/5.41 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
% 0.18/5.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/6.17 % [INFO] Parsing done (174ms).
% 1.18/6.18 % [INFO] Running in sequential loop mode.
% 1.71/6.57 % [INFO] eprover registered as external prover.
% 1.71/6.58 % [INFO] Scanning for conjecture ...
% 1.90/6.65 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/6.66 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.90/6.69 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.03/6.73 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.03/6.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.03/6.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.03/6.74 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.03/6.74 % [INFO] Type checking passed.
% 2.03/6.75 % [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 ...
% 3.85/7.54 % [INFO] Killing All external provers ...
% 3.85/7.55 % Time passed: 1996ms (effective reasoning time: 1359ms)
% 3.85/7.55 % 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)>
% 3.85/7.55 % Axioms used in derivation (2): powersetI, emptysetE
% 3.85/7.55 % No. of inferences in proof: 27
% 3.85/7.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1996 ms resp. 1359 ms w/o parsing
% 4.21/7.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.21/7.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------