%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU829^1 : 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 : 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 : Wed Sep 30 08:29:26 AM UTC 2026
% Result : Theorem 7.55s 3.71s
% Output : Refutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 16 unt; 0 typ; 5 def)
% Number of atoms : 177 ( 46 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 205 ( 64 ~; 47 |; 0 &; 93 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 31 ^; 35 !; 0 ?; 68 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subseteq_decl,type,
subseteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(powerset_decl,type,
powerset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(emptyset_decl,type,
emptyset: $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(subseteq_def,definition,
( subseteq
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(powerset_def,definition,
( powerset
= ( ^ [A: $i > $o,B: $i > $o] : ( subseteq @ B @ A ) ) ) ).
thf(emptyset_def,definition,
( emptyset
= ( ^ [A: $i] : $false ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ~ ( sk1 @ A ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ~ ( sk1 @ B ) ) ) ).
thf(1,conjecture,
( ( powerset @ emptyset )
= ( ^ [A: $i > $o] : ( A = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( powerset @ emptyset )
!= ( ^ [A: $i > $o] : ( A = emptyset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ^ [A: $i > $o] :
! [B: $i] :
~ ( A @ B ) )
!= ( ^ [A: $i > $o] :
( A
= ( ^ [B: $i] : $false ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i > $o] :
! [B: $i] :
~ ( A @ B ) )
!= ( ^ [A: $i > $o] :
( A
= ( ^ [B: $i] : $false ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i] :
~ ( sk1 @ A ) )
!= ( sk1
= ( ^ [A: $i] : $false ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(6,plain,
( ~ ! [A: $i] :
~ ( sk1 @ A )
| ( sk1
!= ( ^ [A: $i] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( sk1
!= ( ^ [A: $i] : $false ) )
| ~ ! [A: $i] :
~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
( ( sk1
!= ( ^ [A: $i] : $false ) )
| ( sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(7,plain,
( ! [A: $i] :
~ ( sk1 @ A )
| ( sk1
= ( ^ [A: $i] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( sk1
= ( ^ [A: $i] : $false ) )
| ! [A: $i] :
~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(11,plain,
! [A: $i] :
( ( sk1
= ( ^ [B: $i] : $false ) )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(12,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( ( ( ^ [B: $i] : $false )
= ( ^ [B: $i] : $false ) )
!= ( ! [B: $i] :
~ ( sk1 @ B ) ) )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[11,5]) ).
thf(13,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ~ ! [B: $i] :
~ ( sk1 @ B )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[12]) ).
thf(14,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ~ ! [B: $i] :
~ ( sk1 @ B ) ),
inference(pattern_uni,[status(thm)],[13:[]]) ).
thf(21,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(31,plain,
! [A: $i] :
( ( sk1
!= ( ^ [B: $i] : $false ) )
| ~ $true
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1 @ sk2 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,21]) ).
thf(32,plain,
! [A: $i] :
( ( sk1
!= ( ^ [B: $i] : $false ) )
| ( sk1 @ ( sk3 @ A ) )
| ( ( sk1 @ sk2 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(33,plain,
( ( sk1
!= ( ^ [A: $i] : $false ) )
| ( sk1 @ ( sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk2 ))]]) ).
thf(49,plain,
( ( sk1 @ sk4 )
| ( sk1 @ ( sk3 @ sk2 ) ) ),
inference(func_ext,[status(esa)],[33]) ).
thf(15,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( ( ^ [B: $i] : $false )
!= ( ^ [B: $i] : $false ) )
| ( sk1 @ sk2 )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(16,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( sk1 @ sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[15]) ).
thf(17,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[16:[]]) ).
thf(62,plain,
! [A: $i] :
( ( sk1 @ sk4 )
| ~ $true
| ( sk1 @ sk2 )
| ( ( sk1 @ ( sk3 @ sk2 ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,17]) ).
thf(63,plain,
! [A: $i] :
( ( sk1 @ sk4 )
| ( sk1 @ sk2 )
| ( ( sk1 @ ( sk3 @ sk2 ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(64,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( sk3 @ sk2 ))]]) ).
thf(80,plain,
! [A: $i] :
( ( sk1 @ sk2 )
| ~ $true
| ( sk1 @ sk2 )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[64,17]) ).
thf(81,plain,
! [A: $i] :
( ( sk1 @ sk2 )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
sk1 @ sk2,
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( sk4 ))]]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A )
| ~ $true
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1 @ sk2 )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17,21]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk3 @ B ) )
| ( ( sk1 @ sk2 )
!= ( sk1 @ B ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(42,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( sk1 @ ( sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(117,plain,
! [A: $i] :
( ~ $true
| ( sk1 @ ( sk3 @ sk2 ) )
| ( ( sk1 @ sk2 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82,42]) ).
thf(118,plain,
! [A: $i] :
( ( sk1 @ ( sk3 @ sk2 ) )
| ( ( sk1 @ sk2 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(119,plain,
sk1 @ ( sk3 @ sk2 ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( sk2 ))]]) ).
thf(120,plain,
! [A: $i] :
( ( sk1
= ( ^ [B: $i] : $false ) )
| ~ $true
| ( ( sk1 @ sk2 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82,11]) ).
thf(121,plain,
! [A: $i] :
( ( sk1
= ( ^ [B: $i] : $false ) )
| ( ( sk1 @ sk2 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(122,plain,
( sk1
= ( ^ [A: $i] : $false ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( sk2 ))]]) ).
thf(130,plain,
! [A: $i] :
~ ( sk1 @ A ),
inference(func_ext,[status(esa)],[122]) ).
thf(145,plain,
$false,
inference(rewrite,[status(thm)],[119,130]) ).
thf(146,plain,
$false,
inference(simp,[status(thm)],[145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU829^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.10 % 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
% 0.10/0.29 % Computer : n017.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8046.5625MB
% 0.10/0.29 % OS : Linux 6.8.0-71-generic
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Sep 29 14:30:52 UTC 2026
% 0.26/0.30 % CPUTime :
% 0.26/0.30 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
% 1.35/1.13 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.02/1.40 % [INFO] Parsing done (264ms).
% 2.02/1.42 % [INFO] Running in sequential loop mode.
% 2.73/2.02 % [INFO] eprover registered as external prover.
% 2.73/2.04 % [INFO] Scanning for conjecture ...
% 3.21/2.17 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.28/2.21 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.28/2.22 % [INFO] Problem is higher-order (TPTP THF).
% 3.28/2.22 % [INFO] Type checking passed.
% 3.28/2.23 % [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 ...
% 7.55/3.70 % [INFO] Killing All external provers ...
% 7.55/3.71 % Time passed: 3198ms (effective reasoning time: 2276ms)
% 7.55/3.71 % 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)>
% 7.55/3.71 % Axioms used in derivation (0):
% 7.55/3.71 % No. of inferences in proof: 40
% 7.55/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3198 ms resp. 2276 ms w/o parsing
% 7.11/3.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.11/3.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------