%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU152+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n007.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 08:37:47 AM UTC 2026
% Result : Theorem 5.06s 2.99s
% Output : Refutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 61 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 180 ( 23 ~; 12 |; 4 &; 129 @)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 ^; 37 !; 0 ?; 39 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ( sk1 @ in ) )
=> ( ( A @ ( sk1 @ singleton @ set_union2 ) )
= A ) ) ) ) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
= B )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
( ( ( sk2 @ ( sk1 @ singleton @ set_union2 ) )
!= sk2 )
& ( sk2 @ ( sk1 @ in ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(14,plain,
( ( sk2 @ ( sk1 @ singleton @ set_union2 ) )
!= sk2 ),
inference(cnfConj,[status(thm)],[12]) ).
thf(15,plain,
( ( sk2 @ ( sk1 @ singleton @ set_union2 ) )
!= sk2 ),
inference(lifteq,[status(thm)],[14]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_union2 ) )
!= ( sk2 @ ( sk1 @ singleton @ set_union2 ) ) )
| ( B != sk2 )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[36,15]) ).
thf(135,plain,
( ( sk2 != sk2 )
| ~ ( sk2 @ ( sk1 @ singleton @ subset ) ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( sk1 @ singleton )),bind(B,$thf( sk2 ))]]) ).
thf(147,plain,
~ ( sk2 @ ( sk1 @ singleton @ subset ) ),
inference(simp,[status(thm)],[135]) ).
thf(13,plain,
sk2 @ ( sk1 @ in ),
inference(cnfConj,[status(thm)],[12]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(miniscope,[status(thm)],[26]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ singleton @ subset ) )
| ~ ( D @ ( C @ in ) ) )
& ( ( B @ ( A @ in ) )
| ~ ( B @ ( A @ singleton @ subset ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ singleton @ subset ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ singleton @ subset ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ singleton @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,31]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
sk2 @ ( sk1 @ singleton @ subset ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(148,plain,
~ $true,
inference(rewrite,[status(thm)],[147,102]) ).
thf(149,plain,
$false,
inference(simp,[status(thm)],[148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU152+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.14/0.41 % Computer : n007.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 08:39:24 UTC 2026
% 0.07/0.41 % CPUTime :
% 0.07/0.41 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
% 1.25/1.16 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.60/1.32 % [INFO] Parsing done (155ms).
% 1.60/1.33 % [INFO] Running in sequential loop mode.
% 2.21/1.74 % [INFO] eprover registered as external prover.
% 2.21/1.75 % [INFO] Scanning for conjecture ...
% 2.38/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.38/1.87 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.38/1.89 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.89 % [INFO] Type checking passed.
% 2.54/1.90 % [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 ...
% 5.06/2.98 % [INFO] Killing All external provers ...
% 5.06/2.99 % Time passed: 2361ms (effective reasoning time: 1647ms)
% 5.06/2.99 % 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)>
% 5.06/2.99 % Axioms used in derivation (2): t12_xboole_1, l2_zfmisc_1
% 5.06/2.99 % No. of inferences in proof: 25
% 5.06/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2361 ms resp. 1647 ms w/o parsing
% 5.42/3.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.42/3.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------