%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU148+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 : 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 : Sun Sep 27 08:37:45 AM UTC 2026
% Result : Theorem 17.92s 5.69s
% Output : Refutation 18.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 142 ( 88 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 333 ( 51 ~; 45 |; 16 &; 195 @)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 82 ( 4 ^; 73 !; 1 ?; 82 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ singleton @ ( sk1 @ singleton @ subset ) )
=> ( sk1 = A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
( ( sk1 != sk2 )
& ( sk2 @ singleton @ ( sk1 @ singleton @ subset ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
sk2 @ singleton @ ( sk1 @ singleton @ subset ),
inference(cnfConj,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49,plain,
( ! [A: $i,B: $i] :
( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(miniscope,[status(thm)],[48]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ singleton @ ( C @ subset ) )
| ( C
!= ( D @ singleton ) ) )
& ( ( D @ singleton @ ( C @ subset ) )
| ( C != empty_set ) )
& ( ( A
= ( B @ singleton ) )
| ( A = empty_set )
| ~ ( B @ singleton @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ singleton ) )
| ( A = empty_set )
| ~ ( B @ singleton @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[50]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( B @ singleton @ ( A @ subset ) )
| ( A
= ( B @ singleton ) )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(2938,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ singleton @ ( sk1 @ singleton @ subset ) )
!= ( B @ singleton @ ( A @ subset ) ) )
| ~ $true
| ( A
= ( B @ singleton ) )
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[15,54]) ).
thf(2939,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ singleton @ ( sk1 @ singleton @ subset ) )
!= ( B @ singleton @ ( A @ subset ) ) )
| ( A
= ( B @ singleton ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[2938]) ).
thf(2940,plain,
( ( ( sk2 @ singleton )
= ( sk1 @ singleton ) )
| ( ( sk1 @ singleton )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[2939:[bind(A,$thf( sk1 @ singleton )),bind(B,$thf( sk2 ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk4 ) @ in ) )
| ( ( E @ ( F @ sk3 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk4 ) )
= E )
| ( ( E @ ( F @ sk3 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk4 ) @ in ) )
| ( F @ ( E @ ( F @ sk3 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk4 ) )
= E )
| ( F @ ( E @ ( F @ sk3 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(40,plain,
! [A: $i] : ( A @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[39]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ in ) )
| ( C = A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( A @ singleton @ ( B @ in ) )
| ( B = A ) ),
inference(simp,[status(thm)],[29]) ).
thf(16,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[14]) ).
thf(17,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[16]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( A != sk1 )
| ~ ( A @ singleton @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[30,17]) ).
thf(109,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ singleton @ ( sk2 @ in ) ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(194,plain,
~ ( sk1 @ singleton @ ( sk2 @ in ) ),
inference(simp,[status(thm)],[109]) ).
thf(256,plain,
! [A: $i] :
( ( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,194]) ).
thf(257,plain,
! [A: $i] :
( ( A @ singleton @ ( A @ in ) )
!= ( sk1 @ singleton @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(270,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk1 @ singleton ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[257]) ).
thf(274,plain,
( ( sk2 @ singleton )
!= ( sk1 @ singleton ) ),
inference(simp,[status(thm)],[270]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(44,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(45,plain,
~ ? [A: $i] :
( ( A @ singleton )
= empty_set ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(lifteq,[status(thm)],[46]) ).
thf(3673,plain,
$false,
inference(simplifyReflect,[status(thm)],[2940,274,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU148+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
% 0.14/0.40 % Computer : n017.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 08:35:34 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.41 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
% 0.83/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.16 % [INFO] Parsing done (180ms).
% 1.23/1.17 % [INFO] Running in sequential loop mode.
% 1.72/1.54 % [INFO] eprover registered as external prover.
% 1.72/1.55 % [INFO] Scanning for conjecture ...
% 1.72/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.94/1.61 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.94/1.62 % [INFO] Problem is first-order (TPTP FOF).
% 1.94/1.62 % [INFO] Type checking passed.
% 1.94/1.62 % [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 ...
% 17.92/5.68 % [INFO] Killing All external provers ...
% 17.92/5.69 % Time passed: 5141ms (effective reasoning time: 4506ms)
% 17.92/5.69 % 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)>
% 17.92/5.69 % Axioms used in derivation (3): l4_zfmisc_1, d1_tarski, l1_zfmisc_1
% 17.92/5.69 % No. of inferences in proof: 39
% 17.92/5.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5141 ms resp. 4506 ms w/o parsing
% 18.41/5.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.41/5.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------