%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU160+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 08:37:49 AM UTC 2026
% Result : Theorem 3.17s 6.66s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 13 unt; 0 typ; 4 def)
% Number of atoms : 170 ( 89 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 325 ( 60 ~; 75 |; 10 &; 165 @)
% ( 3 <=>; 12 =>; 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 : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 48 !; 0 ?; 52 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ singleton @ ( sk2 @ subset ) )
=> ( ( sk2
= ( A @ singleton ) )
| ( sk2 = empty_set ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( sk4
= ( A @ singleton ) )
| ( sk4 = empty_set ) )
=> ( A @ singleton @ ( sk4 @ subset ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,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)],[2]) ).
thf(11,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)],[10]) ).
thf(12,plain,
( ( ~ ( sk5 @ singleton @ ( sk4 @ subset ) )
| sk1 )
& ( ( sk4
= ( sk5 @ singleton ) )
| ( sk4 = empty_set )
| sk1 )
& ( ~ sk1
| ( sk2
!= ( sk3 @ singleton ) ) )
& ( ~ sk1
| ( sk2 != empty_set ) )
& ( ~ sk1
| ( sk3 @ singleton @ ( sk2 @ subset ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(15,plain,
( ~ sk1
| ( sk3 @ singleton @ ( sk2 @ subset ) ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(14,plain,
( ( sk4
= ( sk5 @ singleton ) )
| ( sk4 = empty_set )
| sk1 ),
inference(cnfConj,[status(thm)],[12]) ).
thf(18,plain,
( sk1
| ( ( sk5 @ singleton )
= sk4 )
| ( sk4 = empty_set ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(26,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[26]) ).
thf(16,plain,
( ~ ( sk5 @ singleton @ ( sk4 @ subset ) )
| sk1 ),
inference(cnfConj,[status(thm)],[12]) ).
thf(60,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk5 @ singleton @ ( sk4 @ subset ) ) )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[27,16]) ).
thf(61,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk5 @ singleton @ ( sk4 @ subset ) ) )
| sk1 ),
inference(simp,[status(thm)],[60]) ).
thf(62,plain,
! [A: $i] :
( ( A
!= ( sk5 @ singleton ) )
| ( A != sk4 )
| sk1 ),
inference(simp,[status(thm)],[61]) ).
thf(63,plain,
( ( ( sk5 @ singleton )
!= sk4 )
| sk1 ),
inference(simp,[status(thm)],[62]) ).
thf(65,plain,
( ( ( sk5 @ singleton )
!= ( sk5 @ singleton ) )
| ( sk4 != sk4 )
| sk1
| sk1
| ( sk4 = empty_set ) ),
inference(paramod_ordered,[status(thm)],[18,63]) ).
thf(66,plain,
( ( ( sk5 @ singleton )
!= ( sk5 @ singleton ) )
| sk1
| ( sk4 = empty_set ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
( sk1
| ( sk4 = empty_set ) ),
inference(pattern_uni,[status(thm)],[66:[]]) ).
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(31,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(32,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)],[31]) ).
thf(33,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)],[32]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ subset ) )
| ( A != empty_set ) ),
inference(cnfConj,[status(thm)],[33]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ subset ) )
| ( A != empty_set ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(39,plain,
! [A: $i] : ( A @ singleton @ ( empty_set @ subset ) ),
inference(simp,[status(thm)],[38]) ).
thf(57,plain,
! [A: $i] :
( ( ( A @ singleton @ ( empty_set @ subset ) )
!= ( sk5 @ singleton @ ( sk4 @ subset ) ) )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[39,16]) ).
thf(58,plain,
! [A: $i] :
( ( ( A @ singleton @ ( empty_set @ subset ) )
!= ( sk5 @ singleton @ ( sk4 @ subset ) ) )
| sk1 ),
inference(simp,[status(thm)],[57]) ).
thf(59,plain,
! [A: $i] :
( ( ( A @ singleton )
!= ( sk5 @ singleton ) )
| ( sk4 != empty_set )
| sk1 ),
inference(simp,[status(thm)],[58]) ).
thf(68,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk4 != empty_set )
| sk1 ),
inference(simp,[status(thm)],[59]) ).
thf(75,plain,
( ( sk4 != empty_set )
| sk1 ),
inference(simp,[status(thm)],[68]) ).
thf(76,plain,
( ( sk4 != sk4 )
| ( empty_set != empty_set )
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[67,75]) ).
thf(77,plain,
( ( sk4 != sk4 )
| sk1 ),
inference(simp,[status(thm)],[76]) ).
thf(78,plain,
sk1,
inference(pattern_uni,[status(thm)],[77:[]]) ).
thf(86,plain,
( ~ $true
| ( sk3 @ singleton @ ( sk2 @ subset ) ) ),
inference(rewrite,[status(thm)],[15,78]) ).
thf(87,plain,
sk3 @ singleton @ ( sk2 @ subset ),
inference(simp,[status(thm)],[86]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ singleton ) )
| ( A = empty_set )
| ~ ( B @ singleton @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[33]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( B @ singleton @ ( A @ subset ) )
| ( A
= ( B @ singleton ) )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ singleton @ ( sk2 @ subset ) )
!= ( B @ singleton @ ( A @ subset ) ) )
| ~ $true
| ( A
= ( B @ singleton ) )
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[87,37]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ singleton @ ( sk2 @ subset ) )
!= ( B @ singleton @ ( A @ subset ) ) )
| ( A
= ( B @ singleton ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
( ( ( sk3 @ singleton )
= sk2 )
| ( sk2 = empty_set ) ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(17,plain,
( ~ sk1
| ( sk2
!= ( sk3 @ singleton ) ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(20,plain,
( ~ sk1
| ( ( sk3 @ singleton )
!= sk2 ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(82,plain,
( ~ $true
| ( ( sk3 @ singleton )
!= sk2 ) ),
inference(rewrite,[status(thm)],[20,78]) ).
thf(83,plain,
( ( sk3 @ singleton )
!= sk2 ),
inference(simp,[status(thm)],[82]) ).
thf(13,plain,
( ~ sk1
| ( sk2 != empty_set ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(19,plain,
( ~ sk1
| ( sk2 != empty_set ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(84,plain,
( ~ $true
| ( sk2 != empty_set ) ),
inference(rewrite,[status(thm)],[19,78]) ).
thf(85,plain,
sk2 != empty_set,
inference(simp,[status(thm)],[84]) ).
thf(131,plain,
$false,
inference(simplifyReflect,[status(thm)],[121,83,85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU160+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.12/5.39 % Computer : n007.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sat Sep 26 08:40:29 UTC 2026
% 0.12/5.40 % CPUTime :
% 0.12/5.40 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
% 0.16/5.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/5.86 % [INFO] Parsing done (86ms).
% 0.16/5.87 % [INFO] Running in sequential loop mode.
% 1.32/6.05 % [INFO] eprover registered as external prover.
% 1.32/6.05 % [INFO] Scanning for conjecture ...
% 1.32/6.09 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 1.32/6.11 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.32/6.12 % [INFO] Problem is first-order (TPTP FOF).
% 1.32/6.12 % [INFO] Type checking passed.
% 1.32/6.12 % [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 ...
% 3.17/6.66 % [INFO] Killing All external provers ...
% 3.17/6.66 % Time passed: 1119ms (effective reasoning time: 789ms)
% 3.17/6.66 % 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)>
% 3.17/6.66 % Axioms used in derivation (2): reflexivity_r1_tarski, l4_zfmisc_1
% 3.17/6.66 % No. of inferences in proof: 50
% 3.17/6.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1119 ms resp. 789 ms w/o parsing
% 3.58/6.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.58/6.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------