%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU158+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 : n016.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 08:37:48 AM UTC 2026
% Result : Theorem 7.48s 23.50s
% Output : Refutation 7.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 112 ( 12 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 326 ( 37 ~; 31 |; 8 &; 235 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 ( 0 ^; 42 !; 0 ?; 46 :)
% ( 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(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ( sk1 @ singleton @ subset ) )
=> ( A @ ( sk1 @ in ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ( sk3 @ in ) )
=> ( A @ ( sk3 @ singleton @ subset ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,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)],[2]) ).
thf(8,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)],[7]) ).
thf(9,plain,
( ( ~ ( sk4 @ ( sk3 @ singleton @ subset ) )
| ~ ( sk2 @ ( sk1 @ in ) ) )
& ( ( sk4 @ ( sk3 @ in ) )
| ~ ( sk2 @ ( sk1 @ in ) ) )
& ( ~ ( sk4 @ ( sk3 @ singleton @ subset ) )
| ( sk2 @ ( sk1 @ singleton @ subset ) ) )
& ( ( sk4 @ ( sk3 @ in ) )
| ( sk2 @ ( sk1 @ singleton @ subset ) ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(13,plain,
( ~ ( sk4 @ ( sk3 @ singleton @ subset ) )
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(10,plain,
( ( sk4 @ ( sk3 @ in ) )
| ( sk2 @ ( sk1 @ singleton @ subset ) ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(19,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)],[6]) ).
thf(20,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)],[19]) ).
thf(21,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)],[20]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ singleton @ subset ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ singleton @ subset ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ singleton @ subset ) )
| ~ $true
| ( sk2 @ ( sk1 @ singleton @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[10,24]) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ singleton @ subset ) )
| ( sk2 @ ( sk1 @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
( ( sk4 @ ( sk3 @ singleton @ subset ) )
| ( sk2 @ ( sk1 @ singleton @ subset ) ) ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(11,plain,
( ~ ( sk4 @ ( sk3 @ singleton @ subset ) )
| ( sk2 @ ( sk1 @ singleton @ subset ) ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(314,plain,
( ( ( sk4 @ ( sk3 @ singleton @ subset ) )
!= ( sk4 @ ( sk3 @ singleton @ subset ) ) )
| ~ $true
| ( sk2 @ ( sk1 @ singleton @ subset ) )
| ( sk2 @ ( sk1 @ singleton @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[289,11]) ).
thf(315,plain,
( ( ( sk4 @ ( sk3 @ singleton @ subset ) )
!= ( sk4 @ ( sk3 @ singleton @ subset ) ) )
| ( sk2 @ ( sk1 @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[314]) ).
thf(316,plain,
sk2 @ ( sk1 @ singleton @ subset ),
inference(pattern_uni,[status(thm)],[315:[]]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in ) )
| ~ ( B @ ( A @ singleton @ subset ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(333,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ singleton @ subset ) )
!= ( B @ ( A @ singleton @ subset ) ) )
| ( B @ ( A @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[316,22]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ singleton @ subset ) )
!= ( B @ ( A @ singleton @ subset ) ) )
| ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[333]) ).
thf(335,plain,
sk2 @ ( sk1 @ in ),
inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(345,plain,
( ~ ( sk4 @ ( sk3 @ singleton @ subset ) )
| ~ $true ),
inference(rewrite,[status(thm)],[13,335]) ).
thf(346,plain,
~ ( sk4 @ ( sk3 @ singleton @ subset ) ),
inference(simp,[status(thm)],[345]) ).
thf(12,plain,
( ( sk4 @ ( sk3 @ in ) )
| ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(351,plain,
( ( sk4 @ ( sk3 @ in ) )
| ~ $true ),
inference(rewrite,[status(thm)],[12,335]) ).
thf(352,plain,
sk4 @ ( sk3 @ in ),
inference(simp,[status(thm)],[351]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ singleton @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[352,24]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ in ) )
!= ( B @ ( A @ in ) ) )
| ( B @ ( A @ singleton @ subset ) ) ),
inference(simp,[status(thm)],[381]) ).
thf(383,plain,
sk4 @ ( sk3 @ singleton @ subset ),
inference(pattern_uni,[status(thm)],[382:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(431,plain,
~ $true,
inference(rewrite,[status(thm)],[346,383]) ).
thf(432,plain,
$false,
inference(simp,[status(thm)],[431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU158+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
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.14/20.49 % CPULimit : 300
% 0.14/20.49 % WCLimit : 300
% 0.14/20.49 % DateTime : Sat Sep 26 08:43:00 UTC 2026
% 0.14/20.49 % CPUTime :
% 0.14/20.49 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
% 1.16/21.07 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.43/21.25 % [INFO] Parsing done (178ms).
% 1.43/21.27 % [INFO] Running in sequential loop mode.
% 1.98/21.66 % [INFO] eprover registered as external prover.
% 1.98/21.67 % [INFO] Scanning for conjecture ...
% 2.17/21.76 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.32/21.80 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.32/21.81 % [INFO] Problem is first-order (TPTP FOF).
% 2.32/21.81 % [INFO] Type checking passed.
% 2.32/21.82 % [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 ...
% 7.05/23.49 % [INFO] Killing All external provers ...
% 7.05/23.49 % Time passed: 2863ms (effective reasoning time: 2219ms)
% 7.05/23.49 % 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)>
% 7.05/23.50 % Axioms used in derivation (1): l2_zfmisc_1
% 7.05/23.50 % No. of inferences in proof: 34
% 7.48/23.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2863 ms resp. 2219 ms w/o parsing
% 7.48/23.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.48/23.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------