%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU122+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 : n011.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 08:37:38 AM UTC 2026
% Result : Theorem 6.67s 3.79s
% Output : Refutation 7.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 68 ( 6 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 172 ( 23 ~; 13 |; 7 &; 118 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 50 ( 2 ^; 44 !; 2 ?; 50 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( A @ ( empty_set @ subset ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
~ ( sk1 @ ( empty_set @ subset ) ),
inference(cnf,[status(esa)],[13]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(miniscope,[status(thm)],[17]) ).
thf(19,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk2 ) @ in ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk2 ) @ in ) ) )
& ( ( B @ ( C @ in ) )
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk2 ) @ in ) ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk2 ) @ in ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(6,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(26,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(37,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[26,39]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(159,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk2 ) @ in ) )
!= ( empty_set @ ( C @ in ) ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[23,159]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk2 ) @ in ) )
!= ( empty_set @ ( C @ in ) ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( empty_set @ ( D @ sk2 ) ))]]) ).
thf(176,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(simp,[status(thm)],[173]) ).
thf(179,plain,
~ $true,
inference(rewrite,[status(thm)],[14,176]) ).
thf(180,plain,
$false,
inference(simp,[status(thm)],[179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU122+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.26/0.49 % Computer : n011.cluster.edu
% 0.26/0.49 % Model : x86_64 x86_64
% 0.26/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.49 % Memory : 8046.5625MB
% 0.26/0.49 % OS : Linux 6.8.0-71-generic
% 0.26/0.49 % CPULimit : 300
% 0.26/0.49 % WCLimit : 300
% 0.26/0.49 % DateTime : Sat Sep 26 08:37:29 UTC 2026
% 0.26/0.50 % CPUTime :
% 0.26/0.50 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
% 1.21/1.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.71/1.52 % [INFO] Parsing done (244ms).
% 1.71/1.54 % [INFO] Running in sequential loop mode.
% 2.43/2.10 % [INFO] eprover registered as external prover.
% 2.43/2.10 % [INFO] Scanning for conjecture ...
% 2.77/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.77/2.25 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.77/2.28 % [INFO] Problem is first-order (TPTP FOF).
% 2.77/2.28 % [INFO] Type checking passed.
% 2.77/2.29 % [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 ...
% 6.67/3.78 % [INFO] Killing All external provers ...
% 6.67/3.79 % Time passed: 3084ms (effective reasoning time: 2233ms)
% 6.67/3.79 % 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)>
% 6.67/3.79 % Axioms used in derivation (3): d3_tarski, fc1_xboole_0, t7_boole
% 6.67/3.79 % No. of inferences in proof: 25
% 6.67/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3084 ms resp. 2233 ms w/o parsing
% 7.10/3.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.10/3.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------