%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU163+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/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 08:37:50 AM UTC 2026
% Result : Theorem 3.61s 2.55s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 34 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 94 ( 14 ~; 4 |; 1 &; 68 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 0 ^; 17 !; 0 ?; 19 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i ).
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 @ union @ ( A @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ( sk1 @ in ) )
=> ( A @ union @ ( sk1 @ subset ) ) ) ) ) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B @ union @ ( A @ subset ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ~ ( sk2 @ union @ ( sk1 @ subset ) )
& ( sk2 @ ( sk1 @ in ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(10,plain,
~ ( sk2 @ union @ ( sk1 @ subset ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( ( B @ union @ ( A @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[17,10]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( ( B @ union @ ( A @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
~ ( sk2 @ ( sk1 @ in ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(9,plain,
sk2 @ ( sk1 @ in ),
inference(cnfConj,[status(thm)],[8]) ).
thf(46,plain,
~ $true,
inference(rewrite,[status(thm)],[37,9]) ).
thf(47,plain,
$false,
inference(simp,[status(thm)],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU163+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 08:47:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.75/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.04/1.11 % [INFO] Parsing done (224ms).
% 1.04/1.13 % [INFO] Running in sequential loop mode.
% 1.72/1.64 % [INFO] eprover registered as external prover.
% 1.72/1.65 % [INFO] Scanning for conjecture ...
% 1.88/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.88/1.79 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.88/1.79 % [INFO] Problem is first-order (TPTP FOF).
% 2.01/1.80 % [INFO] Type checking passed.
% 2.01/1.80 % [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 ...
% 3.61/2.54 % [INFO] Killing All external provers ...
% 3.61/2.54 % Time passed: 2067ms (effective reasoning time: 1404ms)
% 3.61/2.54 % 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)>
% 3.61/2.54 % Axioms used in derivation (1): l50_zfmisc_1
% 3.61/2.54 % No. of inferences in proof: 14
% 3.61/2.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2067 ms resp. 1404 ms w/o parsing
% 3.61/2.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.61/2.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------