%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU633^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n015.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 : Wed Sep 30 08:28:50 AM UTC 2026
% Result : Theorem 6.04s 3.19s
% Output : Refutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 94 ( 24 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 265 ( 50 ~; 31 |; 9 &; 157 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 42 ( 3 ^; 31 !; 5 ?; 42 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(setunionE_decl,type,
setunionE: $o ).
thf(sk1_decl,type,
sk1: $o > $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(setunionE_def,definition,
( setunionE
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( in @ B @ D )
=> ( ( in @ D @ A )
=> C ) )
=> C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $o,B: $i,C: $i] :
@+[D: $i] :
~ ( ( in @ B @ D )
=> ( ( in @ D @ C )
=> A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( in @ A @ ( setunion @ sk2 ) )
=> ? [B: $i] :
( ( in @ B @ sk2 )
& ( in @ A @ B ) ) ) ) ) ).
thf(1,conjecture,
( setunionE
=> ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(2,negated_conjecture,
~ ( setunionE
=> ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( in @ B @ D )
=> ( ( in @ D @ A )
=> C ) )
=> C ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [D: $i,C: $o,B: $i,A: $i] :
( ( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ B @ ( sk1 @ C @ B @ A ) )
| C )
& ( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| C )
& ( ~ ( in @ B @ ( setunion @ A ) )
| ~ C
| C )
& ( in @ sk3 @ ( setunion @ sk2 ) )
& ( ~ ( in @ D @ sk2 )
| ~ ( in @ sk3 @ D ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [C: $o,B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| C ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ ( in @ sk3 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ ( in @ sk3 @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(7,plain,
in @ sk3 @ ( setunion @ sk2 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
! [A: $i] :
( ~ $true
| ~ ( in @ sk3 @ A )
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7,10]) ).
thf(12,plain,
! [A: $i] :
( ~ ( in @ sk3 @ A )
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(17,plain,
! [A: $i] :
( ~ ( in @ sk3 @ A )
| ( sk3 != A )
| ( ( setunion @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[12]) ).
thf(20,plain,
( ~ ( in @ sk3 @ sk3 )
| ( ( setunion @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[17]) ).
thf(13,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ $true
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,10]) ).
thf(14,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
~ ( in @ ( setunion @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( setunion @ sk2 ))]]) ).
thf(16,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( ( in @ sk3 @ A )
!= ( in @ A @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10]) ).
thf(19,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( sk3 != A )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[16]) ).
thf(21,plain,
( ~ ( in @ sk3 @ sk2 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[19]) ).
thf(25,plain,
( ~ $true
| ( sk3 != sk2 )
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7,21]) ).
thf(26,plain,
( ( sk3 != sk2 )
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
( ( sk3 != sk2 )
| ( sk3 != sk3 )
| ( ( setunion @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[26]) ).
thf(28,plain,
( ( sk3 != sk2 )
| ( ( setunion @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[27]) ).
thf(123,plain,
$false,
inference(e,[status(thm)],[5,10,20,7,3,15,28,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU633^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % 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
% 0.11/0.26 % Computer : n015.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 14:03:47 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 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
% 1.33/1.10 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/1.32 % [INFO] Parsing done (217ms).
% 1.83/1.33 % [INFO] Running in sequential loop mode.
% 2.47/1.76 % [INFO] eprover registered as external prover.
% 2.47/1.77 % [INFO] Scanning for conjecture ...
% 2.71/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.92/1.91 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.92/1.91 % [INFO] Problem is higher-order (TPTP THF).
% 2.92/1.92 % [INFO] Type checking passed.
% 2.92/1.92 % [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 ...
% 6.04/3.19 % External prover 'e' found a proof!
% 6.04/3.19 % [INFO] Killing All external provers ...
% 6.04/3.19 % Time passed: 2715ms (effective reasoning time: 1851ms)
% 6.04/3.19 % 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)>
% 6.04/3.19 % Axioms used in derivation (0):
% 6.04/3.19 % No. of inferences in proof: 23
% 6.04/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2715 ms resp. 1851 ms w/o parsing
% 6.22/3.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.22/3.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------