%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET171^3 : TPTP v9.3.1. Released v3.6.0.
% 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 : n003.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 08:22:55 AM UTC 2026
% Result : Theorem 4.10s 2.22s
% Output : Refutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 14 unt; 0 typ; 5 def)
% Number of atoms : 106 ( 15 equ; 0 cnn)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 236 ( 43 ~; 51 |; 26 &; 116 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 33 ( 18 ^; 12 !; 0 ?; 33 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(intersection_decl,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i > $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(union_def,definition,
( union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(intersection_def,definition,
( intersection
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ! [B: $i > $o,C: $i > $o] :
( ( ^ [D: $i] :
( ( A @ D )
| ( ( B @ D )
& ( C @ D ) ) ) )
= ( ^ [D: $i] :
( ( ( A @ D )
| ( B @ D ) )
& ( ( A @ D )
| ( C @ D ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
~ ! [B: $i > $o] :
( ( ^ [C: $i] :
( ( sk1 @ C )
| ( ( A @ C )
& ( B @ C ) ) ) )
= ( ^ [C: $i] :
( ( ( sk1 @ C )
| ( A @ C ) )
& ( ( sk1 @ C )
| ( B @ C ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $o] :
( ( ^ [B: $i] :
( ( sk1 @ B )
| ( ( sk2 @ B )
& ( A @ B ) ) ) )
!= ( ^ [B: $i] :
( ( ( sk1 @ B )
| ( sk2 @ B ) )
& ( ( sk1 @ B )
| ( A @ B ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( union @ A @ ( intersection @ B @ C ) )
= ( intersection @ ( union @ A @ B ) @ ( union @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_distributes_over_intersection) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( union @ A @ ( intersection @ B @ C ) )
= ( intersection @ ( union @ A @ B ) @ ( union @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( ^ [D: $i] :
( ( A @ D )
| ( ( B @ D )
& ( C @ D ) ) ) )
= ( ^ [D: $i] :
( ( ( A @ D )
| ( B @ D ) )
& ( ( A @ D )
| ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i] :
( ( sk1 @ A )
| ( ( sk2 @ A )
& ( sk3 @ A ) ) ) )
!= ( ^ [A: $i] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ( ( sk1 @ A )
| ( sk3 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ( ( sk1 @ A )
| ( sk3 @ A ) ) ) )
!= ( ^ [A: $i] :
( ( sk1 @ A )
| ( ( sk2 @ A )
& ( sk3 @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk3 @ sk4 ) ) )
!= ( ( sk1 @ sk4 )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(7,plain,
( ~ ( ( ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk3 @ sk4 ) ) )
| ~ ( ( sk1 @ sk4 )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 ) )
& ( ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(10,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(18,plain,
~ ( sk1 @ sk4 ),
inference(simp,[status(thm)],[10]) ).
thf(32,plain,
( ( ( $false
| ( sk2 @ sk4 ) )
& ( $false
| ( sk3 @ sk4 ) ) )
!= ( $false
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[6,18]) ).
thf(33,plain,
$false,
inference(simp,[status(thm)],[32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET171^3 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.10/0.21 % Computer : n003.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:38:58 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.06/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.03 % [INFO] Parsing done (224ms).
% 1.55/1.04 % [INFO] Running in sequential loop mode.
% 2.21/1.43 % [INFO] eprover registered as external prover.
% 2.21/1.44 % [INFO] Scanning for conjecture ...
% 2.44/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.44/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.44/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.66/1.60 % [INFO] Type checking passed.
% 2.66/1.60 % [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 ...
% 4.10/2.22 % [INFO] Killing All external provers ...
% 4.10/2.22 % Time passed: 1866ms (effective reasoning time: 1171ms)
% 4.10/2.22 % 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)>
% 4.10/2.22 % Axioms used in derivation (0):
% 4.10/2.22 % No. of inferences in proof: 12
% 4.10/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1866 ms resp. 1171 ms w/o parsing
% 4.10/2.28 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.10/2.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------