%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET611^3 : TPTP v9.3.1. Released v3.6.0.
% 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 : n001.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 08:23:01 AM UTC 2026
% Result : Theorem 9.36s 3.32s
% Output : Refutation 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 6
% Syntax : Number of formulae : 59 ( 15 unt; 0 typ; 5 def)
% Number of atoms : 269 ( 52 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 428 ( 104 ~; 86 |; 38 &; 200 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 65 ( 34 ^; 29 !; 0 ?; 65 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(emptyset_decl,type,
emptyset: $i > $o ).
thf(intersection_decl,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(setminus_decl,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(emptyset_def,definition,
( emptyset
= ( ^ [A: $i] : $false ) ) ).
thf(intersection_def,definition,
( intersection
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(setminus_def,definition,
( setminus
= ( ^ [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] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: $i] : $false ) )
= ( ( ^ [C: $i] :
( ( A @ C )
& ~ ( B @ C ) ) )
= A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
( ( ( ^ [B: $i] :
( ( sk1 @ B )
& ( A @ B ) ) )
= ( ^ [B: $i] : $false ) )
!= ( ( ^ [B: $i] :
( ( sk1 @ B )
& ~ ( A @ B ) ) )
= sk1 ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $o] :
( ( ( intersection @ A @ B )
= emptyset )
= ( ( setminus @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o] :
( ( ( intersection @ A @ B )
= emptyset )
= ( ( setminus @ A @ B )
= A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $o] :
( ( ( ^ [C: $i] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: $i] : $false ) )
= ( ( ^ [C: $i] :
( ( A @ C )
& ~ ( B @ C ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: $i] : $false ) )
!= ( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= sk1 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= sk1 )
!= ( ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: $i] : $false ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= sk1 )
| ( ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= sk1 )
| ( ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: $i] : $false ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(13,plain,
( ( ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
!= ( sk1 @ sk5 ) )
| ( ( sk1 @ sk6 )
& ( sk2 @ sk6 ) ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(14,plain,
( ( ( ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
!= ( sk1 @ sk5 ) )
| ( sk1 @ sk6 ) )
& ( ( ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
!= ( sk1 @ sk5 ) )
| ( sk2 @ sk6 ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
( ( ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
!= ( sk1 @ sk5 ) )
| ( sk1 @ sk6 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(54,plain,
( ( sk1 @ sk6 )
| ~ ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
| ~ ( sk1 @ sk5 ) ),
inference(bool_ext,[status(thm)],[15]) ).
thf(59,plain,
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ~ ( sk1 @ sk5 ) ),
inference(cnf,[status(esa)],[54]) ).
thf(60,plain,
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ( sk2 @ sk5 ) ),
inference(simp,[status(thm)],[59]) ).
thf(8,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= sk1 )
| ( ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: $i] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
( ( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= sk1 )
| ( ( ^ [A: $i] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: $i] : $false ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
= ( sk1 @ A ) )
| ~ ( ( sk1 @ B )
& ( sk2 @ B ) ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
= ( sk1 @ A ) )
| ~ ( sk1 @ B )
| ~ ( sk2 @ B ) ),
inference(cnf,[status(esa)],[17]) ).
thf(557,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ B )
| ~ ( sk2 @ B )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
| ~ ( sk1 @ A ) ),
inference(bool_ext,[status(thm)],[29]) ).
thf(637,plain,
! [B: $i,A: $i] :
( ( ~ ( sk1 @ B )
| ~ ( sk2 @ B )
| ( sk1 @ A )
| ~ ( sk1 @ A ) )
& ( ~ ( sk1 @ B )
| ~ ( sk2 @ B )
| ~ ( sk2 @ A )
| ~ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[557]) ).
thf(639,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ B )
| ~ ( sk2 @ B )
| ~ ( sk2 @ A )
| ~ ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[637]) ).
thf(774,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ B )
| ~ ( sk2 @ B )
| ~ ( sk1 @ A )
| ( ( sk2 @ A )
!= ( sk2 @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[639]) ).
thf(775,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A )
| ~ ( sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[774:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(780,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[775]) ).
thf(799,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ~ ( sk1 @ A )
| ~ $true
| ( ( sk2 @ sk5 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60,780]) ).
thf(800,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ~ ( sk1 @ A )
| ( ( sk2 @ sk5 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[799]) ).
thf(801,plain,
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ~ ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( sk5 ))]]) ).
thf(817,plain,
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[801]) ).
thf(16,plain,
( ( ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
!= ( sk1 @ sk5 ) )
| ( sk2 @ sk6 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(257,plain,
( ( sk2 @ sk6 )
| ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
| ( sk1 @ sk5 ) ),
inference(bool_ext,[status(thm)],[16]) ).
thf(278,plain,
( ( ( sk2 @ sk6 )
| ( sk1 @ sk5 )
| ( sk1 @ sk5 ) )
& ( ( sk2 @ sk6 )
| ~ ( sk2 @ sk5 )
| ( sk1 @ sk5 ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(279,plain,
( ( sk2 @ sk6 )
| ( sk1 @ sk5 )
| ( sk1 @ sk5 ) ),
inference(cnfConj,[status(thm)],[278]) ).
thf(281,plain,
( ( sk2 @ sk6 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[279]) ).
thf(55,plain,
( ( sk1 @ sk6 )
| ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
| ( sk1 @ sk5 ) ),
inference(bool_ext,[status(thm)],[15]) ).
thf(61,plain,
( ( ( sk1 @ sk6 )
| ( sk1 @ sk5 )
| ( sk1 @ sk5 ) )
& ( ( sk1 @ sk6 )
| ~ ( sk2 @ sk5 )
| ( sk1 @ sk5 ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(62,plain,
( ( sk1 @ sk6 )
| ( sk1 @ sk5 )
| ( sk1 @ sk5 ) ),
inference(cnfConj,[status(thm)],[61]) ).
thf(64,plain,
( ( sk1 @ sk6 )
| ( sk1 @ sk5 ) ),
inference(simp,[status(thm)],[62]) ).
thf(793,plain,
! [A: $i] :
( ( sk1 @ sk5 )
| ~ $true
| ~ ( sk2 @ A )
| ( ( sk1 @ sk6 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[64,780]) ).
thf(794,plain,
! [A: $i] :
( ( sk1 @ sk5 )
| ~ ( sk2 @ A )
| ( ( sk1 @ sk6 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[793]) ).
thf(795,plain,
( ( sk1 @ sk5 )
| ~ ( sk2 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[794:[bind(A,$thf( sk6 ))]]) ).
thf(869,plain,
( ( sk1 @ sk5 )
| ( sk1 @ sk5 )
| ~ $true
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[281,795]) ).
thf(870,plain,
( ( sk1 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk6 ) ) ),
inference(simp,[status(thm)],[869]) ).
thf(871,plain,
sk1 @ sk5,
inference(pattern_uni,[status(thm)],[870:[]]) ).
thf(878,plain,
( ~ ( $true
& ~ ( sk2 @ sk5 ) )
| ( sk2 @ sk6 ) ),
inference(rewrite,[status(thm)],[16,871]) ).
thf(879,plain,
( ( sk2 @ sk5 )
| ( sk2 @ sk6 ) ),
inference(simp,[status(thm)],[878]) ).
thf(889,plain,
! [A: $i] :
( ~ $true
| ~ ( sk2 @ A )
| ( ( sk1 @ sk5 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[871,780]) ).
thf(890,plain,
! [A: $i] :
( ~ ( sk2 @ A )
| ( ( sk1 @ sk5 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[889]) ).
thf(891,plain,
~ ( sk2 @ sk5 ),
inference(pattern_uni,[status(thm)],[890:[bind(A,$thf( sk5 ))]]) ).
thf(896,plain,
( $false
| ( sk2 @ sk6 ) ),
inference(rewrite,[status(thm)],[879,891]) ).
thf(897,plain,
sk2 @ sk6,
inference(simp,[status(thm)],[896]) ).
thf(906,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ~ $true
| ( ( sk2 @ sk6 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[897,780]) ).
thf(907,plain,
! [A: $i] :
( ~ ( sk1 @ A )
| ( ( sk2 @ sk6 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[906]) ).
thf(908,plain,
~ ( sk1 @ sk6 ),
inference(pattern_uni,[status(thm)],[907:[bind(A,$thf( sk6 ))]]) ).
thf(926,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[817,871,908]) ).
thf(927,plain,
$false,
inference(simp,[status(thm)],[926]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET611^3 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.10/0.20 % Computer : n001.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:45:05 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.91/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.01 % [INFO] Parsing done (217ms).
% 1.24/1.03 % [INFO] Running in sequential loop mode.
% 2.20/1.42 % [INFO] eprover registered as external prover.
% 2.20/1.43 % [INFO] Scanning for conjecture ...
% 2.40/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.40/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.40/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.64/1.60 % [INFO] Type checking passed.
% 2.64/1.60 % [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 ...
% 9.36/3.31 % [INFO] Killing All external provers ...
% 9.36/3.32 % Time passed: 2971ms (effective reasoning time: 2282ms)
% 9.36/3.32 % 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)>
% 9.36/3.32 % Axioms used in derivation (0):
% 9.36/3.32 % No. of inferences in proof: 54
% 9.36/3.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2971 ms resp. 2282 ms w/o parsing
% 9.36/3.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.36/3.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------