%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV444^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n018.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 08:37:17 AM UTC 2026
% Result : Theorem 6.49s 3.19s
% Output : Refutation 6.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 18 unt; 0 typ; 3 def)
% Number of atoms : 161 ( 55 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 171 ( 22 ~; 11 |; 0 &; 138 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 44 ( 0 ^; 41 !; 0 ?; 44 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk3_decl,type,
sk3: skt1 ).
thf(sk7_decl,type,
sk7: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
~ ! [B: skt1 > $o] :
( ( A = B )
= ( ! [C: skt1] :
( ( 'const/sets/IN' @ skt1 @ C @ A )
= ( 'const/sets/IN' @ skt1 @ C @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
( ( sk1 = A )
!= ( ! [B: skt1] :
( ( 'const/sets/IN' @ skt1 @ B @ sk1 )
= ( 'const/sets/IN' @ skt1 @ B @ A ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
!= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( 'const/sets/IN' @ TA @ C @ A )
= ( 'const/sets/IN' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( sk1 = sk2 )
!= ( ! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( sk1 = sk2 )
!= ( ! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(10,plain,
( ( sk1 != sk2 )
| ~ ! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(12,plain,
( ( sk2 != sk1 )
| ~ ! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(14,plain,
( ( sk2 != sk1 )
| ( ( 'const/sets/IN' @ skt1 @ sk3 @ sk1 )
!= ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(15,plain,
( ( ( 'const/sets/IN' @ skt1 @ sk3 @ sk2 )
!= ( 'const/sets/IN' @ skt1 @ sk3 @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(55,plain,
( ( sk3 != sk3 )
| ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[15]) ).
thf(63,plain,
sk2 != sk1,
inference(simp,[status(thm)],[55]) ).
thf(65,plain,
( ( sk2 @ sk7 )
!= ( sk1 @ sk7 ) ),
inference(func_ext,[status(esa)],[63]) ).
thf(11,plain,
( ( sk1 = sk2 )
| ! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(13,plain,
( ( sk2 = sk1 )
| ! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(16,plain,
! [A: skt1] :
( ( sk2 = sk1 )
| ( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
= ( 'const/sets/IN' @ skt1 @ A @ sk2 ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(17,plain,
! [A: skt1] :
( ( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
= ( 'const/sets/IN' @ skt1 @ A @ sk1 ) )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(66,plain,
! [A: skt1] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
= ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ),
inference(simplifyReflect,[status(thm)],[17,63]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(7,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(75,plain,
! [TA: $tType,C: TA,B: TA > $o,A: skt1] :
( ( ( 'const/sets/IN' @ skt1 @ A @ sk1 )
= ( B @ C ) )
| ( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
!= ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[66,9]) ).
thf(76,plain,
! [A: skt1] :
( ( sk2 @ A )
= ( 'const/sets/IN' @ skt1 @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A )),bind_type(TA,$thf( skt1 ))]]) ).
thf(207,plain,
( ( 'const/sets/IN' @ skt1 @ sk7 @ sk1 )
!= ( sk1 @ sk7 ) ),
inference(rewrite,[status(thm)],[65,76]) ).
thf(228,plain,
$false,
inference(simplifyReflect,[status(thm)],[207,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV444^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % 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
% 0.11/0.20 % Computer : n018.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 15:49:26 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 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
% 0.87/0.75 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.94 % [INFO] Parsing done (189ms).
% 1.20/0.96 % [INFO] Running in sequential loop mode.
% 1.81/1.36 % [INFO] eprover registered as external prover.
% 1.81/1.37 % [INFO] Scanning for conjecture ...
% 2.03/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.19/1.50 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.19/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.51 % [INFO] Type checking passed.
% 2.19/1.52 % [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 ...
% 6.49/3.18 % [INFO] Killing All external provers ...
% 6.49/3.18 % Time passed: 2864ms (effective reasoning time: 2216ms)
% 6.49/3.18 % 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)>
% 6.49/3.18 % Axioms used in derivation (1): thm/sets/IN_
% 6.49/3.18 % No. of inferences in proof: 25
% 6.49/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2864 ms resp. 2216 ms w/o parsing
% 6.70/3.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.70/3.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------