%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV457^1 : 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 : n004.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 08:37:19 AM UTC 2026
% Result : Theorem 4.75s 2.62s
% Output : Refutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 67 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 133 ( 9 ~; 1 |; 0 &; 123 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 26 ( 0 ^; 24 !; 0 ?; 26 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/INSERT_decl',type,
'const/sets/INSERT':
!>[TA: $tType] : ( TA > ( TA > $o ) > TA > $o ) ).
thf(sk1_decl,type,
sk1: skt1 ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1] :
~ ! [B: skt1 > $o] :
( ( 'const/sets/INSERT' @ skt1 @ A @ ( 'const/sets/INSERT' @ skt1 @ A @ B ) )
= ( 'const/sets/INSERT' @ skt1 @ A @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
( ( 'const/sets/INSERT' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ A ) )
!= ( 'const/sets/INSERT' @ skt1 @ sk1 @ A ) ) ) ) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( 'const/sets/INSERT' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/sets/INSERT' @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INSERT_INSERT_') ).
thf(7,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( 'const/sets/INSERT' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/sets/INSERT' @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( 'const/sets/INSERT' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/sets/INSERT' @ TA @ A @ B ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( 'const/sets/INSERT' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/sets/INSERT' @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: TA > $o] :
( ( 'const/sets/INSERT' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/sets/INSERT' @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INSERT_AC_1') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: TA > $o] :
( ( 'const/sets/INSERT' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/sets/INSERT' @ TA @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,A: TA,B: TA > $o] :
( ( 'const/sets/INSERT' @ TA @ A @ ( 'const/sets/INSERT' @ TA @ A @ B ) )
= ( 'const/sets/INSERT' @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( 'const/sets/INSERT' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) )
!= ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( 'const/sets/INSERT' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) )
!= ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(46,plain,
! [B: skt1 > $o,A: skt1] :
( ( ( 'const/sets/INSERT' @ skt1 @ A @ B )
!= ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) )
| ( ( 'const/sets/INSERT' @ skt1 @ A @ ( 'const/sets/INSERT' @ skt1 @ A @ B ) )
!= ( 'const/sets/INSERT' @ skt1 @ sk1 @ ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,6]) ).
thf(47,plain,
( ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 )
!= ( 'const/sets/INSERT' @ skt1 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(80,plain,
$false,
inference(simp,[status(thm)],[47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV457^1 : 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
% 0.10/0.20 % Computer : n004.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 15:48:37 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
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (185ms).
% 1.17/0.99 % [INFO] Running in sequential loop mode.
% 1.75/1.37 % [INFO] eprover registered as external prover.
% 1.75/1.38 % [INFO] Scanning for conjecture ...
% 1.92/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.09/1.51 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.09/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.52 % [INFO] Type checking passed.
% 2.09/1.52 % [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 ...
% 4.75/2.61 % [INFO] Killing All external provers ...
% 4.75/2.61 % Time passed: 2271ms (effective reasoning time: 1615ms)
% 4.75/2.61 % 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)>
% 4.75/2.61 % Axioms used in derivation (1): thm/sets/INSERT_INSERT_
% 4.75/2.61 % No. of inferences in proof: 12
% 4.75/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2271 ms resp. 1615 ms w/o parsing
% 4.75/2.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.75/2.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------