%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV445^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n009.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 08:37:18 AM UTC 2026
% Result : Theorem 3.74s 2.27s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 39 ( 10 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 56 ( 7 ~; 1 |; 0 &; 48 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-3 aty)
% Number of variables : 29 ( 6 ^; 22 !; 0 ?; 29 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/UNIV_decl',type,
'const/sets/UNIV':
!>[TA: $tType] : ( TA > $o ) ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(sk1_decl,type,
sk1: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1] :
~ ( 'const/sets/IN' @ skt1 @ A @ ( 'const/sets/UNIV' @ skt1 ) ) ) ) ).
thf(3,axiom,
! [TA: $tType] :
( ( 'const/sets/UNIV' @ TA )
= ( ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/UNIV_') ).
thf(7,plain,
! [TA: $tType] :
( ( 'const/sets/UNIV' @ TA )
= ( ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType] :
( ( 'const/sets/UNIV' @ TA )
= ( ^ [A: TA] : $true ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [TA: $tType] :
( ( 'const/sets/UNIV' @ TA )
= ( ^ [A: TA] : $true ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(1,conjecture,
! [TA: $tType,A: TA] : ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNIV_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA] : ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA] : ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( 'const/sets/IN' @ skt1 @ sk1 @ ( 'const/sets/UNIV' @ skt1 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(14,plain,
( ~ ( 'const/sets/IN' @ skt1 @ sk1
@ ^ [A: skt1] : $true )
| ( ( 'const/sets/UNIV' @ skt1 )
!= ( 'const/sets/UNIV' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[9,6]) ).
thf(15,plain,
~ ( 'const/sets/IN' @ skt1 @ sk1
@ ^ [A: skt1] : $true ),
inference(pattern_uni,[status(thm)],[14:[]]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(10,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(19,plain,
$false,
inference(simplifyReflect,[status(thm)],[15,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV445^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.10/0.20 % Computer : n009.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 15:47:15 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (180ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 1.83/1.40 % [INFO] eprover registered as external prover.
% 2.02/1.40 % [INFO] Scanning for conjecture ...
% 2.02/1.46 % [INFO] No direction of definition thm/sets/UNIV_ detected. Treating as axiom ...
% 2.02/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.19/1.53 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.19/1.53 % [INFO] No direction of definition thm/sets/UNIV_ detected. Treating as axiom ...
% 2.19/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.54 % [INFO] Type checking passed.
% 2.19/1.55 % [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 ...
% 3.74/2.27 % [INFO] Killing All external provers ...
% 3.74/2.27 % Time passed: 1916ms (effective reasoning time: 1267ms)
% 3.74/2.27 % 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)>
% 3.74/2.27 % Axioms used in derivation (2): thm/sets/UNIV_, thm/sets/IN_
% 3.74/2.27 % No. of inferences in proof: 15
% 3.74/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1916 ms resp. 1267 ms w/o parsing
% 4.02/2.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.02/2.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------