%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV476^1 : 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 : n017.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 08:37:20 AM UTC 2026
% Result : Theorem 4.48s 2.57s
% Output : Refutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 88 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 179 ( 21 ~; 11 |; 3 &; 137 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 39 ( 0 ^; 37 !; 0 ?; 39 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/SUBSET_decl',type,
'const/sets/SUBSET':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf('const/sets/FINITE_decl',type,
'const/sets/FINITE':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('const/sets/DIFF_decl',type,
'const/sets/DIFF':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
~ ! [B: skt1 > $o] :
( ( 'const/sets/FINITE' @ skt1 @ A )
=> ( 'const/sets/FINITE' @ skt1 @ ( 'const/sets/DIFF' @ skt1 @ A @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
~ ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
=> ( 'const/sets/FINITE' @ skt1 @ ( 'const/sets/DIFF' @ skt1 @ sk1 @ A ) ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( 'const/sets/FINITE' @ TA @ ( 'const/sets/DIFF' @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_DIFF_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( 'const/sets/FINITE' @ TA @ ( 'const/sets/DIFF' @ TA @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( 'const/sets/FINITE' @ TA @ ( 'const/sets/DIFF' @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/sets/FINITE' @ skt1 @ sk1 )
& ~ ( 'const/sets/FINITE' @ skt1 @ ( 'const/sets/DIFF' @ skt1 @ sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
'const/sets/FINITE' @ skt1 @ sk1,
inference(cnfConj,[status(thm)],[6]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ B )
& ( 'const/sets/SUBSET' @ TA @ A @ B ) )
=> ( 'const/sets/FINITE' @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(11,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ B )
& ( 'const/sets/SUBSET' @ TA @ A @ B ) )
=> ( 'const/sets/FINITE' @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/FINITE' @ TA @ B )
| ~ ( 'const/sets/SUBSET' @ TA @ A @ B )
| ( 'const/sets/FINITE' @ TA @ A ) ),
inference(cnf,[status(esa)],[11]) ).
thf(22,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ~ $true
| ~ ( 'const/sets/SUBSET' @ TA @ A @ B )
| ( 'const/sets/FINITE' @ TA @ A )
| ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
!= ( 'const/sets/FINITE' @ TA @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7,12]) ).
thf(23,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ~ ( 'const/sets/SUBSET' @ TA @ A @ B )
| ( 'const/sets/FINITE' @ TA @ A )
| ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
!= ( 'const/sets/FINITE' @ TA @ B ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
! [A: skt1 > $o] :
( ~ ( 'const/sets/SUBSET' @ skt1 @ A @ sk1 )
| ( 'const/sets/FINITE' @ skt1 @ A ) ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(8,plain,
~ ( 'const/sets/FINITE' @ skt1 @ ( 'const/sets/DIFF' @ skt1 @ sk1 @ sk2 ) ),
inference(cnfConj,[status(thm)],[6]) ).
thf(43,plain,
! [A: skt1 > $o] :
( ~ ( 'const/sets/SUBSET' @ skt1 @ A @ sk1 )
| ~ $true
| ( ( 'const/sets/FINITE' @ skt1 @ A )
!= ( 'const/sets/FINITE' @ skt1 @ ( 'const/sets/DIFF' @ skt1 @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,8]) ).
thf(44,plain,
! [A: skt1 > $o] :
( ~ ( 'const/sets/SUBSET' @ skt1 @ A @ sk1 )
| ( ( 'const/sets/FINITE' @ skt1 @ A )
!= ( 'const/sets/FINITE' @ skt1 @ ( 'const/sets/DIFF' @ skt1 @ sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(45,plain,
~ ( 'const/sets/SUBSET' @ skt1 @ ( 'const/sets/DIFF' @ skt1 @ sk1 @ sk2 ) @ sk1 ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( 'const/sets/DIFF' @ skt1 @ sk1 @ sk2 ))]]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( 'const/sets/SUBSET' @ TA @ ( 'const/sets/DIFF' @ TA @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_DIFF_') ).
thf(9,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( 'const/sets/SUBSET' @ TA @ ( 'const/sets/DIFF' @ TA @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] : ( 'const/sets/SUBSET' @ TA @ ( 'const/sets/DIFF' @ TA @ A @ B ) @ A ),
inference(cnf,[status(esa)],[9]) ).
thf(46,plain,
~ $true,
inference(rewrite,[status(thm)],[45,10]) ).
thf(47,plain,
$false,
inference(simp,[status(thm)],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV476^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.09/0.23 % Computer : n017.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 15:45:22 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 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
% 0.97/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.14/1.00 % [INFO] Parsing done (196ms).
% 1.14/1.02 % [INFO] Running in sequential loop mode.
% 1.88/1.42 % [INFO] eprover registered as external prover.
% 1.88/1.43 % [INFO] Scanning for conjecture ...
% 2.04/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.04/1.55 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.04/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.56 % [INFO] Type checking passed.
% 2.04/1.56 % [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 ...
% 4.48/2.56 % [INFO] Killing All external provers ...
% 4.48/2.57 % Time passed: 2198ms (effective reasoning time: 1541ms)
% 4.48/2.57 % 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)>
% 4.48/2.57 % Axioms used in derivation (2): thm/sets/FINITE_SUBSET_, thm/sets/SUBSET_DIFF_
% 4.48/2.57 % No. of inferences in proof: 20
% 4.48/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2198 ms resp. 1541 ms w/o parsing
% 4.90/2.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.90/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------