%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV472^1 : 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 : n007.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 7.51s 3.17s
% Output : Refutation 7.90s
% 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 : 114 ( 6 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 283 ( 21 ~; 11 |; 16 &; 228 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 65 ( 13 ^; 37 !; 13 ?; 65 :)
% ( 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/SETSPEC_decl',type,
'const/sets/SETSPEC':
!>[TA: $tType] : ( TA > $o > TA > $o ) ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('const/sets/GSPEC_decl',type,
'const/sets/GSPEC':
!>[TA: $tType] : ( ( TA > $o ) > TA > $o ) ).
thf('const/sets/FINITE_decl',type,
'const/sets/FINITE':
!>[TA: $tType] : ( ( TA > $o ) > $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/GSPEC' @ skt1
@ ^ [C: skt1] :
? [D: skt1] :
( 'const/sets/SETSPEC' @ skt1 @ C
@ ( ( 'const/sets/IN' @ skt1 @ D @ A )
& ( B @ D ) )
@ D ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
~ ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
=> ( 'const/sets/FINITE' @ skt1
@ ( 'const/sets/GSPEC' @ skt1
@ ^ [B: skt1] :
? [C: skt1] :
( 'const/sets/SETSPEC' @ skt1 @ B
@ ( ( 'const/sets/IN' @ skt1 @ C @ sk1 )
& ( A @ C ) )
@ C ) ) ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( 'const/sets/FINITE' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [C: TA] :
? [D: TA] :
( 'const/sets/SETSPEC' @ TA @ C
@ ( ( 'const/sets/IN' @ TA @ D @ A )
& ( B @ D ) )
@ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_RESTRICT_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( 'const/sets/FINITE' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [C: TA] :
? [D: TA] :
( 'const/sets/SETSPEC' @ TA @ C
@ ( ( 'const/sets/IN' @ TA @ D @ A )
& ( B @ D ) )
@ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
=> ( 'const/sets/FINITE' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [C: TA] :
? [D: TA] :
( 'const/sets/SETSPEC' @ TA @ C
@ ( ( 'const/sets/IN' @ TA @ D @ A )
& ( B @ D ) )
@ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ( 'const/sets/FINITE' @ skt1 @ sk1 )
& ~ ( 'const/sets/FINITE' @ skt1
@ ( 'const/sets/GSPEC' @ skt1
@ ^ [A: skt1] :
? [B: skt1] :
( 'const/sets/SETSPEC' @ skt1 @ A
@ ( ( 'const/sets/IN' @ skt1 @ B @ sk1 )
& ( sk2 @ B ) )
@ B ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
'const/sets/FINITE' @ skt1 @ sk1,
inference(cnfConj,[status(thm)],[7]) ).
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(13,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(14,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)],[13]) ).
thf(39,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)],[8,14]) ).
thf(40,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)],[39]) ).
thf(41,plain,
! [A: skt1 > $o] :
( ~ ( 'const/sets/SUBSET' @ skt1 @ A @ sk1 )
| ( 'const/sets/FINITE' @ skt1 @ A ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(9,plain,
~ ( 'const/sets/FINITE' @ skt1
@ ( 'const/sets/GSPEC' @ skt1
@ ^ [A: skt1] :
? [B: skt1] :
( 'const/sets/SETSPEC' @ skt1 @ A
@ ( ( 'const/sets/IN' @ skt1 @ B @ sk1 )
& ( sk2 @ B ) )
@ B ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(47,plain,
! [A: skt1 > $o] :
( ~ ( 'const/sets/SUBSET' @ skt1 @ A @ sk1 )
| ~ $true
| ( ( 'const/sets/FINITE' @ skt1 @ A )
!= ( 'const/sets/FINITE' @ skt1
@ ( 'const/sets/GSPEC' @ skt1
@ ^ [B: skt1] :
? [C: skt1] :
( 'const/sets/SETSPEC' @ skt1 @ B
@ ( ( 'const/sets/IN' @ skt1 @ C @ sk1 )
& ( sk2 @ C ) )
@ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,9]) ).
thf(48,plain,
! [A: skt1 > $o] :
( ~ ( 'const/sets/SUBSET' @ skt1 @ A @ sk1 )
| ( ( 'const/sets/FINITE' @ skt1 @ A )
!= ( 'const/sets/FINITE' @ skt1
@ ( 'const/sets/GSPEC' @ skt1
@ ^ [B: skt1] :
? [C: skt1] :
( 'const/sets/SETSPEC' @ skt1 @ B
@ ( ( 'const/sets/IN' @ skt1 @ C @ sk1 )
& ( sk2 @ C ) )
@ C ) ) ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
~ ( 'const/sets/SUBSET' @ skt1
@ ( 'const/sets/GSPEC' @ skt1
@ ^ [A: skt1] :
? [B: skt1] :
( 'const/sets/SETSPEC' @ skt1 @ A
@ ( ( 'const/sets/IN' @ skt1 @ B @ sk1 )
& ( sk2 @ B ) )
@ B ) )
@ sk1 ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( 'const/sets/GSPEC' @ skt1 @ ^ [B: skt1] : ? [C: skt1] : ( 'const/sets/SETSPEC' @ skt1 @ B @ ( ( 'const/sets/IN' @ skt1 @ C @ sk1 ) & ( sk2 @ C ) ) @ C ) ))]]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( 'const/sets/SUBSET' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [C: TA] :
? [D: TA] :
( 'const/sets/SETSPEC' @ TA @ C
@ ( ( 'const/sets/IN' @ TA @ D @ A )
& ( B @ D ) )
@ D ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_RESTRICT_') ).
thf(15,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( 'const/sets/SUBSET' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [C: TA] :
? [D: TA] :
( 'const/sets/SETSPEC' @ TA @ C
@ ( ( 'const/sets/IN' @ TA @ D @ A )
& ( B @ D ) )
@ D ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( 'const/sets/SUBSET' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [C: TA] :
? [D: TA] :
( 'const/sets/SETSPEC' @ TA @ C
@ ( ( 'const/sets/IN' @ TA @ D @ A )
& ( B @ D ) )
@ D ) )
@ A ),
inference(cnf,[status(esa)],[15]) ).
thf(58,plain,
~ $true,
inference(rewrite,[status(thm)],[49,16]) ).
thf(59,plain,
$false,
inference(simp,[status(thm)],[58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV472^1 : 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
% 0.11/0.20 % Computer : n007.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 15:47:40 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
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.02 % [INFO] Parsing done (211ms).
% 1.48/1.03 % [INFO] Running in sequential loop mode.
% 2.04/1.44 % [INFO] eprover registered as external prover.
% 2.04/1.45 % [INFO] Scanning for conjecture ...
% 2.25/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.25/1.59 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.42/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.42/1.60 % [INFO] Type checking passed.
% 2.42/1.61 % [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 ...
% 7.51/3.17 % [INFO] Killing All external provers ...
% 7.51/3.17 % Time passed: 2827ms (effective reasoning time: 2133ms)
% 7.51/3.17 % 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)>
% 7.51/3.17 % Axioms used in derivation (2): thm/sets/FINITE_SUBSET_, thm/sets/SUBSET_RESTRICT_
% 7.51/3.17 % No. of inferences in proof: 20
% 7.51/3.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2827 ms resp. 2133 ms w/o parsing
% 7.90/3.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.90/3.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------