%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA068^1 : 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 : 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 07:45:43 AM UTC 2026
% Result : Theorem 6.39s 2.98s
% Output : Refutation 6.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 10 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 239 ( 30 ~; 17 |; 2 &; 188 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 67 ( 6 ^; 54 !; 7 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf('type/realax/real_type',type,
'type/realax/real': $tType ).
thf('const/sets/UNIV_decl',type,
'const/sets/UNIV':
!>[TA: $tType] : ( TA > $o ) ).
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/INFINITE_decl',type,
'const/sets/INFINITE':
!>[TA: $tType] : ( ( 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('const/realax/real_le_decl',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(6,axiom,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/INFINITE' @ TA @ A )
= ( ~ ( 'const/sets/FINITE' @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INFINITE_') ).
thf(15,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/INFINITE' @ TA @ A )
= ( ~ ( 'const/sets/FINITE' @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/INFINITE' @ TA @ A )
= ( ~ ( 'const/sets/FINITE' @ TA @ A ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [TA: $tType,A: TA > $o] :
( ( ~ ( 'const/sets/FINITE' @ TA @ A ) )
= ( 'const/sets/INFINITE' @ TA @ A ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(18,plain,
! [TA: $tType,A: TA > $o] :
( ~ ~ ( 'const/sets/FINITE' @ TA @ A )
| ( 'const/sets/INFINITE' @ TA @ A ) ),
inference(bool_ext,[status(thm)],[17]) ).
thf(20,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
| ( 'const/sets/INFINITE' @ TA @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o] : ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_UNIV_') ).
thf(11,plain,
! [TA: $tType,A: TA > $o] : ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [TA: $tType,A: TA > $o] : ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) ),
inference(cnf,[status(esa)],[11]) ).
thf(5,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/sandbox2/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)],[5]) ).
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(34,plain,
! [TA: $tType,TB: $tType,C: TB > $o,B: TB > $o,A: TA > $o] :
( ~ ( 'const/sets/FINITE' @ TB @ C )
| ~ $true
| ( 'const/sets/FINITE' @ TB @ B )
| ( ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) )
!= ( 'const/sets/SUBSET' @ TB @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(35,plain,
! [TA: $tType,TB: $tType,C: TB > $o,B: TB > $o,A: TA > $o] :
( ~ ( 'const/sets/FINITE' @ TB @ C )
| ( 'const/sets/FINITE' @ TB @ B )
| ( ( 'const/sets/SUBSET' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) )
!= ( 'const/sets/SUBSET' @ TB @ B @ C ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(36,plain,
! [TB: $tType,A: TB > $o] :
( ~ ( 'const/sets/FINITE' @ TB @ ( 'const/sets/UNIV' @ TB ) )
| ( 'const/sets/FINITE' @ TB @ A ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( 'const/sets/UNIV' @ TB )),bind_type(TA,$thf( TB ))]]) ).
thf(38,plain,
! [TA: $tType,A: TA > $o] :
( ~ ( 'const/sets/FINITE' @ TA @ ( 'const/sets/UNIV' @ TA ) )
| ( 'const/sets/FINITE' @ TA @ A ) ),
inference(simp,[status(thm)],[36]) ).
thf(3,axiom,
! [A: 'type/realax/real'] :
~ ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [B: 'type/realax/real'] :
? [C: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ B @ ( 'const/realax/real_le' @ A @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_REAL_INTERVAL_1') ).
thf(8,plain,
! [A: 'type/realax/real'] :
~ ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [B: 'type/realax/real'] :
? [C: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ B @ ( 'const/realax/real_le' @ A @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
~ ? [A: 'type/realax/real'] :
( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [B: 'type/realax/real'] :
? [C: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ B @ ( 'const/realax/real_le' @ A @ C ) @ C ) ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(10,plain,
! [A: 'type/realax/real'] :
~ ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [B: 'type/realax/real'] :
? [C: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ B @ ( 'const/realax/real_le' @ A @ C ) @ C ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(56,plain,
! [TA: $tType,B: 'type/realax/real',A: TA > $o] :
( ~ ( 'const/sets/FINITE' @ TA @ ( 'const/sets/UNIV' @ TA ) )
| ~ $true
| ( ( 'const/sets/FINITE' @ TA @ A )
!= ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [C: 'type/realax/real'] :
? [D: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ C @ ( 'const/realax/real_le' @ B @ D ) @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,10]) ).
thf(57,plain,
! [TA: $tType,B: 'type/realax/real',A: TA > $o] :
( ~ ( 'const/sets/FINITE' @ TA @ ( 'const/sets/UNIV' @ TA ) )
| ( ( 'const/sets/FINITE' @ TA @ A )
!= ( 'const/sets/FINITE' @ 'type/realax/real'
@ ( 'const/sets/GSPEC' @ 'type/realax/real'
@ ^ [C: 'type/realax/real'] :
? [D: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ C @ ( 'const/realax/real_le' @ B @ D ) @ D ) ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(58,plain,
~ ( 'const/sets/FINITE' @ 'type/realax/real' @ ( 'const/sets/UNIV' @ 'type/realax/real' ) ),
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( 'const/sets/GSPEC' @ 'type/realax/real' @ ^ [C: 'type/realax/real'] : ? [D: 'type/realax/real'] : ( 'const/sets/SETSPEC' @ 'type/realax/real' @ C @ ( 'const/realax/real_le' @ B @ D ) @ D ) )),bind(B,$thf( B )),bind_type(TA,$thf( 'type/realax/real' ))]]) ).
thf(84,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/INFINITE' @ TA @ A )
| ~ $true
| ( ( 'const/sets/FINITE' @ TA @ A )
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ ( 'const/sets/UNIV' @ 'type/realax/real' ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,58]) ).
thf(85,plain,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/INFINITE' @ TA @ A )
| ( ( 'const/sets/FINITE' @ TA @ A )
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ ( 'const/sets/UNIV' @ 'type/realax/real' ) ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(86,plain,
'const/sets/INFINITE' @ 'type/realax/real' @ ( 'const/sets/UNIV' @ 'type/realax/real' ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( 'const/sets/UNIV' @ 'type/realax/real' )),bind_type(TA,$thf( 'type/realax/real' ))]]) ).
thf(1,conjecture,
'const/sets/INFINITE' @ 'type/realax/real' @ ( 'const/sets/UNIV' @ 'type/realax/real' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/real_INFINITE_') ).
thf(2,negated_conjecture,
~ ( 'const/sets/INFINITE' @ 'type/realax/real' @ ( 'const/sets/UNIV' @ 'type/realax/real' ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( 'const/sets/INFINITE' @ 'type/realax/real' @ ( 'const/sets/UNIV' @ 'type/realax/real' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(106,plain,
$false,
inference(rewrite,[status(thm)],[86,7]) ).
thf(107,plain,
$false,
inference(simp,[status(thm)],[106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA068^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n004.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:39:07 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.01 % [INFO] Parsing done (206ms).
% 1.53/1.03 % [INFO] Running in sequential loop mode.
% 2.09/1.43 % [INFO] eprover registered as external prover.
% 2.09/1.44 % [INFO] Scanning for conjecture ...
% 2.29/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.29/1.56 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.29/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.29/1.59 % [INFO] Type checking passed.
% 2.29/1.59 % [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 ...
% 6.39/2.97 % [INFO] Killing All external provers ...
% 6.39/2.97 % Time passed: 2601ms (effective reasoning time: 1937ms)
% 6.39/2.97 % 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)>
% 6.39/2.98 % Axioms used in derivation (4): thm/sets/INFINITE_, thm/sets/SUBSET_UNIV_, thm/sets/FINITE_SUBSET_, thm/sets/FINITE_REAL_INTERVAL_1
% 6.39/2.98 % No. of inferences in proof: 31
% 6.39/2.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2601 ms resp. 1937 ms w/o parsing
% 6.99/3.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.99/3.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------