%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV486^1 : 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 : n001.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 08:37:21 AM UTC 2026
% Result : Theorem 4.91s 2.57s
% Output : Refutation 5.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 101 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 261 ( 18 ~; 8 |; 6 &; 229 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 72 ( 16 ^; 39 !; 16 ?; 72 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf('type/nums/num_type',type,
'type/nums/num': $tType ).
thf('const/sets/SETSPEC_decl',type,
'const/sets/SETSPEC':
!>[TA: $tType] : ( TA > $o > TA > $o ) ).
thf('const/sets/HAS_SIZE_decl',type,
'const/sets/HAS_SIZE':
!>[TA: $tType] : ( ( TA > $o ) > 'type/nums/num' > $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/sets/CARD_decl',type,
'const/sets/CARD':
!>[TA: $tType] : ( ( TA > $o ) > 'type/nums/num' ) ).
thf('const/arith/<_decl',type,
'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o ).
thf(sk1_decl,type,
sk1: 'type/nums/num' ).
thf(sk1_def,definition,
( sk1
= ( @+[A: 'type/nums/num'] :
~ ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [B: 'type/nums/num'] :
? [C: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ B @ ( 'const/arith/<' @ C @ A ) @ C ) ) ) ) ) ).
thf(3,axiom,
! [A: 'type/nums/num'] :
( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [B: 'type/nums/num'] :
? [C: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ B @ ( 'const/arith/<' @ C @ A ) @ C ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_NUMSEG_LT_') ).
thf(7,plain,
! [A: 'type/nums/num'] :
( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [B: 'type/nums/num'] :
? [C: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ B @ ( 'const/arith/<' @ C @ A ) @ C ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [A: 'type/nums/num'] :
( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [B: 'type/nums/num'] :
? [C: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ B @ ( 'const/arith/<' @ C @ A ) @ C ) )
@ A ),
inference(cnf,[status(esa)],[7]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ TA @ A @ B )
= ( ( 'const/sets/FINITE' @ TA @ A )
& ( ( 'const/sets/CARD' @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_') ).
thf(9,plain,
! [TA: $tType,A: TA > $o,B: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ TA @ A @ B )
= ( ( 'const/sets/FINITE' @ TA @ A )
& ( ( 'const/sets/CARD' @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,plain,
! [TA: $tType,B: 'type/nums/num',A: TA > $o] :
( ( 'const/sets/HAS_SIZE' @ TA @ A @ B )
= ( ( 'const/sets/FINITE' @ TA @ A )
& ( ( 'const/sets/CARD' @ TA @ A )
= B ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: 'type/nums/num',A: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ A )
& ( ( 'const/sets/CARD' @ TA @ A )
= B ) )
= ( 'const/sets/HAS_SIZE' @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(13,plain,
! [TA: $tType,B: 'type/nums/num',A: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ A )
& ( ( 'const/sets/CARD' @ TA @ A )
= B ) )
| ~ ( 'const/sets/HAS_SIZE' @ TA @ A @ B ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(17,plain,
! [TA: $tType,B: 'type/nums/num',A: TA > $o] :
( ( ( 'const/sets/FINITE' @ TA @ A )
| ~ ( 'const/sets/HAS_SIZE' @ TA @ A @ B ) )
& ( ( ( 'const/sets/CARD' @ TA @ A )
= B )
| ~ ( 'const/sets/HAS_SIZE' @ TA @ A @ B ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(18,plain,
! [TA: $tType,B: 'type/nums/num',A: TA > $o] :
( ( 'const/sets/FINITE' @ TA @ A )
| ~ ( 'const/sets/HAS_SIZE' @ TA @ A @ B ) ),
inference(cnfConj,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: 'type/nums/num'] :
( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [B: 'type/nums/num'] :
? [C: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ B @ ( 'const/arith/<' @ C @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_NUMSEG_LT_') ).
thf(2,negated_conjecture,
~ ! [A: 'type/nums/num'] :
( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [B: 'type/nums/num'] :
? [C: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ B @ ( 'const/arith/<' @ C @ A ) @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: 'type/nums/num'] :
( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [B: 'type/nums/num'] :
? [C: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ B @ ( 'const/arith/<' @ C @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [A: 'type/nums/num'] :
? [B: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ A @ ( 'const/arith/<' @ B @ sk1 ) @ B ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(21,plain,
! [TA: $tType,B: 'type/nums/num',A: TA > $o] :
( ~ ( 'const/sets/HAS_SIZE' @ TA @ A @ B )
| ~ $true
| ( ( 'const/sets/FINITE' @ TA @ A )
!= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [C: 'type/nums/num'] :
? [D: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ C @ ( 'const/arith/<' @ D @ sk1 ) @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,6]) ).
thf(22,plain,
! [TA: $tType,B: 'type/nums/num',A: TA > $o] :
( ~ ( 'const/sets/HAS_SIZE' @ TA @ A @ B )
| ( ( 'const/sets/FINITE' @ TA @ A )
!= ( 'const/sets/FINITE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [C: 'type/nums/num'] :
? [D: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ C @ ( 'const/arith/<' @ D @ sk1 ) @ D ) ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
! [A: 'type/nums/num'] :
~ ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [B: 'type/nums/num'] :
? [C: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ B @ ( 'const/arith/<' @ C @ sk1 ) @ C ) )
@ A ),
inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( 'const/sets/GSPEC' @ 'type/nums/num' @ ^ [C: 'type/nums/num'] : ? [D: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ C @ ( 'const/arith/<' @ D @ sk1 ) @ D ) )),bind(B,$thf( B )),bind_type(TA,$thf( 'type/nums/num' ))]]) ).
thf(30,plain,
! [A: 'type/nums/num'] :
~ ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [B: 'type/nums/num'] :
? [C: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ B @ ( 'const/arith/<' @ C @ sk1 ) @ C ) )
@ A ),
inference(simp,[status(thm)],[23]) ).
thf(32,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ~ $true
| ( ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [C: 'type/nums/num'] :
? [D: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ C @ ( 'const/arith/<' @ D @ A ) @ D ) )
@ A )
!= ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [C: 'type/nums/num'] :
? [D: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ C @ ( 'const/arith/<' @ D @ sk1 ) @ D ) )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,30]) ).
thf(33,plain,
! [B: 'type/nums/num',A: 'type/nums/num'] :
( ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [C: 'type/nums/num'] :
? [D: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ C @ ( 'const/arith/<' @ D @ A ) @ D ) )
@ A )
!= ( 'const/sets/HAS_SIZE' @ 'type/nums/num'
@ ( 'const/sets/GSPEC' @ 'type/nums/num'
@ ^ [C: 'type/nums/num'] :
? [D: 'type/nums/num'] : ( 'const/sets/SETSPEC' @ 'type/nums/num' @ C @ ( 'const/arith/<' @ D @ sk1 ) @ D ) )
@ B ) ),
inference(simp,[status(thm)],[32]) ).
thf(34,plain,
$false,
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV486^1 : 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
% 0.11/0.21 % Computer : n001.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 15:59:35 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.97 % [INFO] Parsing done (180ms).
% 1.16/0.99 % [INFO] Running in sequential loop mode.
% 1.74/1.38 % [INFO] eprover registered as external prover.
% 1.74/1.39 % [INFO] Scanning for conjecture ...
% 1.92/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.07/1.53 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.07/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.07/1.54 % [INFO] Type checking passed.
% 2.07/1.55 % [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 ...
% 4.91/2.56 % [INFO] Killing All external provers ...
% 4.91/2.57 % Time passed: 2211ms (effective reasoning time: 1573ms)
% 4.91/2.57 % 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)>
% 4.91/2.57 % Axioms used in derivation (2): thm/sets/HAS_SIZE_NUMSEG_LT_, thm/sets/HAS_SIZE_
% 4.91/2.57 % No. of inferences in proof: 21
% 4.91/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2211 ms resp. 1573 ms w/o parsing
% 5.43/2.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.43/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------