%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV481^1 : 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 : n020.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 45.14s 34.60s
% Output : Refutation 45.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 168 ( 5 equ; 0 cnn)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 534 ( 23 ~; 13 |; 26 &; 462 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 3 con; 0-6 aty)
% Number of variables : 108 ( 22 ^; 51 !; 32 ?; 108 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
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('const/pair/,_decl',type,
'const/pair/,':
!>[TA: $tType,TB: $tType] : ( TB > TA > ( 'type/pair/prod' @ TB @ TA ) ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk2_decl,type,
sk2: skt2 > $o ).
thf(sk3_decl,type,
sk3:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB > TC > $o ) > ( TB > $o ) > ( TB > TC > TA ) > TB ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
~ ! [B: skt2 > $o] :
( ( ( 'const/sets/FINITE' @ skt1 @ A )
& ( 'const/sets/FINITE' @ skt2 @ B ) )
=> ( 'const/sets/FINITE' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ( 'const/sets/GSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ^ [C: 'type/pair/prod' @ skt1 @ skt2] :
? [D: skt1,E: skt2] :
( 'const/sets/SETSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ C
@ ( ( 'const/sets/IN' @ skt1 @ D @ A )
& ( 'const/sets/IN' @ skt2 @ E @ B ) )
@ ( 'const/pair/,' @ skt1 @ skt2 @ D @ E ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt2 > $o] :
~ ( ( ( 'const/sets/FINITE' @ skt1 @ sk1 )
& ( 'const/sets/FINITE' @ skt2 @ A ) )
=> ( 'const/sets/FINITE' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ( 'const/sets/GSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ^ [B: 'type/pair/prod' @ skt1 @ skt2] :
? [C: skt1,D: skt2] :
( 'const/sets/SETSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ B
@ ( ( 'const/sets/IN' @ skt1 @ C @ sk1 )
& ( 'const/sets/IN' @ skt2 @ D @ A ) )
@ ( 'const/pair/,' @ skt1 @ skt2 @ C @ D ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > $o,B: TB > $o,C: TB > TC > TA] :
@+[D: TB] :
~ ( ( 'const/sets/IN' @ TB @ D @ B )
=> ( 'const/sets/FINITE' @ TC @ ( A @ D ) ) ) ) ) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > TC,B: TB > $o,C: TB > TA > $o] :
( ( ( 'const/sets/FINITE' @ TB @ B )
& ! [D: TB] :
( ( 'const/sets/IN' @ TB @ D @ B )
=> ( 'const/sets/FINITE' @ TA @ ( C @ D ) ) ) )
=> ( 'const/sets/FINITE' @ TC
@ ( 'const/sets/GSPEC' @ TC
@ ^ [D: TC] :
? [E: TB,F: TA] :
( 'const/sets/SETSPEC' @ TC @ D
@ ( ( 'const/sets/IN' @ TB @ E @ B )
& ( 'const/sets/IN' @ TA @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_DEPENDENT_') ).
thf(9,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > TC,B: TB > $o,C: TB > TA > $o] :
( ( ( 'const/sets/FINITE' @ TB @ B )
& ! [D: TB] :
( ( 'const/sets/IN' @ TB @ D @ B )
=> ( 'const/sets/FINITE' @ TA @ ( C @ D ) ) ) )
=> ( 'const/sets/FINITE' @ TC
@ ( 'const/sets/GSPEC' @ TC
@ ^ [D: TC] :
? [E: TB,F: TA] :
( 'const/sets/SETSPEC' @ TC @ D
@ ( ( 'const/sets/IN' @ TB @ E @ B )
& ( 'const/sets/IN' @ TA @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC > $o,B: TB > $o,A: TB > TC > TA] :
( ( ~ ( 'const/sets/FINITE' @ TB @ B )
| ( 'const/sets/IN' @ TB @ ( sk3 @ TC @ TB @ TA @ C @ B @ A ) @ B )
| ( 'const/sets/FINITE' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [D: TA] :
? [E: TB,F: TC] :
( 'const/sets/SETSPEC' @ TA @ D
@ ( ( 'const/sets/IN' @ TB @ E @ B )
& ( 'const/sets/IN' @ TC @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) ) )
& ( ~ ( 'const/sets/FINITE' @ TB @ B )
| ~ ( 'const/sets/FINITE' @ TC @ ( C @ ( sk3 @ TC @ TB @ TA @ C @ B @ A ) ) )
| ( 'const/sets/FINITE' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [D: TA] :
? [E: TB,F: TC] :
( 'const/sets/SETSPEC' @ TA @ D
@ ( ( 'const/sets/IN' @ TB @ E @ B )
& ( 'const/sets/IN' @ TC @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(12,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC > $o,B: TB > $o,A: TB > TC > TA] :
( ~ ( 'const/sets/FINITE' @ TB @ B )
| ~ ( 'const/sets/FINITE' @ TC @ ( C @ ( sk3 @ TC @ TB @ TA @ C @ B @ A ) ) )
| ( 'const/sets/FINITE' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [D: TA] :
? [E: TB,F: TC] :
( 'const/sets/SETSPEC' @ TA @ D
@ ( ( 'const/sets/IN' @ TB @ E @ B )
& ( 'const/sets/IN' @ TC @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
( ( ( 'const/sets/FINITE' @ TB @ A )
& ( 'const/sets/FINITE' @ TA @ B ) )
=> ( 'const/sets/FINITE' @ ( 'type/pair/prod' @ TB @ TA )
@ ( 'const/sets/GSPEC' @ ( 'type/pair/prod' @ TB @ TA )
@ ^ [C: 'type/pair/prod' @ TB @ TA] :
? [D: TB,E: TA] :
( 'const/sets/SETSPEC' @ ( 'type/pair/prod' @ TB @ TA ) @ C
@ ( ( 'const/sets/IN' @ TB @ D @ A )
& ( 'const/sets/IN' @ TA @ E @ B ) )
@ ( 'const/pair/,' @ TB @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
( ( ( 'const/sets/FINITE' @ TB @ A )
& ( 'const/sets/FINITE' @ TA @ B ) )
=> ( 'const/sets/FINITE' @ ( 'type/pair/prod' @ TB @ TA )
@ ( 'const/sets/GSPEC' @ ( 'type/pair/prod' @ TB @ TA )
@ ^ [C: 'type/pair/prod' @ TB @ TA] :
? [D: TB,E: TA] :
( 'const/sets/SETSPEC' @ ( 'type/pair/prod' @ TB @ TA ) @ C
@ ( ( 'const/sets/IN' @ TB @ D @ A )
& ( 'const/sets/IN' @ TA @ E @ B ) )
@ ( 'const/pair/,' @ TB @ TA @ D @ E ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
( ( ( 'const/sets/FINITE' @ TB @ A )
& ( 'const/sets/FINITE' @ TA @ B ) )
=> ( 'const/sets/FINITE' @ ( 'type/pair/prod' @ TB @ TA )
@ ( 'const/sets/GSPEC' @ ( 'type/pair/prod' @ TB @ TA )
@ ^ [C: 'type/pair/prod' @ TB @ TA] :
? [D: TB,E: TA] :
( 'const/sets/SETSPEC' @ ( 'type/pair/prod' @ TB @ TA ) @ C
@ ( ( 'const/sets/IN' @ TB @ D @ A )
& ( 'const/sets/IN' @ TA @ E @ B ) )
@ ( 'const/pair/,' @ TB @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( 'const/sets/FINITE' @ skt1 @ sk1 )
& ( 'const/sets/FINITE' @ skt2 @ sk2 )
& ~ ( 'const/sets/FINITE' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ( 'const/sets/GSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ^ [A: 'type/pair/prod' @ skt1 @ skt2] :
? [B: skt1,C: skt2] :
( 'const/sets/SETSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ A
@ ( ( 'const/sets/IN' @ skt1 @ B @ sk1 )
& ( 'const/sets/IN' @ skt2 @ C @ sk2 ) )
@ ( 'const/pair/,' @ skt1 @ skt2 @ B @ C ) ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
~ ( 'const/sets/FINITE' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ( 'const/sets/GSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ^ [A: 'type/pair/prod' @ skt1 @ skt2] :
? [B: skt1,C: skt2] :
( 'const/sets/SETSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ A
@ ( ( 'const/sets/IN' @ skt1 @ B @ sk1 )
& ( 'const/sets/IN' @ skt2 @ C @ sk2 ) )
@ ( 'const/pair/,' @ skt1 @ skt2 @ B @ C ) ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(55,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC > $o,B: TB > $o,A: TB > TC > TA] :
( ~ ( 'const/sets/FINITE' @ TB @ B )
| ~ ( 'const/sets/FINITE' @ TC @ ( C @ ( sk3 @ TC @ TB @ TA @ C @ B @ A ) ) )
| ~ $true
| ( ( 'const/sets/FINITE' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [D: TA] :
? [E: TB,F: TC] :
( 'const/sets/SETSPEC' @ TA @ D
@ ( ( 'const/sets/IN' @ TB @ E @ B )
& ( 'const/sets/IN' @ TC @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) )
!= ( 'const/sets/FINITE' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ( 'const/sets/GSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ^ [D: 'type/pair/prod' @ skt1 @ skt2] :
? [E: skt1,F: skt2] :
( 'const/sets/SETSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ D
@ ( ( 'const/sets/IN' @ skt1 @ E @ sk1 )
& ( 'const/sets/IN' @ skt2 @ F @ sk2 ) )
@ ( 'const/pair/,' @ skt1 @ skt2 @ E @ F ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(56,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC > $o,B: TB > $o,A: TB > TC > TA] :
( ~ ( 'const/sets/FINITE' @ TB @ B )
| ~ ( 'const/sets/FINITE' @ TC @ ( C @ ( sk3 @ TC @ TB @ TA @ C @ B @ A ) ) )
| ( ( 'const/sets/FINITE' @ TA
@ ( 'const/sets/GSPEC' @ TA
@ ^ [D: TA] :
? [E: TB,F: TC] :
( 'const/sets/SETSPEC' @ TA @ D
@ ( ( 'const/sets/IN' @ TB @ E @ B )
& ( 'const/sets/IN' @ TC @ F @ ( C @ E ) ) )
@ ( A @ E @ F ) ) ) )
!= ( 'const/sets/FINITE' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ( 'const/sets/GSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 )
@ ^ [D: 'type/pair/prod' @ skt1 @ skt2] :
? [E: skt1,F: skt2] :
( 'const/sets/SETSPEC' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ D
@ ( ( 'const/sets/IN' @ skt1 @ E @ sk1 )
& ( 'const/sets/IN' @ skt2 @ F @ sk2 ) )
@ ( 'const/pair/,' @ skt1 @ skt2 @ E @ F ) ) ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(57,plain,
( ~ ( 'const/sets/FINITE' @ skt1 @ sk1 )
| ~ ( 'const/sets/FINITE' @ skt2 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( 'const/pair/,' @ skt1 @ skt2 )),bind(B,$thf( sk1 )),bind(C,$thf( ^ [D: skt1] : sk2 )),bind_type(TA,$thf( 'type/pair/prod' @ skt1 @ skt2 )),bind_type(TB,$thf( skt1 )),bind_type(TC,$thf( skt2 ))]]) ).
thf(6,plain,
'const/sets/FINITE' @ skt1 @ sk1,
inference(cnfConj,[status(thm)],[5]) ).
thf(7,plain,
'const/sets/FINITE' @ skt2 @ sk2,
inference(cnfConj,[status(thm)],[5]) ).
thf(68,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[57,6,7]) ).
thf(69,plain,
$false,
inference(simp,[status(thm)],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV481^1 : 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
% 0.10/0.22 % Computer : n020.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 15:53:49 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (208ms).
% 1.24/1.02 % [INFO] Running in sequential loop mode.
% 2.06/1.43 % [INFO] eprover registered as external prover.
% 2.06/1.44 % [INFO] Scanning for conjecture ...
% 2.26/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.26/1.59 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.43/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.43/1.61 % [INFO] Type checking passed.
% 2.43/1.61 % [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 ...
% 44.78/34.60 % [INFO] Killing All external provers ...
% 45.14/34.60 % Time passed: 34239ms (effective reasoning time: 33572ms)
% 45.14/34.60 % 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)>
% 45.14/34.60 % Axioms used in derivation (1): thm/sets/FINITE_PRODUCT_DEPENDENT_
% 45.14/34.60 % No. of inferences in proof: 16
% 45.14/34.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 34239 ms resp. 33572 ms w/o parsing
% 45.14/34.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 45.14/34.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------