%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV482^1 : 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 15.67s 6.47s
% Output : Refutation 16.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 22 unt; 0 typ; 3 def)
% Number of atoms : 183 ( 28 equ; 0 cnn)
% Maximal formula atoms : 2 ( 7 avg)
% Number of connectives : 556 ( 16 ~; 2 |; 19 &; 495 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-5 aty)
% Number of variables : 126 ( 18 ^; 105 !; 0 ?; 126 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('const/sets/CROSS_decl',type,
'const/sets/CROSS':
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TA > $o ) > ( 'type/pair/prod' @ TB @ TA ) > $o ) ).
thf('const/pair/,_decl',type,
'const/pair/,':
!>[TA: $tType,TB: $tType] : ( TB > TA > ( 'type/pair/prod' @ TB @ TA ) ) ).
thf(sk1_decl,type,
sk1: ( 'type/pair/prod' @ skt1 @ skt2 ) > $o ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk3_decl,type,
sk3: skt2 > $o ).
thf(sk17_decl,type,
sk17: skt1 ).
thf(sk18_decl,type,
sk18: skt2 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( 'type/pair/prod' @ skt1 @ skt2 ) > $o] :
~ ! [B: skt1 > $o,C: skt2 > $o] :
( ( ! [D: 'type/pair/prod' @ skt1 @ skt2] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ D @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: skt1,E: skt2] :
( ( ( 'const/sets/IN' @ skt1 @ D @ B )
& ( 'const/sets/IN' @ skt2 @ E @ C ) )
=> ( A @ ( 'const/pair/,' @ skt1 @ skt2 @ D @ E ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
~ ! [B: skt2 > $o] :
( ( ! [C: 'type/pair/prod' @ skt1 @ skt2] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ C @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ A @ B ) )
=> ( sk1 @ C ) ) )
= ( ! [C: skt1,D: skt2] :
( ( ( 'const/sets/IN' @ skt1 @ C @ A )
& ( 'const/sets/IN' @ skt2 @ D @ B ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ C @ D ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt2 > $o] :
( ( ! [B: 'type/pair/prod' @ skt1 @ skt2] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ B @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ A ) )
=> ( sk1 @ B ) ) )
!= ( ! [B: skt1,C: skt2] :
( ( ( 'const/sets/IN' @ skt1 @ B @ sk2 )
& ( 'const/sets/IN' @ skt2 @ C @ A ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ B @ C ) ) ) ) ) ) ) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: ( 'type/pair/prod' @ TB @ TA ) > $o] :
( ( ! [B: 'type/pair/prod' @ TB @ TA] : ( A @ B ) )
= ( ! [B: TB,C: TA] : ( A @ ( 'const/pair/,' @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/pair/FORALL_PAIR_THM_') ).
thf(11,plain,
! [TA: $tType,TB: $tType,A: ( 'type/pair/prod' @ TB @ TA ) > $o] :
( ( ! [B: 'type/pair/prod' @ TB @ TA] : ( A @ B ) )
= ( ! [B: TB,C: TA] : ( A @ ( 'const/pair/,' @ TB @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [TA: $tType,TB: $tType,A: ( 'type/pair/prod' @ TA @ TB ) > $o] :
( ( ! [B: 'type/pair/prod' @ TA @ TB] : ( A @ B ) )
= ( ! [B: TA,C: TB] : ( A @ ( 'const/pair/,' @ TA @ TB @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [TA: $tType,TB: $tType,A: ( 'type/pair/prod' @ TA @ TB ) > $o] :
( ( ! [B: 'type/pair/prod' @ TA @ TB] : ( A @ B ) )
= ( ! [B: TA,C: TB] : ( A @ ( 'const/pair/,' @ TA @ TB @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,A: ( 'type/pair/prod' @ TB @ TA ) > $o,B: TB > $o,C: TA > $o] :
( ( ! [D: 'type/pair/prod' @ TB @ TA] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ TB @ TA ) @ D @ ( 'const/sets/CROSS' @ TB @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TB,E: TA] :
( ( ( 'const/sets/IN' @ TB @ D @ B )
& ( 'const/sets/IN' @ TA @ E @ C ) )
=> ( A @ ( 'const/pair/,' @ TB @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FORALL_IN_CROSS_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,A: ( 'type/pair/prod' @ TB @ TA ) > $o,B: TB > $o,C: TA > $o] :
( ( ! [D: 'type/pair/prod' @ TB @ TA] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ TB @ TA ) @ D @ ( 'const/sets/CROSS' @ TB @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TB,E: TA] :
( ( ( 'const/sets/IN' @ TB @ D @ B )
& ( 'const/sets/IN' @ TA @ E @ C ) )
=> ( A @ ( 'const/pair/,' @ TB @ TA @ D @ E ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,TB: $tType,A: ( 'type/pair/prod' @ TB @ TA ) > $o,B: TB > $o,C: TA > $o] :
( ( ! [D: 'type/pair/prod' @ TB @ TA] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ TB @ TA ) @ D @ ( 'const/sets/CROSS' @ TB @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TB,E: TA] :
( ( ( 'const/sets/IN' @ TB @ D @ B )
& ( 'const/sets/IN' @ TA @ E @ C ) )
=> ( A @ ( 'const/pair/,' @ TB @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( ! [A: 'type/pair/prod' @ skt1 @ skt2] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ A @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ A ) ) )
!= ( ! [A: skt1,B: skt2] :
( ( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
& ( 'const/sets/IN' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [A: 'type/pair/prod' @ skt1 @ skt2] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ A @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ A ) ) )
!= ( ! [A: skt1,B: skt2] :
( ( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
& ( 'const/sets/IN' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(20,plain,
! [TA: $tType,TB: $tType,A: ( 'type/pair/prod' @ TA @ TB ) > $o] :
( ( ( ! [B: TA,C: TB] : ( A @ ( 'const/pair/,' @ TA @ TB @ B @ C ) ) )
!= ( ! [B: skt1,C: skt2] :
( ( ( 'const/sets/IN' @ skt1 @ B @ sk2 )
& ( 'const/sets/IN' @ skt2 @ C @ sk3 ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ B @ C ) ) ) ) )
| ( ( ! [B: 'type/pair/prod' @ TA @ TB] : ( A @ B ) )
!= ( ! [B: 'type/pair/prod' @ skt1 @ skt2] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ B @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,7]) ).
thf(21,plain,
( ( ! [A: skt1,B: skt2] :
( ( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
& ( 'const/sets/IN' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) ) )
!= ( ! [A: skt1,B: skt2] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( ^ [B: 'type/pair/prod' @ skt1 @ skt2] : ( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ B @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) ) => ( sk1 @ B ) ) )),bind_type(TA,$thf( skt1 )),bind_type(TB,$thf( skt2 ))]]) ).
thf(33,plain,
( ( ^ [A: skt1] :
! [B: skt2] :
( ( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
& ( 'const/sets/IN' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) ) )
!= ( ^ [A: skt1] :
! [B: skt2] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(46,plain,
( ( ^ [A: skt1,B: skt2] :
( ( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
& ( 'const/sets/IN' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) ) )
!= ( ^ [A: skt1,B: skt2] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(105,plain,
( ( ( ^ [A: skt1,B: skt2] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
& ( 'const/sets/IN' @ skt2 @ B @ sk3 ) ) )
!= ( ^ [A: skt1,B: skt2] : ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) ) ) )
| ( ( ^ [A: skt1,B: skt2] : ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) )
!= ( ^ [A: skt1,B: skt2] : ( sk1 @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(107,plain,
( ( ^ [A: skt1,B: skt2] :
( ( 'const/sets/IN' @ skt1 @ A @ sk2 )
& ( 'const/sets/IN' @ skt2 @ B @ sk3 ) ) )
!= ( ^ [A: skt1,B: skt2] : ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ ( 'const/pair/,' @ skt1 @ skt2 @ A @ B ) @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(108,plain,
( ( ( 'const/sets/IN' @ skt1 @ sk17 @ sk2 )
& ( 'const/sets/IN' @ skt2 @ sk18 @ sk3 ) )
!= ( 'const/sets/IN' @ ( 'type/pair/prod' @ skt1 @ skt2 ) @ ( 'const/pair/,' @ skt1 @ skt2 @ sk17 @ sk18 ) @ ( 'const/sets/CROSS' @ skt1 @ skt2 @ sk2 @ sk3 ) ) ),
inference(func_ext,[status(esa)],[107]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB > $o,D: TA > $o] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ TB @ TA ) @ ( 'const/pair/,' @ TB @ TA @ A @ B ) @ ( 'const/sets/CROSS' @ TB @ TA @ C @ D ) )
= ( ( 'const/sets/IN' @ TB @ A @ C )
& ( 'const/sets/IN' @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_CROSS_') ).
thf(8,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB > $o,D: TA > $o] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ TB @ TA ) @ ( 'const/pair/,' @ TB @ TA @ A @ B ) @ ( 'const/sets/CROSS' @ TB @ TA @ C @ D ) )
= ( ( 'const/sets/IN' @ TB @ A @ C )
& ( 'const/sets/IN' @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TA > $o,B: TB,A: TA] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ TA @ TB ) @ ( 'const/pair/,' @ TA @ TB @ A @ B ) @ ( 'const/sets/CROSS' @ TA @ TB @ C @ D ) )
= ( ( 'const/sets/IN' @ TA @ A @ C )
& ( 'const/sets/IN' @ TB @ B @ D ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TA > $o,B: TB,A: TA] :
( ( 'const/sets/IN' @ ( 'type/pair/prod' @ TA @ TB ) @ ( 'const/pair/,' @ TA @ TB @ A @ B ) @ ( 'const/sets/CROSS' @ TA @ TB @ C @ D ) )
= ( ( 'const/sets/IN' @ TA @ A @ C )
& ( 'const/sets/IN' @ TB @ B @ D ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(109,plain,
$false,
inference(simplifyReflect,[status(thm)],[108,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV482^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % 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
% 0.10/0.19 % Computer : n001.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 15:59:20 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 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
% 0.89/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.97 % [INFO] Parsing done (210ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 1.91/1.39 % [INFO] eprover registered as external prover.
% 1.91/1.39 % [INFO] Scanning for conjecture ...
% 2.28/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.28/1.55 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.28/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.28/1.57 % [INFO] Type checking passed.
% 2.28/1.58 % [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 ...
% 15.67/6.46 % [INFO] Killing All external provers ...
% 15.67/6.47 % Time passed: 6144ms (effective reasoning time: 5471ms)
% 15.67/6.47 % 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)>
% 15.67/6.47 % Axioms used in derivation (2): thm/pair/FORALL_PAIR_THM_, thm/sets/IN_CROSS_
% 15.67/6.47 % No. of inferences in proof: 21
% 15.67/6.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6144 ms resp. 5471 ms w/o parsing
% 16.06/6.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.06/6.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------