%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV451^1 : 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 : n010.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 08:37:18 AM UTC 2026
% Result : Theorem 14.81s 4.89s
% Output : Refutation 15.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 22 unt; 0 typ; 1 def)
% Number of atoms : 118 ( 22 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 233 ( 15 ~; 12 |; 0 &; 206 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 100 ( 8 ^; 91 !; 0 ?; 100 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/sets/UNIV_decl',type,
'const/sets/UNIV':
!>[TA: $tType] : ( TA > $o ) ).
thf('const/sets/UNION_decl',type,
'const/sets/UNION':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf('const/sets/IN_decl',type,
'const/sets/IN':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk3_decl,type,
sk3: skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
( ( 'const/sets/UNION' @ skt1 @ A @ ( 'const/sets/UNIV' @ skt1 ) )
!= ( 'const/sets/UNIV' @ skt1 ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o] :
( ( 'const/sets/UNION' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) )
= ( 'const/sets/UNIV' @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/UNION_UNIV_1') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] :
( ( 'const/sets/UNION' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) )
= ( 'const/sets/UNIV' @ TA ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,A: TA > $o] :
( ( 'const/sets/UNION' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) )
= ( 'const/sets/UNIV' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( 'const/sets/UNION' @ skt1 @ sk1 @ ( 'const/sets/UNIV' @ skt1 ) )
!= ( 'const/sets/UNIV' @ skt1 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( 'const/sets/UNION' @ skt1 @ sk1 @ ( 'const/sets/UNIV' @ skt1 ) )
!= ( 'const/sets/UNIV' @ skt1 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(12,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(3,axiom,
! [TA: $tType,A: TA] : ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNIV_') ).
thf(10,plain,
! [TA: $tType,A: TA] : ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [TA: $tType,A: TA] : ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) ),
inference(cnf,[status(esa)],[10]) ).
thf(27,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( 'const/sets/IN' @ TA @ B @ A )
!= ( 'const/sets/IN' @ TB @ C @ ( 'const/sets/UNIV' @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,11]) ).
thf(28,plain,
! [TB: $tType,A: TB] : ( 'const/sets/UNIV' @ TB @ A ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( 'const/sets/UNIV' @ TB )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(39,plain,
! [TA: $tType,A: TA] : ( 'const/sets/UNIV' @ TA @ A ),
inference(simp,[status(thm)],[28]) ).
thf(182,plain,
( ( 'const/sets/UNION' @ skt1 @ sk1
@ ^ [A: skt1] : $true )
!= ( ^ [A: skt1] : $true ) ),
inference(rewrite,[status(thm)],[9,39]) ).
thf(194,plain,
~ ( 'const/sets/UNION' @ skt1 @ sk1
@ ^ [A: skt1] : $true
@ sk3 ),
inference(func_ext,[status(esa)],[182]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
= ( ( 'const/sets/IN' @ TA @ C @ A )
| ( 'const/sets/IN' @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNION_') ).
thf(15,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
= ( ( 'const/sets/IN' @ TA @ C @ A )
| ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
= ( ( 'const/sets/IN' @ TA @ C @ A )
| ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
( ( 'const/sets/IN' @ TA @ C @ ( 'const/sets/UNION' @ TA @ A @ B ) )
= ( ( 'const/sets/IN' @ TA @ C @ A )
| ( 'const/sets/IN' @ TA @ C @ B ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(140,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TB > $o,A: TA] :
( ( ( ( 'const/sets/IN' @ TB @ D @ B )
| $true )
= ( 'const/sets/IN' @ TB @ D @ ( 'const/sets/UNION' @ TB @ B @ C ) ) )
| ( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) )
!= ( 'const/sets/IN' @ TB @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,17]) ).
thf(141,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TB > $o,A: TA] :
( ( 'const/sets/IN' @ TB @ D @ ( 'const/sets/UNION' @ TB @ B @ C ) )
| ( ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNIV' @ TA ) )
!= ( 'const/sets/IN' @ TB @ D @ C ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(142,plain,
! [TB: $tType,B: TB > $o,A: TB] : ( 'const/sets/IN' @ TB @ A @ ( 'const/sets/UNION' @ TB @ B @ ( 'const/sets/UNIV' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( 'const/sets/UNIV' @ TB )),bind(D,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(165,plain,
! [TA: $tType,B: TA > $o,A: TA] : ( 'const/sets/IN' @ TA @ A @ ( 'const/sets/UNION' @ TA @ B @ ( 'const/sets/UNIV' @ TA ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(860,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( 'const/sets/IN' @ TA @ A
@ ( 'const/sets/UNION' @ TA @ B
@ ^ [C: TA] : $true ) ),
inference(rewrite,[status(thm)],[165,39]) ).
thf(24,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( 'const/sets/IN' @ TA @ B @ A )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(878,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA] :
( ~ $true
| ( C @ D )
| ( ( 'const/sets/IN' @ TA @ A
@ ( 'const/sets/UNION' @ TA @ B
@ ^ [E: TA] : $true ) )
!= ( 'const/sets/IN' @ TB @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[860,24]) ).
thf(879,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA] :
( ( C @ D )
| ( ( 'const/sets/IN' @ TA @ A
@ ( 'const/sets/UNION' @ TA @ B
@ ^ [E: TA] : $true ) )
!= ( 'const/sets/IN' @ TB @ D @ C ) ) ),
inference(simp,[status(thm)],[878]) ).
thf(880,plain,
! [TB: $tType,B: TB > $o,A: TB] :
( 'const/sets/UNION' @ TB @ B
@ ^ [C: TB] : $true
@ A ),
inference(pattern_uni,[status(thm)],[879:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( 'const/sets/UNION' @ TB @ B @ ^ [E: TB] : $true )),bind(D,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(905,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( 'const/sets/UNION' @ TA @ B
@ ^ [C: TA] : $true
@ A ),
inference(simp,[status(thm)],[880]) ).
thf(915,plain,
~ $true,
inference(rewrite,[status(thm)],[194,905]) ).
thf(916,plain,
$false,
inference(simp,[status(thm)],[915]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV451^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % 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
% 0.09/0.18 % Computer : n010.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:48:47 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.90/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/0.96 % [INFO] Parsing done (196ms).
% 1.26/0.98 % [INFO] Running in sequential loop mode.
% 1.86/1.39 % [INFO] eprover registered as external prover.
% 1.86/1.39 % [INFO] Scanning for conjecture ...
% 2.06/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.24/1.52 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.24/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.54 % [INFO] Type checking passed.
% 2.24/1.55 % [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 ...
% 14.81/4.88 % [INFO] Killing All external provers ...
% 14.81/4.88 % Time passed: 4559ms (effective reasoning time: 3896ms)
% 14.81/4.88 % 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)>
% 14.81/4.89 % Axioms used in derivation (3): thm/sets/IN_, thm/sets/IN_UNIV_, thm/sets/IN_UNION_
% 14.81/4.89 % No. of inferences in proof: 33
% 14.81/4.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4559 ms resp. 3896 ms w/o parsing
% 15.33/4.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.33/4.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------