%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET673^3 : TPTP v9.3.1. Released v3.6.0.
% 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 : n011.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 08:23:06 AM UTC 2026
% Result : Theorem 4.19s 2.43s
% Output : Refutation 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 18 unt; 0 typ; 7 def)
% Number of atoms : 96 ( 21 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 227 ( 23 ~; 16 |; 30 &; 138 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 83 ( 23 ^; 49 !; 7 ?; 83 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(is_rel_on_decl,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(restrict_rel_codomain_decl,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $i > $o ).
thf(sk3_decl,type,
sk3: $i > $o ).
thf(sk4_decl,type,
sk4: $i > $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(subset_def,definition,
( subset
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(is_rel_on_def,definition,
( is_rel_on
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
! [D: $i,E: $i] :
( ( A @ D @ E )
=> ( ( B @ D )
& ( C @ E ) ) ) ) ) ).
thf(restrict_rel_codomain_def,definition,
( restrict_rel_codomain
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i,D: $i] :
( ( B @ D )
& ( A @ C @ D ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ! [B: $i > $i > $o] :
( ? [C: $i > $o,D: $i > $o] :
( ! [E: $i,F: $i] :
( ( B @ E @ F )
=> ( ( C @ E )
& ( D @ F ) ) )
& ! [E: $i] :
( ( D @ E )
=> ( A @ E ) ) )
=> ( ( ^ [C: $i,D: $i] :
( ( A @ D )
& ( B @ C @ D ) ) )
= B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $o] :
~ ( ? [B: $i > $o,C: $i > $o] :
( ! [D: $i,E: $i] :
( ( A @ D @ E )
=> ( ( B @ D )
& ( C @ E ) ) )
& ! [D: $i] :
( ( C @ D )
=> ( sk1 @ D ) ) )
=> ( ( ^ [B: $i,C: $i] :
( ( sk1 @ C )
& ( A @ B @ C ) ) )
= A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $o] :
? [B: $i > $o] :
( ! [C: $i,D: $i] :
( ( sk2 @ C @ D )
=> ( ( A @ C )
& ( B @ D ) ) )
& ! [C: $i] :
( ( B @ C )
=> ( sk1 @ C ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $o] :
( ! [B: $i,C: $i] :
( ( sk2 @ B @ C )
=> ( ( sk3 @ B )
& ( A @ C ) ) )
& ! [B: $i] :
( ( A @ B )
=> ( sk1 @ B ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( ( is_rel_on @ B @ C @ D )
& ( subset @ D @ A ) )
=> ( ( restrict_rel_codomain @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( ( is_rel_on @ B @ C @ D )
& ( subset @ D @ A ) )
=> ( ( restrict_rel_codomain @ B @ A )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $i > $o,C: $i > $o,D: $i > $o] :
( ( ! [E: $i,F: $i] :
( ( B @ E @ F )
=> ( ( C @ E )
& ( D @ F ) ) )
& ! [E: $i] :
( ( D @ E )
=> ( A @ E ) ) )
=> ( ( ^ [E: $i,F: $i] :
( ( A @ F )
& ( B @ E @ F ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: $i > $o,B: $i > $i > $o] :
( ? [C: $i > $o,D: $i > $o] :
( ! [E: $i,F: $i] :
( ( B @ E @ F )
=> ( ( C @ E )
& ( D @ F ) ) )
& ! [E: $i] :
( ( D @ E )
=> ( A @ E ) ) )
=> ( ( ^ [C: $i,D: $i] :
( ( A @ D )
& ( B @ C @ D ) ) )
= B ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [C: $i,B: $i,A: $i] :
( ( ~ ( sk2 @ A @ B )
| ( sk3 @ A ) )
& ( ~ ( sk2 @ A @ B )
| ( sk4 @ B ) )
& ( ~ ( sk4 @ C )
| ( sk1 @ C ) )
& ( ( ^ [D: $i,E: $i] :
( ( sk1 @ E )
& ( sk2 @ D @ E ) ) )
!= sk2 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
( ( ^ [A: $i,B: $i] :
( ( sk1 @ B )
& ( sk2 @ A @ B ) ) )
!= sk2 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(11,plain,
( ( ^ [A: $i,B: $i] :
( ( sk1 @ B )
& ( sk2 @ A @ B ) ) )
!= sk2 ),
inference(lifteq,[status(thm)],[9]) ).
thf(12,plain,
( ( ( sk1 @ sk6 )
& ( sk2 @ sk5 @ sk6 ) )
!= ( sk2 @ sk5 @ sk6 ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(14,plain,
( ( ( sk1 @ sk6 )
& ( sk2 @ sk5 @ sk6 ) )
| ( sk2 @ sk5 @ sk6 ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(17,plain,
( ( ( sk1 @ sk6 )
| ( sk2 @ sk5 @ sk6 ) )
& ( ( sk2 @ sk5 @ sk6 )
| ( sk2 @ sk5 @ sk6 ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(19,plain,
( ( sk2 @ sk5 @ sk6 )
| ( sk2 @ sk5 @ sk6 ) ),
inference(cnfConj,[status(thm)],[17]) ).
thf(20,plain,
sk2 @ sk5 @ sk6,
inference(simp,[status(thm)],[19]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ~ ( sk2 @ A @ B )
| ( sk4 @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ $true
| ( sk4 @ B )
| ( ( sk2 @ sk5 @ sk6 )
!= ( sk2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20,7]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( sk4 @ B )
| ( ( sk2 @ sk5 @ sk6 )
!= ( sk2 @ A @ B ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
sk4 @ sk6,
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(8,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ( sk1 @ A ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [A: $i] :
( ~ ( sk4 @ A )
| ( sk1 @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(33,plain,
! [A: $i] :
( ~ $true
| ( sk1 @ A )
| ( ( sk4 @ sk6 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32,10]) ).
thf(34,plain,
! [A: $i] :
( ( sk1 @ A )
| ( ( sk4 @ sk6 )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
sk1 @ sk6,
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( sk6 ))]]) ).
thf(21,plain,
~ ( ( sk1 @ sk6 )
& $true ),
inference(rewrite,[status(thm)],[12,20]) ).
thf(22,plain,
~ ( sk1 @ sk6 ),
inference(simp,[status(thm)],[21]) ).
thf(36,plain,
$false,
inference(rewrite,[status(thm)],[35,22]) ).
thf(37,plain,
$false,
inference(simp,[status(thm)],[36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET673^3 : TPTP v9.3.1. Released v3.6.0.
% 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 : n011.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 13:40:46 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.02/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.57/1.05 % [INFO] Parsing done (251ms).
% 1.57/1.07 % [INFO] Running in sequential loop mode.
% 2.17/1.46 % [INFO] eprover registered as external prover.
% 2.17/1.47 % [INFO] Scanning for conjecture ...
% 2.58/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.58/1.67 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.58/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 2.58/1.68 % [INFO] Type checking passed.
% 2.58/1.68 % [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 ...
% 4.19/2.42 % [INFO] Killing All external provers ...
% 4.19/2.42 % Time passed: 2053ms (effective reasoning time: 1347ms)
% 4.19/2.42 % 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)>
% 4.19/2.43 % Axioms used in derivation (0):
% 4.19/2.43 % No. of inferences in proof: 25
% 4.19/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2053 ms resp. 1347 ms w/o parsing
% 4.47/2.50 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.47/2.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------