%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET669^3 : TPTP v9.3.1. Released v3.6.0.
% 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 : n003.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 4.39s 2.39s
% Output : Refutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 13 unt; 0 typ; 7 def)
% Number of atoms : 88 ( 28 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 140 ( 26 ~; 11 |; 6 &; 89 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 84 ( 35 ^; 32 !; 15 ?; 84 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(id_rel_decl,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(sub_rel_decl,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(rel_codomain_decl,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(rel_domain_decl,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(subset_def,definition,
( subset
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(id_rel_def,definition,
( id_rel
= ( ^ [A: $i > $o,B: $i,C: $i] :
( ( A @ B )
& ( B = C ) ) ) ) ).
thf(sub_rel_def,definition,
( sub_rel
= ( ^ [A: $i > $i > $o,B: $i > $i > $o] :
! [C: $i,D: $i] :
( ( A @ C @ D )
=> ( B @ C @ D ) ) ) ) ).
thf(rel_codomain_def,definition,
( rel_codomain
= ( ^ [A: $i > $i > $o,B: $i] :
? [C: $i] : ( A @ C @ B ) ) ) ).
thf(rel_domain_def,definition,
( rel_domain
= ( ^ [A: $i > $i > $o,B: $i] :
? [C: $i] : ( A @ B @ C ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $o] :
~ ( ! [B: $i,C: $i] :
( ( B = C )
=> ( A @ B @ C ) )
=> ( ! [B: $i] :
? [C: $i] : ( A @ B @ C )
& ( ( ^ [B: $i] : $true )
= ( ^ [B: $i] :
? [C: $i] : ( A @ C @ B ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ? [B: $i] : ( sk1 @ A @ B ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [B: $i] : $true )
@ A )
=> ( ( subset
@ ^ [B: $i] : $true
@ ( rel_domain @ A ) )
& ( ( ^ [B: $i] : $true )
= ( rel_codomain @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [B: $i] : $true )
@ A )
=> ( ( subset
@ ^ [B: $i] : $true
@ ( rel_domain @ A ) )
& ( ( ^ [B: $i] : $true )
= ( rel_codomain @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ! [B: $i,C: $i] :
( ( B = C )
=> ( A @ B @ C ) )
=> ( ! [B: $i] :
? [C: $i] : ( A @ B @ C )
& ( ( ^ [B: $i] : $true )
= ( ^ [B: $i] :
? [C: $i] : ( A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A != B )
| ( sk1 @ A @ B ) )
& ( ~ ( sk1 @ sk2 @ C )
| ( ( ^ [D: $i] : $true )
!= ( ^ [D: $i] :
? [E: $i] : ( sk1 @ E @ D ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( sk1 @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( sk1 @ A @ B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(8,plain,
! [A: $i] : ( sk1 @ A @ A ),
inference(simp,[status(thm)],[7]) ).
thf(6,plain,
! [A: $i] :
( ~ ( sk1 @ sk2 @ A )
| ( ( ^ [B: $i] : $true )
!= ( ^ [B: $i] :
? [C: $i] : ( sk1 @ C @ B ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i] :
( ( ( ^ [B: $i] :
? [C: $i] : ( sk1 @ C @ B ) )
!= ( ^ [B: $i] : $true ) )
| ~ ( sk1 @ sk2 @ A ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
! [A: $i] :
( ( ( ^ [B: $i] :
? [C: $i] : ( sk1 @ C @ B ) )
!= ( ^ [B: $i] : $true ) )
| ~ ( sk1 @ sk2 @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i] :
? [D: $i] : ( sk1 @ D @ C ) )
!= ( ^ [C: $i] : $true ) )
| ~ $true
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,10]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( ( ^ [C: $i] :
? [D: $i] : ( sk1 @ D @ C ) )
!= ( ^ [C: $i] : $true ) )
| ( ( sk1 @ A @ A )
!= ( sk1 @ sk2 @ B ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(14,plain,
( ( ^ [A: $i] :
? [B: $i] : ( sk1 @ B @ A ) )
!= ( ^ [A: $i] : $true ) ),
inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(16,plain,
~ ? [A: $i] : ( sk1 @ A @ sk4 ),
inference(func_ext,[status(esa)],[14]) ).
thf(17,plain,
! [A: $i] :
~ ( sk1 @ A @ sk4 ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( sk1 @ A @ A )
!= ( sk1 @ B @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[8,17]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( sk1 @ A @ A )
!= ( sk1 @ B @ sk4 ) ),
inference(simp,[status(thm)],[18]) ).
thf(20,plain,
$false,
inference(pattern_uni,[status(thm)],[19:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET669^3 : TPTP v9.3.1. Released v3.6.0.
% 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 : n003.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 13:42:13 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.57/1.07 % [INFO] Parsing done (275ms).
% 1.57/1.08 % [INFO] Running in sequential loop mode.
% 2.35/1.48 % [INFO] eprover registered as external prover.
% 2.35/1.49 % [INFO] Scanning for conjecture ...
% 2.79/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.02/1.70 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.02/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 3.02/1.70 % [INFO] Type checking passed.
% 3.02/1.71 % [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 ...
% 4.39/2.38 % [INFO] Killing All external provers ...
% 4.39/2.39 % Time passed: 2030ms (effective reasoning time: 1295ms)
% 4.39/2.39 % 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)>
% 4.39/2.39 % Axioms used in derivation (0):
% 4.39/2.39 % No. of inferences in proof: 18
% 4.39/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2030 ms resp. 1295 ms w/o parsing
% 4.71/2.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.71/2.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------