%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET027^3 : TPTP v9.3.1. Released v8.1.0.
% 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 : n004.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 08:22:52 AM UTC 2026
% Result : Theorem 2.61s 1.23s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 15 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 52 ( 7 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 87 ( 2 ~; 0 |; 2 &; 80 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 34 ( 22 ^; 10 !; 2 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_decl,type,
mrel: mworld > mworld > $o ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mand_decl,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_decl,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mequiv_decl,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mforall_di_decl,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(member_decl,type,
member: $i > $i > mworld > $o ).
thf(subset_decl,type,
subset: $i > $i > mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] : ( A @ C @ B ) ) ) ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ C ) ) @ ( subset @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ C ) ) @ ( subset @ A @ C ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B @ mactual )
& ( subset @ B @ C @ mactual ) )
=> ( subset @ A @ C @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mworld] :
? [B: mworld] : ( mrel @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_serial) ).
thf(11,plain,
! [A: mworld] :
? [B: mworld] : ( mrel @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( subset @ A @ B )
@ ( mforall_di
@ ^ [C: $i] : ( mimplies @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(13,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B @ mactual )
= ( ! [C: $i] :
( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(16,plain,
! [A: $i] : ( subset @ A @ A @ mactual ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,plain,
$false,
inference(e,[status(thm)],[6,11,13,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027^3 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.09/0.22 % Computer : n004.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 13:35:22 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.67/0.53 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.00/0.64 % [INFO] Parsing done (111ms).
% 1.00/0.65 % [INFO] Running in sequential loop mode.
% 1.42/0.84 % [INFO] eprover registered as external prover.
% 1.42/0.85 % [INFO] Scanning for conjecture ...
% 1.68/0.91 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.68/0.93 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.68/0.93 % [INFO] Problem is higher-order (TPTP THF).
% 1.68/0.93 % [INFO] Type checking passed.
% 1.68/0.93 % [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 ...
% 2.61/1.23 % External prover 'e' found a proof!
% 2.61/1.23 % [INFO] Killing All external provers ...
% 2.61/1.23 % Time passed: 919ms (effective reasoning time: 579ms)
% 2.61/1.23 % 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)>
% 2.61/1.23 % Axioms used in derivation (3): mrel_serial, subset_defn, reflexivity_of_subset
% 2.61/1.23 % No. of inferences in proof: 10
% 2.61/1.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 919 ms resp. 579 ms w/o parsing
% 2.61/1.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.61/1.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------