TSTP Solution File: SET002^3 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET002^3 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:04:45 EDT 2024
% Result : Theorem 6.18s 2.82s
% Output : Refutation 6.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 33 ( 17 unt; 11 typ; 4 def)
% Number of atoms : 82 ( 20 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 181 ( 9 ~; 6 |; 0 &; 166 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 41 ( 17 ^ 24 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mactual_type,type,
mactual: mworld ).
thf(mlocal_type,type,
mlocal: ( mworld > $o ) > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mor_type,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mor_def,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mequiv_type,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(mforall_di_type,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] : ( A @ C @ B ) ) ) ).
thf(qmltpeq_type,type,
qmltpeq: $i > $i > mworld > $o ).
thf(member_type,type,
member: $i > $i > mworld > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( qmltpeq @ A @ B )
@ ( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( qmltpeq @ A @ B @ mactual )
= ( ! [C: $i] :
( ( member @ C @ A @ mactual )
= ( member @ C @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( qmltpeq @ A @ B @ mactual )
= ( ! [C: $i] :
( ( member @ C @ A @ mactual )
= ( member @ C @ B @ mactual ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( qmltpeq @ A @ B @ mactual )
= ( ! [C: $i] :
( ( member @ C @ A @ mactual )
= ( member @ C @ B @ mactual ) ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ ( union @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ ( union @ A @ A ) @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i] : ( qmltpeq @ ( union @ A @ A ) @ A @ mactual ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
~ ( qmltpeq @ ( union @ sk1 @ sk1 ) @ sk1 @ mactual ),
inference(cnf,[status(esa)],[19]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ~ ! [C: $i] :
( ( member @ C @ A @ mactual )
= ( member @ C @ B @ mactual ) )
| ( ( qmltpeq @ A @ B @ mactual )
!= ( qmltpeq @ ( union @ sk1 @ sk1 ) @ sk1 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[36,20]) ).
thf(155,plain,
~ ! [A: $i] :
( ( member @ A @ ( union @ sk1 @ sk1 ) @ mactual )
= ( member @ A @ sk1 @ mactual ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( union @ sk1 @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(204,plain,
( ( member @ sk10 @ ( union @ sk1 @ sk1 ) @ mactual )
!= ( member @ sk10 @ sk1 @ mactual ) ),
inference(cnf,[status(esa)],[155]) ).
thf(205,plain,
( ( member @ sk10 @ ( union @ sk1 @ sk1 ) @ mactual )
!= ( member @ sk10 @ sk1 @ mactual ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(5,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ C @ ( union @ A @ B ) ) @ ( mor @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(25,plain,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) @ mactual )
= ( ( member @ C @ A @ mactual )
| ( member @ C @ B @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( union @ A @ B ) @ mactual )
= ( ( member @ C @ A @ mactual )
| ( member @ C @ B @ mactual ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ C @ ( union @ A @ B ) @ mactual )
= ( ( member @ C @ A @ mactual )
| ( member @ C @ B @ mactual ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(255,plain,
( ( ( member @ sk10 @ sk1 @ mactual )
| ( member @ sk10 @ sk1 @ mactual ) )
!= ( member @ sk10 @ sk1 @ mactual ) ),
inference(rewrite,[status(thm)],[205,27]) ).
thf(256,plain,
$false,
inference(simp,[status(thm)],[255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET002^3 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 13:06:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.01/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.13 % [INFO] Parsing done (147ms).
% 1.51/1.14 % [INFO] Running in sequential loop mode.
% 1.96/1.38 % [INFO] nitpick registered as external prover.
% 1.96/1.39 % [INFO] Scanning for conjecture ...
% 2.20/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 2.34/1.55 % [INFO] Axiom selection finished. Selected 16 axioms (removed 1 axioms).
% 2.40/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.40/1.60 % [INFO] Type checking passed.
% 2.40/1.60 % [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 ...
% 6.18/2.81 % [INFO] Killing All external provers ...
% 6.18/2.82 % Time passed: 2315ms (effective reasoning time: 1669ms)
% 6.18/2.82 % 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)>
% 6.18/2.82 % Axioms used in derivation (2): equal_member_defn, union_defn
% 6.18/2.82 % No. of inferences in proof: 18
% 6.18/2.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2315 ms resp. 1669 ms w/o parsing
% 6.18/2.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.18/2.88 % [INFO] Killing All external provers ...
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