TSTP Solution File: SET926^20 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET926^20 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 03:07:23 EDT 2024
% Result : Theorem 45.69s 7.74s
% Output : Refutation 45.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 45 ( 13 unt; 15 typ; 5 def)
% Number of atoms : 110 ( 19 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 321 ( 28 ~; 21 |; 0 &; 265 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 40 ( 19 ^ 21 !; 0 ?; 40 :)
% 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(mnot_type,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
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(eiw_di_type,type,
eiw_di: $i > mworld > $o ).
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] :
( ( eiw_di @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(empty_set_type,type,
empty_set: $i ).
thf(qmltpeq_type,type,
qmltpeq: $i > $i > mworld > $o ).
thf(in_type,type,
in: $i > $i > mworld > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
eiw_di @ sk1 @ mactual,
inference(cnf,[status(esa)],[21]) ).
thf(24,plain,
eiw_di @ sk2 @ mactual,
inference(cnf,[status(esa)],[21]) ).
thf(18,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(58,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual )
= ( in @ A @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual )
= ( in @ A @ B @ mactual ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( ( in @ A @ B @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual ) )
| ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(2594,plain,
! [B: $i,A: $i] :
( ( ( in @ A @ B @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set @ mactual ) )
| ~ ( eiw_di @ A @ mactual )
| ( ( eiw_di @ sk2 @ mactual )
!= ( eiw_di @ B @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[24,60]) ).
thf(2595,plain,
! [A: $i] :
( ( ( in @ A @ sk2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ sk2 ) @ empty_set @ mactual ) )
| ~ ( eiw_di @ A @ mactual ) ),
inference(pattern_uni,[status(thm)],[2594:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(4128,plain,
! [A: $i] :
( ( ( in @ A @ sk2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ sk2 ) @ empty_set @ mactual ) )
| ( ( eiw_di @ sk1 @ mactual )
!= ( eiw_di @ A @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[25,2595]) ).
thf(4129,plain,
( ( in @ sk1 @ sk2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ empty_set @ mactual ) ),
inference(pattern_uni,[status(thm)],[4128:[bind(A,$thf( sk1 ))]]) ).
thf(23,plain,
~ ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ empty_set @ mactual ),
inference(cnf,[status(esa)],[21]) ).
thf(16,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(53,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual )
= ( ~ ( in @ A @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual )
= ( ~ ( in @ A @ B @ mactual ) ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual )
= ( ~ ( in @ A @ B @ mactual ) ) )
| ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(22,plain,
~ ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ ( singleton @ sk1 ) @ mactual ),
inference(cnf,[status(esa)],[21]) ).
thf(1694,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ( in @ A @ B @ mactual )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual )
!= ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ ( singleton @ sk1 ) @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[55,22]) ).
thf(1695,plain,
( ~ ( eiw_di @ sk1 @ mactual )
| ~ ( eiw_di @ sk2 @ mactual )
| ( in @ sk1 @ sk2 @ mactual ) ),
inference(pattern_uni,[status(thm)],[1694:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(2091,plain,
( ~ $true
| ~ $true
| ( in @ sk1 @ sk2 @ mactual ) ),
inference(rewrite,[status(thm)],[1695,24,25]) ).
thf(2092,plain,
in @ sk1 @ sk2 @ mactual,
inference(simp,[status(thm)],[2091]) ).
thf(4319,plain,
~ $true,
inference(rewrite,[status(thm)],[4129,23,2092]) ).
thf(4320,plain,
$false,
inference(simp,[status(thm)],[4319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SET926^20 : TPTP v8.2.0. Released v8.1.0.
% 0.17/0.18 % Command : run_Leo-III %s %d
% 0.18/0.40 % Computer : n025.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Mon May 20 11:05:54 EDT 2024
% 0.18/0.40 % CPUTime :
% 1.01/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.45/1.09 % [INFO] Parsing done (167ms).
% 1.45/1.09 % [INFO] Running in sequential loop mode.
% 2.03/1.37 % [INFO] nitpick registered as external prover.
% 2.03/1.37 % [INFO] Scanning for conjecture ...
% 2.35/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.52/1.51 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.52/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.52/1.54 % [INFO] Type checking passed.
% 2.52/1.54 % [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 ...
% 45.69/7.73 % [INFO] Killing All external provers ...
% 45.69/7.74 % Time passed: 7171ms (effective reasoning time: 6635ms)
% 45.69/7.74 % 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)>
% 45.69/7.74 % Axioms used in derivation (2): l36_zfmisc_1, l34_zfmisc_1
% 45.69/7.74 % No. of inferences in proof: 25
% 45.69/7.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7171 ms resp. 6635 ms w/o parsing
% 45.73/7.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 45.73/7.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------