TSTP Solution File: SET926^11 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET926^11 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 69.05s 11.63s
% Output : Refutation 69.05s
% 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(19,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(23,plain,
eiw_di @ sk1 @ mactual,
inference(cnf,[status(esa)],[19]) ).
thf(22,plain,
eiw_di @ sk2 @ mactual,
inference(cnf,[status(esa)],[19]) ).
thf(17,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(54,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)],[17]) ).
thf(55,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)],[54]) ).
thf(56,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)],[55]) ).
thf(237,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)],[22,56]) ).
thf(238,plain,
! [A: $i] :
( ( ( in @ A @ sk2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ sk2 ) @ empty_set @ mactual ) )
| ~ ( eiw_di @ A @ mactual ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(18139,plain,
! [A: $i] :
( ( ( in @ A @ sk2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ sk2 ) @ empty_set @ mactual ) )
| ( ( eiw_di @ sk1 @ mactual )
!= ( eiw_di @ A @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[23,238]) ).
thf(18140,plain,
( ( in @ sk1 @ sk2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ empty_set @ mactual ) ),
inference(pattern_uni,[status(thm)],[18139:[bind(A,$thf( sk1 ))]]) ).
thf(21,plain,
~ ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ empty_set @ mactual ),
inference(cnf,[status(esa)],[19]) ).
thf(15,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(49,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)],[15]) ).
thf(50,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)],[49]) ).
thf(51,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)],[50]) ).
thf(20,plain,
~ ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ ( singleton @ sk1 ) @ mactual ),
inference(cnf,[status(esa)],[19]) ).
thf(1252,plain,
! [B: $i,A: $i] :
( ~ ( eiw_di @ A @ mactual )
| ~ ( eiw_di @ B @ mactual )
| ( in @ A @ B @ mactual )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) @ mactual )
!= ( qmltpeq @ ( set_difference @ ( singleton @ sk1 ) @ sk2 ) @ ( singleton @ sk1 ) @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[51,20]) ).
thf(1253,plain,
( ~ ( eiw_di @ sk1 @ mactual )
| ~ ( eiw_di @ sk2 @ mactual )
| ( in @ sk1 @ sk2 @ mactual ) ),
inference(pattern_uni,[status(thm)],[1252:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1642,plain,
( ~ $true
| ~ $true
| ( in @ sk1 @ sk2 @ mactual ) ),
inference(rewrite,[status(thm)],[1253,22,23]) ).
thf(1643,plain,
in @ sk1 @ sk2 @ mactual,
inference(simp,[status(thm)],[1642]) ).
thf(18663,plain,
~ $true,
inference(rewrite,[status(thm)],[18140,21,1643]) ).
thf(18664,plain,
$false,
inference(simp,[status(thm)],[18663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SET926^11 : TPTP v8.2.0. Released v8.1.0.
% 0.06/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n003.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 20 11:55:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.00 % [INFO] Parsing done (145ms).
% 1.31/1.01 % [INFO] Running in sequential loop mode.
% 1.73/1.23 % [INFO] nitpick registered as external prover.
% 1.87/1.24 % [INFO] Scanning for conjecture ...
% 1.97/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.26/1.36 % [INFO] Axiom selection finished. Selected 16 axioms (removed 2 axioms).
% 2.26/1.39 % [INFO] Problem is higher-order (TPTP THF).
% 2.26/1.39 % [INFO] Type checking passed.
% 2.26/1.39 % [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 ...
% 69.05/11.63 % [INFO] Killing All external provers ...
% 69.05/11.63 % Time passed: 11104ms (effective reasoning time: 10612ms)
% 69.05/11.63 % 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)>
% 69.05/11.63 % Axioms used in derivation (2): l36_zfmisc_1, l34_zfmisc_1
% 69.05/11.63 % No. of inferences in proof: 25
% 69.05/11.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11104 ms resp. 10612 ms w/o parsing
% 69.05/11.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.05/11.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------