TSTP Solution File: SET926^11 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET926^11 : TPTP v8.1.2. Released v8.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pGqFqLbhTj true
% Computer : n017.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 : Thu Aug 31 16:16:51 EDT 2023
% Result : Theorem 0.53s 0.83s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 31
% Syntax : Number of formulae : 66 ( 24 unt; 15 typ; 0 def)
% Number of atoms : 170 ( 17 equ; 5 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 567 ( 38 ~; 29 |; 0 &; 444 @)
% ( 15 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 7 con; 0-3 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 80 ( 51 ^; 29 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(qmltpeq_type,type,
qmltpeq: $i > $i > mworld > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(mactual_type,type,
mactual: mworld ).
thf(mequiv_type,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mor_type,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(eiw_di_type,type,
eiw_di: $i > mworld > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf('#sk5_type',type,
'#sk5': $i ).
thf(mnot_type,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mlocal_type,type,
mlocal: ( mworld > $o ) > $o ).
thf(in_type,type,
in: $i > $i > mworld > $o ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(mforall_di_type,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] :
( ( eiw_di @ X @ W )
=> ( A @ X @ W ) ) ) ) ).
thf('0',plain,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] :
( ( eiw_di @ X @ W )
=> ( A @ X @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_di_def]) ).
thf('1',plain,
( mforall_di
= ( ^ [V_1: $i > mworld > $o,V_2: mworld] :
! [X4: $i] :
( ( eiw_di @ X4 @ V_2 )
=> ( V_1 @ X4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(mor_def,axiom,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ) ).
thf('2',plain,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor_def]) ).
thf('3',plain,
( mor
= ( ^ [V_1: mworld > $o,V_2: mworld > $o,V_3: mworld] :
( ( V_1 @ V_3 )
| ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
thf('4',plain,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
inference(simplify_rw_rule,[status(thm)],[mlocal_def]) ).
thf('5',plain,
( mlocal
= ( ^ [V_1: mworld > $o] : ( V_1 @ mactual ) ) ),
define([status(thm)]) ).
thf(t69_zfmisc_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 ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( eiw_di @ X4 @ mactual )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ empty_set @ mactual ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( eiw_di @ X4 @ mactual )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ empty_set @ mactual ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl18,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !!
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl110,plain,
~ ( ( eiw_di @ '#sk4' @ mactual )
=> ( !!
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ Y0 ) @ ( singleton @ '#sk4' ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl112,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ Y0 ) @ ( singleton @ '#sk4' ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ Y0 ) @ empty_set @ mactual ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl113,plain,
~ ( ( eiw_di @ '#sk5' @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ '#sk5' ) @ ( singleton @ '#sk4' ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ '#sk5' ) @ empty_set @ mactual ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl115,plain,
~ ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ '#sk5' ) @ ( singleton @ '#sk4' ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ '#sk5' ) @ empty_set @ mactual ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl117,plain,
~ ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ '#sk5' ) @ empty_set @ mactual ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl115]) ).
thf(mequiv_def,axiom,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ) ).
thf('6',plain,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv_def]) ).
thf('7',plain,
( mequiv
= ( ^ [V_1: mworld > $o,V_2: mworld > $o,V_3: mworld] :
( ( V_1 @ V_3 )
<=> ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(l36_zfmisc_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
( ( eiw_di @ X4 @ mactual )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ empty_set @ mactual )
<=> ( in @ X4 @ X6 @ mactual ) ) ) ) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !!
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual )
<=> ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl132,plain,
! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( !!
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ mactual )
<=> ( in @ X2 @ Y0 @ mactual ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl133,plain,
! [X2: $i] :
( ~ ( eiw_di @ X2 @ mactual )
| ( !!
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ empty_set @ mactual )
<=> ( in @ X2 @ Y0 @ mactual ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl134,plain,
! [X2: $i,X4: $i] :
( ( ( eiw_di @ X4 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X4 ) @ empty_set @ mactual )
<=> ( in @ X2 @ X4 @ mactual ) ) )
| ~ ( eiw_di @ X2 @ mactual ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl135,plain,
! [X2: $i,X4: $i] :
( ~ ( eiw_di @ X4 @ mactual )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X4 ) @ empty_set @ mactual )
<=> ( in @ X2 @ X4 @ mactual ) )
| ~ ( eiw_di @ X2 @ mactual ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl134]) ).
thf(zip_derived_cl136,plain,
! [X2: $i,X4: $i] :
( ~ ( eiw_di @ X4 @ mactual )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X4 ) @ empty_set @ mactual )
= ( in @ X2 @ X4 @ mactual ) )
| ~ ( eiw_di @ X2 @ mactual ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl141,plain,
( ~ ( in @ '#sk4' @ '#sk5' @ mactual )
| ~ ( eiw_di @ '#sk4' @ mactual )
| ~ ( eiw_di @ '#sk5' @ mactual ) ),
inference('sup+',[status(thm)],[zip_derived_cl117,zip_derived_cl136]) ).
thf(zip_derived_cl111,plain,
eiw_di @ '#sk4' @ mactual,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl114,plain,
eiw_di @ '#sk5' @ mactual,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl149,plain,
~ ( in @ '#sk4' @ '#sk5' @ mactual ),
inference(demod,[status(thm)],[zip_derived_cl141,zip_derived_cl111,zip_derived_cl114]) ).
thf(zip_derived_cl116,plain,
~ ( qmltpeq @ ( set_difference @ ( singleton @ '#sk4' ) @ '#sk5' ) @ ( singleton @ '#sk4' ) @ mactual ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl115]) ).
thf(mnot_def,axiom,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ) ).
thf('8',plain,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot_def]) ).
thf('9',plain,
( mnot
= ( ^ [V_1: mworld > $o,V_2: mworld] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf(l34_zfmisc_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
( ( eiw_di @ X4 @ mactual )
=> ! [X6: $i] :
( ( eiw_di @ X6 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ mactual )
<=> ~ ( in @ X4 @ X6 @ mactual ) ) ) ) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !!
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
<=> ( (~) @ ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl155,plain,
! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( !!
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ mactual )
<=> ( (~) @ ( in @ X2 @ Y0 @ mactual ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl156,plain,
! [X2: $i] :
( ~ ( eiw_di @ X2 @ mactual )
| ( !!
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ mactual )
<=> ( (~) @ ( in @ X2 @ Y0 @ mactual ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl155]) ).
thf(zip_derived_cl157,plain,
! [X2: $i,X4: $i] :
( ( ( eiw_di @ X4 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X4 ) @ ( singleton @ X2 ) @ mactual )
<=> ( (~) @ ( in @ X2 @ X4 @ mactual ) ) ) )
| ~ ( eiw_di @ X2 @ mactual ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl156]) ).
thf(zip_derived_cl158,plain,
! [X2: $i,X4: $i] :
( ~ ( eiw_di @ X4 @ mactual )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X4 ) @ ( singleton @ X2 ) @ mactual )
<=> ( (~) @ ( in @ X2 @ X4 @ mactual ) ) )
| ~ ( eiw_di @ X2 @ mactual ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl157]) ).
thf(zip_derived_cl159,plain,
! [X2: $i,X4: $i] :
( ~ ( eiw_di @ X4 @ mactual )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X4 ) @ ( singleton @ X2 ) @ mactual )
!= ( in @ X2 @ X4 @ mactual ) )
| ~ ( eiw_di @ X2 @ mactual ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl158]) ).
thf(zip_derived_cl160,plain,
! [X2: $i,X4: $i] :
( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X4 ) @ ( singleton @ X2 ) @ mactual )
| ( in @ X2 @ X4 @ mactual )
| ~ ( eiw_di @ X2 @ mactual )
| ~ ( eiw_di @ X4 @ mactual ) ),
inference(eq_elim,[status(thm)],[zip_derived_cl159]) ).
thf(zip_derived_cl241,plain,
( ~ ( eiw_di @ '#sk5' @ mactual )
| ~ ( eiw_di @ '#sk4' @ mactual )
| ( in @ '#sk4' @ '#sk5' @ mactual ) ),
inference('sup+',[status(thm)],[zip_derived_cl116,zip_derived_cl160]) ).
thf(zip_derived_cl114_001,plain,
eiw_di @ '#sk5' @ mactual,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl111_002,plain,
eiw_di @ '#sk4' @ mactual,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl252,plain,
in @ '#sk4' @ '#sk5' @ mactual,
inference(demod,[status(thm)],[zip_derived_cl241,zip_derived_cl114,zip_derived_cl111]) ).
thf(zip_derived_cl262,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl149,zip_derived_cl252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET926^11 : TPTP v8.1.2. Released v8.1.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pGqFqLbhTj true
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 10:28:56 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.20/0.66 % Total configuration time : 828
% 0.20/0.66 % Estimated wc time : 1656
% 0.20/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.53/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.53/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.53/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.53/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.53/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.53/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.53/0.83 % Solved by lams/35_full_unif4.sh.
% 0.53/0.83 % done 45 iterations in 0.086s
% 0.53/0.83 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.53/0.83 % SZS output start Refutation
% See solution above
% 0.53/0.83
% 0.53/0.83
% 0.53/0.83 % Terminating...
% 0.55/0.88 % Runner terminated.
% 0.55/0.89 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------