TSTP Solution File: LCL626^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL626^1 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.PrSIy1eXLW true
% Computer : n023.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 09:00:26 EDT 2023
% Result : Theorem 1.34s 0.74s
% Output : Refutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 31
% Syntax : Number of formulae : 69 ( 29 unt; 13 typ; 0 def)
% Number of atoms : 193 ( 21 equ; 4 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 451 ( 32 ~; 16 |; 18 &; 291 @)
% ( 0 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 13 usr; 8 con; 0-3 aty)
% ( 37 !!; 1 ??; 0 @@+; 0 @@-)
% Number of variables : 143 ( 77 ^; 62 !; 4 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(upwards_well_founded_type,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(transitive_type,type,
transitive: ( $i > $i > $o ) > $o ).
thf('#sk5_type',type,
'#sk5': $i ).
thf(mimpl_type,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(r_type,type,
r: $i > $i > $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(mvalid,axiom,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ) ).
thf('0',plain,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('1',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(mbox,axiom,
( mbox
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
! [Y: $i] :
( ( R @ X @ Y )
=> ( P @ Y ) ) ) ) ).
thf('2',plain,
( mbox
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
! [Y: $i] :
( ( R @ X @ Y )
=> ( P @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox]) ).
thf('3',plain,
( mbox
= ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
! [X4: $i] :
( ( V_1 @ V_3 @ X4 )
=> ( V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mimpl,axiom,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
thf(mor,axiom,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ) ).
thf('4',plain,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('5',plain,
( mor
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
| ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(mnot,axiom,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ) ).
thf('6',plain,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('7',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('8',plain,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimpl,'5','7']) ).
thf('9',plain,
( mimpl
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf(k4,conjecture,
! [X: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i > $o,X6: $i] :
( ! [X10: $i] :
( ( r @ X6 @ X10 )
=> ! [X12: $i] :
( ( r @ X10 @ X12 )
=> ! [X14: $i] :
( ( r @ X12 @ X14 )
=> ( X4 @ X14 ) ) ) )
| ~ ! [X8: $i] :
( ( r @ X6 @ X8 )
=> ( X4 @ X8 ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i > $o,X6: $i] :
( ! [X10: $i] :
( ( r @ X6 @ X10 )
=> ! [X12: $i] :
( ( r @ X10 @ X12 )
=> ! [X14: $i] :
( ( r @ X12 @ X14 )
=> ( X4 @ X14 ) ) ) )
| ~ ! [X8: $i] :
( ( r @ X6 @ X8 )
=> ( X4 @ X8 ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( r @ Y2 @ Y3 )
=> ( !!
@ ^ [Y4: $i] :
( ( r @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( r @ Y2 @ Y3 )
=> ( '#sk1' @ Y3 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( '#sk1' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( r @ '#sk2' @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( '#sk1' @ Y2 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( r @ '#sk2' @ Y0 )
=> ( '#sk1' @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( r @ '#sk2' @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( r @ Y1 @ Y2 )
=> ( '#sk1' @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl6,plain,
~ ( ( r @ '#sk2' @ '#sk3' )
=> ( !!
@ ^ [Y0: $i] :
( ( r @ '#sk3' @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( '#sk1' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl9,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( r @ '#sk3' @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( '#sk1' @ Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
~ ( ( r @ '#sk3' @ '#sk4' )
=> ( !!
@ ^ [Y0: $i] :
( ( r @ '#sk4' @ Y0 )
=> ( '#sk1' @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl13,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( r @ '#sk4' @ Y0 )
=> ( '#sk1' @ Y0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl14,plain,
~ ( ( r @ '#sk4' @ '#sk5' )
=> ( '#sk1' @ '#sk5' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl16,plain,
~ ( '#sk1' @ '#sk5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl8,plain,
r @ '#sk2' @ '#sk3',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl12,plain,
r @ '#sk3' @ '#sk4',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(upwards_well_founded,axiom,
( upwards_well_founded
= ( ^ [R: $i > $i > $o] :
! [X: $i > $o,Z: $i] :
( ( X @ Z )
=> ? [Y: $i] :
( ! [W: $i] :
( ( R @ Y @ Y )
=> ~ ( X @ W ) )
& ( X @ Y ) ) ) ) ) ).
thf('10',plain,
( upwards_well_founded
= ( ^ [R: $i > $i > $o] :
! [X: $i > $o,Z: $i] :
( ( X @ Z )
=> ? [Y: $i] :
( ! [W: $i] :
( ( R @ Y @ Y )
=> ~ ( X @ W ) )
& ( X @ Y ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[upwards_well_founded]) ).
thf('11',plain,
( upwards_well_founded
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i > $o,X6: $i] :
( ( X4 @ X6 )
=> ? [X8: $i] :
( ! [X10: $i] :
( ( V_1 @ X8 @ X8 )
=> ~ ( X4 @ X10 ) )
& ( X4 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(transitive,axiom,
( transitive
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ Z ) )
=> ( R @ X @ Z ) ) ) ) ).
thf('12',plain,
( transitive
= ( ^ [R: $i > $i > $o] :
! [X: $i,Y: $i,Z: $i] :
( ( ( R @ X @ Y )
& ( R @ Y @ Z ) )
=> ( R @ X @ Z ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[transitive]) ).
thf('13',plain,
( transitive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X6 )
& ( V_1 @ X6 @ X8 ) )
=> ( V_1 @ X4 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(upwf_trans,axiom,
( ( upwards_well_founded @ r )
& ( transitive @ r ) ) ).
thf(zf_stmt_2,axiom,
( ! [X12: $i,X14: $i,X16: $i] :
( ( ( r @ X14 @ X16 )
& ( r @ X12 @ X14 ) )
=> ( r @ X12 @ X16 ) )
& ! [X4: $i > $o,X6: $i] :
( ( X4 @ X6 )
=> ? [X8: $i] :
( ( X4 @ X8 )
& ! [X10: $i] :
( ( r @ X8 @ X8 )
=> ~ ( X4 @ X10 ) ) ) ) ) ).
thf(zip_derived_cl0,plain,
( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( r @ Y1 @ Y2 )
& ( r @ Y0 @ Y1 ) )
=> ( r @ Y0 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ??
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
& ( !!
@ ^ [Y3: $i] :
( ( r @ Y2 @ Y2 )
=> ( (~) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl21,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( r @ Y1 @ Y2 )
& ( r @ Y0 @ Y1 ) )
=> ( r @ Y0 @ Y2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl23,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( r @ Y0 @ Y1 )
& ( r @ X2 @ Y0 ) )
=> ( r @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( r @ X4 @ Y0 )
& ( r @ X2 @ X4 ) )
=> ( r @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( r @ X4 @ X6 )
& ( r @ X2 @ X4 ) )
=> ( r @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( r @ X4 @ X6 )
& ( r @ X2 @ X4 ) )
| ( r @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( r @ X4 @ X6 )
| ~ ( r @ X2 @ X4 )
| ( r @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl39,plain,
! [X0: $i] :
( ( r @ X0 @ '#sk4' )
| ~ ( r @ X0 @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl32]) ).
thf(zip_derived_cl68,plain,
r @ '#sk2' @ '#sk4',
inference('sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl39]) ).
thf(zip_derived_cl15,plain,
r @ '#sk4' @ '#sk5',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl32_001,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( r @ X4 @ X6 )
| ~ ( r @ X2 @ X4 )
| ( r @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl38,plain,
! [X0: $i] :
( ( r @ X0 @ '#sk5' )
| ~ ( r @ X0 @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl32]) ).
thf(zip_derived_cl71,plain,
r @ '#sk2' @ '#sk5',
inference('sup-',[status(thm)],[zip_derived_cl68,zip_derived_cl38]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( ( r @ '#sk2' @ Y0 )
=> ( '#sk1' @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl7,plain,
! [X2: $i] :
( ( r @ '#sk2' @ X2 )
=> ( '#sk1' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl10,plain,
! [X2: $i] :
( ~ ( r @ '#sk2' @ X2 )
| ( '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl78,plain,
'#sk1' @ '#sk5',
inference('sup-',[status(thm)],[zip_derived_cl71,zip_derived_cl10]) ).
thf(zip_derived_cl84,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl16,zip_derived_cl78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL626^1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.10/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.PrSIy1eXLW true
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Aug 25 07:24:27 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.17/0.33 % Running in HO mode
% 0.17/0.57 % Total configuration time : 828
% 0.17/0.57 % Estimated wc time : 1656
% 0.17/0.57 % Estimated cpu time (8 cpus) : 207.0
% 1.02/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 1.02/0.66 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.02/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.02/0.67 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.02/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.02/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.02/0.68 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.02/0.70 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.02/0.71 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.02/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 1.34/0.74 % Solved by lams/35_full_unif4.sh.
% 1.34/0.74 % done 23 iterations in 0.030s
% 1.34/0.74 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.34/0.74 % SZS output start Refutation
% See solution above
% 1.34/0.74
% 1.34/0.74
% 1.34/0.74 % Terminating...
% 1.34/0.78 % Runner terminated.
% 1.55/0.79 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------