TSTP Solution File: NUM669^4 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM669^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xFM9ULYk9K true
% Computer : n008.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 12:43:17 EDT 2023
% Result : Theorem 9.42s 1.85s
% Output : Refutation 9.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 47
% Syntax : Number of formulae : 78 ( 42 unt; 18 typ; 0 def)
% Number of atoms : 167 ( 55 equ; 2 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 255 ( 23 ~; 6 |; 0 &; 201 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 7 con; 0-3 aty)
% ( 5 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 88 ( 73 ^; 15 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_29_ii_type,type,
d_29_ii: $i > $i > $o ).
thf(n_1_type,type,
n_1: $i ).
thf(nat_type,type,
nat: $i ).
thf(is_of_type,type,
is_of: $i > ( $i > $o ) > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf('#sk693_type',type,
'#sk693': $i ).
thf(non_type,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(l_some_type,type,
l_some: $i > ( $i > $o ) > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(imp_type,type,
imp: $o > $o > $o ).
thf(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(diffprop_type,type,
diffprop: $i > $i > $i > $o ).
thf(n_some_type,type,
n_some: ( $i > $o ) > $o ).
thf(ordsucc_type,type,
ordsucc: $i > $i ).
thf(d_not_type,type,
d_not: $o > $o ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf(n_pl_type,type,
n_pl: $i > $i > $i ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).
thf('0',plain,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).
thf('1',plain,
( e_is
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
define([status(thm)]) ).
thf('2',plain,
( n_is
= ( e_is @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_is,'1']) ).
thf('3',plain,
( n_is
= ( e_is @ nat ) ),
define([status(thm)]) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ) ).
thf('4',plain,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).
thf('5',plain,
( is_of
= ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
define([status(thm)]) ).
thf('6',plain,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_all_of,'5']) ).
thf('7',plain,
( all_of
= ( ^ [V_1: $i > $o,V_2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ V_1 )
=> ( V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(satz4a,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] : ( n_is @ ( n_pl @ X0 @ n_1 ) @ ( ordsucc @ X0 ) ) ) ).
thf(zf_stmt_0,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ( ( n_pl @ X4 @ n_1 )
= ( ordsucc @ X4 ) ) ) ).
thf(zip_derived_cl123,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_pl @ Y0 @ n_1 )
= ( ordsucc @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl847,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( ( n_pl @ X2 @ n_1 )
= ( ordsucc @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl123]) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ) ).
thf(zip_derived_cl108,plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(cnf,[status(esa)],[def_n_1]) ).
thf(zip_derived_cl848,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( ( n_pl @ X2 @ ( ordsucc @ emptyset ) )
= ( ordsucc @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl847,zip_derived_cl108]) ).
thf(zip_derived_cl849,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( ( n_pl @ X2 @ ( ordsucc @ emptyset ) )
= ( ordsucc @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl848]) ).
thf(zip_derived_cl850,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( ( n_pl @ X2 @ ( ordsucc @ emptyset ) )
= ( ordsucc @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl849]) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ).
thf('8',plain,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_diffprop,'3','1']) ).
thf('9',plain,
( diffprop
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( n_is @ V_1 @ ( n_pl @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X0: $i,X1: $i > $o] :
( d_not
@ ( all_of
@ ^ [X2: $i] : ( in @ X2 @ X0 )
@ ( non @ X0 @ X1 ) ) ) ) ) ).
thf(def_non,axiom,
( non
= ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).
thf(def_imp,axiom,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ) ).
thf('10',plain,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_imp]) ).
thf('11',plain,
( imp
= ( ^ [V_1: $o,V_2: $o] :
( V_1
=> V_2 ) ) ),
define([status(thm)]) ).
thf('12',plain,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_not,'11']) ).
thf('13',plain,
( d_not
= ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
define([status(thm)]) ).
thf('14',plain,
( non
= ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_non,'13','11']) ).
thf('15',plain,
( non
= ( ^ [V_1: $i,V_2: $i > $o,V_3: $i] : ( d_not @ ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('16',plain,
( l_some
= ( ^ [X0: $i,X1: $i > $o] :
( d_not
@ ( all_of
@ ^ [X2: $i] : ( in @ X2 @ X0 )
@ ( non @ X0 @ X1 ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_some,'15','13','11','7','5']) ).
thf('17',plain,
( l_some
= ( ^ [V_1: $i,V_2: $i > $o] :
( d_not
@ ( all_of
@ ^ [V_3: $i] : ( in @ V_3 @ V_1 )
@ ( non @ V_1 @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf('18',plain,
( n_some
= ( l_some @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_some,'17','15','13','11','7','5']) ).
thf('19',plain,
( n_some
= ( l_some @ nat ) ),
define([status(thm)]) ).
thf('20',plain,
( d_29_ii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_29_ii,'9','19','3','1','17','15','13','11','7','5']) ).
thf('21',plain,
( d_29_ii
= ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(satz18b,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] : ( d_29_ii @ ( ordsucc @ X0 ) @ X0 ) ) ).
thf(zf_stmt_1,conjecture,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ~ ! [X6: $i] :
( ( in @ X6 @ nat )
=> ( ( ordsucc @ X4 )
!= ( n_pl @ X4 @ X6 ) ) ) ) ).
thf(zf_stmt_2,negated_conjecture,
~ ! [X4: $i] :
( ( in @ X4 @ nat )
=> ~ ! [X6: $i] :
( ( in @ X6 @ nat )
=> ( ( ordsucc @ X4 )
!= ( n_pl @ X4 @ X6 ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl163,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( ordsucc @ Y0 )
!= ( n_pl @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl1022,plain,
~ ( ( in @ '#sk693' @ nat )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ordsucc @ '#sk693' )
!= ( n_pl @ '#sk693' @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl163]) ).
thf(zip_derived_cl1024,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( ordsucc @ '#sk693' )
!= ( n_pl @ '#sk693' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1022]) ).
thf(zip_derived_cl1025,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( ( ordsucc @ '#sk693' )
!= ( n_pl @ '#sk693' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1024]) ).
thf(zip_derived_cl1026,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( ( ordsucc @ '#sk693' )
!= ( n_pl @ '#sk693' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1025]) ).
thf(zip_derived_cl1027,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( ( ordsucc @ '#sk693' )
!= ( n_pl @ '#sk693' @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl1026]) ).
thf(zip_derived_cl1161,plain,
( ( ( ordsucc @ '#sk693' )
!= ( ordsucc @ '#sk693' ) )
| ~ ( in @ '#sk693' @ nat )
| ~ ( in @ ( ordsucc @ emptyset ) @ nat ) ),
inference('sup-',[status(thm)],[zip_derived_cl850,zip_derived_cl1027]) ).
thf(zip_derived_cl1023,plain,
in @ '#sk693' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1022]) ).
thf(n_1_p,axiom,
( is_of @ n_1
@ ^ [X0: $i] : ( in @ X0 @ nat ) ) ).
thf(zf_stmt_3,axiom,
in @ n_1 @ nat ).
thf(zip_derived_cl109,plain,
in @ n_1 @ nat,
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl108_001,plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(cnf,[status(esa)],[def_n_1]) ).
thf(zip_derived_cl164,plain,
in @ ( ordsucc @ emptyset ) @ nat,
inference(demod,[status(thm)],[zip_derived_cl109,zip_derived_cl108]) ).
thf(zip_derived_cl1163,plain,
( ( ordsucc @ '#sk693' )
!= ( ordsucc @ '#sk693' ) ),
inference(demod,[status(thm)],[zip_derived_cl1161,zip_derived_cl1023,zip_derived_cl164]) ).
thf(zip_derived_cl1164,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl1163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM669^4 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.xFM9ULYk9K true
% 0.14/0.35 % Computer : n008.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 : Fri Aug 25 15:05:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.66 % Total configuration time : 828
% 0.22/0.66 % Estimated wc time : 1656
% 0.22/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.79 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.38/0.83 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 9.42/1.85 % Solved by lams/35_full_unif4.sh.
% 9.42/1.85 % done 210 iterations in 1.082s
% 9.42/1.85 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 9.42/1.85 % SZS output start Refutation
% See solution above
% 9.42/1.85
% 9.42/1.85
% 9.42/1.85 % Terminating...
% 10.09/1.97 % Runner terminated.
% 10.09/1.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------