TSTP Solution File: NUM684^4 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM684^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.X6VKFK5VWv true
% Computer : n031.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 12:43:25 EDT 2023
% Result : Theorem 20.34s 4.46s
% Output : Refutation 20.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 27
% Syntax : Number of formulae : 40 ( 13 unt; 15 typ; 0 def)
% Number of atoms : 120 ( 44 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 322 ( 41 ~; 7 |; 0 &; 257 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 86 ( 71 ^; 15 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
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(d_Sep_type,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(sk__3_type,type,
sk__3: $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(omega_type,type,
omega: $i ).
thf(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(sk__4_type,type,
sk__4: $i ).
thf(plus_type,type,
plus: $i > $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf(n_pl_type,type,
n_pl: $i > $i > $i ).
thf(def_n_pl,axiom,
( n_pl
= ( ^ [X0: $i] : ( ap @ ( plus @ X0 ) ) ) ) ).
thf('0',plain,
( n_pl
= ( ^ [X0: $i] : ( ap @ ( plus @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_pl]) ).
thf('1',plain,
( n_pl
= ( ^ [V_1: $i] : ( ap @ ( plus @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ) ).
thf(def_nat,axiom,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).
thf('2',plain,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nat]) ).
thf('3',plain,
( nat
= ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
define([status(thm)]) ).
thf('4',plain,
( n_is
= ( e_is @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_is,'3']) ).
thf('5',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('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]) ).
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(satz20e,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( n_is @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) )
=> ( n_is @ X0 @ X1 ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ! [X8: $i] :
( ( is_of @ X8
@ ^ [V_5: $i] :
( in @ V_5
@ ( d_Sep @ omega
@ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
=> ( ( e_is
@ ( d_Sep @ omega
@ ^ [V_7: $i] : ( V_7 != emptyset ) )
@ ( ap @ ( plus @ X8 ) @ X4 )
@ ( ap @ ( plus @ X8 ) @ X6 ) )
=> ( e_is
@ ( d_Sep @ omega
@ ^ [V_8: $i] : ( V_8 != emptyset ) )
@ X4
@ X6 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ! [X8: $i] :
( ( is_of @ X8
@ ^ [V_5: $i] :
( in @ V_5
@ ( d_Sep @ omega
@ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
=> ( ( e_is
@ ( d_Sep @ omega
@ ^ [V_7: $i] : ( V_7 != emptyset ) )
@ ( ap @ ( plus @ X8 ) @ X4 )
@ ( ap @ ( plus @ X8 ) @ X6 ) )
=> ( e_is
@ ( d_Sep @ omega
@ ^ [V_8: $i] : ( V_8 != emptyset ) )
@ X4
@ X6 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl53,plain,
( e_is
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ( ap @ ( plus @ sk__4 ) @ sk__2 )
@ ( ap @ ( plus @ sk__4 ) @ sk__3 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(satz8a,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) )
=> ( n_is @ X1 @ X2 ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ! [X8: $i] :
( ( is_of @ X8
@ ^ [V_5: $i] :
( in @ V_5
@ ( d_Sep @ omega
@ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
=> ( ( e_is
@ ( d_Sep @ omega
@ ^ [V_7: $i] : ( V_7 != emptyset ) )
@ ( ap @ ( plus @ X4 ) @ X6 )
@ ( ap @ ( plus @ X4 ) @ X8 ) )
=> ( e_is
@ ( d_Sep @ omega
@ ^ [V_8: $i] : ( V_8 != emptyset ) )
@ X6
@ X8 ) ) ) ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( is_of @ X0
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ~ ( e_is
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ( ap @ ( plus @ X1 ) @ X0 )
@ ( ap @ ( plus @ X1 ) @ X2 ) )
| ( e_is
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ X0
@ X2 )
| ~ ( is_of @ X2
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ~ ( is_of @ X1
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl1368,plain,
( ~ ( is_of @ sk__4
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ~ ( is_of @ sk__3
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ( e_is
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ sk__2
@ sk__3 )
| ~ ( is_of @ sk__2
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl10]) ).
thf(zip_derived_cl52,plain,
( is_of @ sk__4
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl55,plain,
( is_of @ sk__3
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl54,plain,
~ ( e_is
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ sk__2
@ sk__3 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl51,plain,
( is_of @ sk__2
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1377,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl1368,zip_derived_cl52,zip_derived_cl55,zip_derived_cl54,zip_derived_cl51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM684^4 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.X6VKFK5VWv true
% 0.11/0.32 % Computer : n031.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Aug 25 13:39:52 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.16/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.32 % Number of cores: 8
% 0.16/0.33 % Python version: Python 3.6.8
% 0.16/0.33 % Running in HO mode
% 0.16/0.61 % Total configuration time : 828
% 0.16/0.61 % Estimated wc time : 1656
% 0.16/0.61 % Estimated cpu time (8 cpus) : 207.0
% 0.16/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.16/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.16/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.16/0.71 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.16/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.85/0.88 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.85/0.91 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.85/0.92 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 20.34/4.46 % Solved by lams/40_c.s.sh.
% 20.34/4.46 % done 138 iterations in 3.696s
% 20.34/4.46 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 20.34/4.46 % SZS output start Refutation
% See solution above
% 20.34/4.46
% 20.34/4.46
% 20.34/4.46 % Terminating...
% 20.66/4.63 % Runner terminated.
% 20.66/4.63 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------