TSTP Solution File: NUM924_1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM924_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6fsWDdOjCv true
% Computer : n021.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 12:44:46 EDT 2023
% Result : Theorem 2.44s 0.98s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 33
% Syntax : Number of formulae : 86 ( 58 unt; 19 typ; 0 def)
% Number of atoms : 78 ( 46 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 344 ( 13 ~; 7 |; 0 &; 320 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(pls_type,type,
pls: int ).
thf(m_type,type,
m: int ).
thf(plus_plus_int_type,type,
plus_plus_int: int > int > int ).
thf(bit0_type,type,
bit0: int > int ).
thf(zero_zero_int_type,type,
zero_zero_int: int ).
thf(ord_less_int_type,type,
ord_less_int: int > int > $o ).
thf(s_type,type,
s: int ).
thf(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
thf(ord_less_eq_int_type,type,
ord_less_eq_int: int > int > $o ).
thf(one_one_int_type,type,
one_one_int: int ).
thf(times_times_int_type,type,
times_times_int: int > int > int ).
thf(plus_plus_nat_type,type,
plus_plus_nat: nat > nat > nat ).
thf(one_one_nat_type,type,
one_one_nat: nat ).
thf(power_power_int_type,type,
power_power_int: int > nat > int ).
thf(t_type,type,
t: int ).
thf(bit1_type,type,
bit1: int > int ).
thf(number_number_of_int_type,type,
number_number_of_int: int > int ).
thf(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) ).
thf(zip_derived_cl2,plain,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
inference(cnf,[status(esa)],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
thf(fact_3_t,axiom,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ) ).
thf(zip_derived_cl3,plain,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
inference(cnf,[status(esa)],[fact_3_t]) ).
thf(zip_derived_cl543,plain,
ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(fact_105_zero__is__num__zero,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ) ).
thf(zip_derived_cl157,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(cnf,[status(esa)],[fact_105_zero__is__num__zero]) ).
thf(fact_24_number__of__is__id,axiom,
! [K_1: int] :
( ( number_number_of_int @ K_1 )
= K_1 ) ).
thf(zip_derived_cl30,plain,
! [X0: int] :
( ( number_number_of_int @ X0 )
= X0 ),
inference(cnf,[status(esa)],[fact_24_number__of__is__id]) ).
thf(zip_derived_cl545,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(fact_23_zle__refl,axiom,
! [W: int] : ( ord_less_eq_int @ W @ W ) ).
thf(zip_derived_cl29,plain,
! [X0: int] : ( ord_less_eq_int @ X0 @ X0 ),
inference(cnf,[status(esa)],[fact_23_zle__refl]) ).
thf(fact_64_le__special_I2_J,axiom,
! [Y_1: int] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_1 ) )
<=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_1 ) ) ).
thf(zip_derived_cl94,plain,
! [X0: int] :
( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ X0 ) )
| ~ ( ord_less_eq_int @ ( bit1 @ pls ) @ X0 ) ),
inference(cnf,[status(esa)],[fact_64_le__special_I2_J]) ).
thf(zip_derived_cl30_001,plain,
! [X0: int] :
( ( number_number_of_int @ X0 )
= X0 ),
inference(cnf,[status(esa)],[fact_24_number__of__is__id]) ).
thf(zip_derived_cl545_002,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(zip_derived_cl1189,plain,
! [X0: int] :
( ( ord_less_eq_int @ one_one_int @ X0 )
| ~ ( ord_less_eq_int @ ( bit1 @ zero_zero_int ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl94,zip_derived_cl30,zip_derived_cl545]) ).
thf(zip_derived_cl1190,plain,
ord_less_eq_int @ one_one_int @ ( bit1 @ zero_zero_int ),
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl1189]) ).
thf(fact_32_zle__antisym,axiom,
! [Z: int,W: int] :
( ( ord_less_eq_int @ Z @ W )
=> ( ( ord_less_eq_int @ W @ Z )
=> ( Z = W ) ) ) ).
thf(zip_derived_cl40,plain,
! [X0: int,X1: int] :
( ~ ( ord_less_eq_int @ X0 @ X1 )
| ( X1 = X0 )
| ~ ( ord_less_eq_int @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[fact_32_zle__antisym]) ).
thf(zip_derived_cl1269,plain,
( ( ( bit1 @ zero_zero_int )
= one_one_int )
| ~ ( ord_less_eq_int @ ( bit1 @ zero_zero_int ) @ one_one_int ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1190,zip_derived_cl40]) ).
thf(zip_derived_cl29_003,plain,
! [X0: int] : ( ord_less_eq_int @ X0 @ X0 ),
inference(cnf,[status(esa)],[fact_23_zle__refl]) ).
thf(fact_63_le__special_I4_J,axiom,
! [X_1: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ X_1 ) @ one_one_int )
<=> ( ord_less_eq_int @ X_1 @ ( bit1 @ pls ) ) ) ).
thf(zip_derived_cl92,plain,
! [X0: int] :
( ( ord_less_eq_int @ ( number_number_of_int @ X0 ) @ one_one_int )
| ~ ( ord_less_eq_int @ X0 @ ( bit1 @ pls ) ) ),
inference(cnf,[status(esa)],[fact_63_le__special_I4_J]) ).
thf(zip_derived_cl30_004,plain,
! [X0: int] :
( ( number_number_of_int @ X0 )
= X0 ),
inference(cnf,[status(esa)],[fact_24_number__of__is__id]) ).
thf(zip_derived_cl545_005,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(zip_derived_cl1162,plain,
! [X0: int] :
( ( ord_less_eq_int @ X0 @ one_one_int )
| ~ ( ord_less_eq_int @ X0 @ ( bit1 @ zero_zero_int ) ) ),
inference(demod,[status(thm)],[zip_derived_cl92,zip_derived_cl30,zip_derived_cl545]) ).
thf(zip_derived_cl1163,plain,
ord_less_eq_int @ ( bit1 @ zero_zero_int ) @ one_one_int,
inference('s_sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl1162]) ).
thf(zip_derived_cl1273,plain,
( ( bit1 @ zero_zero_int )
= one_one_int ),
inference(demod,[status(thm)],[zip_derived_cl1269,zip_derived_cl1163]) ).
thf(fact_104_zadd__commute,axiom,
! [Z: int,W: int] :
( ( plus_plus_int @ Z @ W )
= ( plus_plus_int @ W @ Z ) ) ).
thf(zip_derived_cl156,plain,
! [X0: int,X1: int] :
( ( plus_plus_int @ X1 @ X0 )
= ( plus_plus_int @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[fact_104_zadd__commute]) ).
thf(zip_derived_cl545_006,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(zip_derived_cl1273_007,plain,
( ( bit1 @ zero_zero_int )
= one_one_int ),
inference(demod,[status(thm)],[zip_derived_cl1269,zip_derived_cl1163]) ).
thf(zip_derived_cl30_008,plain,
! [X0: int] :
( ( number_number_of_int @ X0 )
= X0 ),
inference(cnf,[status(esa)],[fact_24_number__of__is__id]) ).
thf(fact_25_zmult__commute,axiom,
! [Z: int,W: int] :
( ( times_times_int @ Z @ W )
= ( times_times_int @ W @ Z ) ) ).
thf(zip_derived_cl31,plain,
! [X0: int,X1: int] :
( ( times_times_int @ X1 @ X0 )
= ( times_times_int @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[fact_25_zmult__commute]) ).
thf(zip_derived_cl156_009,plain,
! [X0: int,X1: int] :
( ( plus_plus_int @ X1 @ X0 )
= ( plus_plus_int @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[fact_104_zadd__commute]) ).
thf(fact_66_mult__Pls,axiom,
! [W: int] :
( ( times_times_int @ pls @ W )
= pls ) ).
thf(zip_derived_cl96,plain,
! [X0: int] :
( ( times_times_int @ pls @ X0 )
= pls ),
inference(cnf,[status(esa)],[fact_66_mult__Pls]) ).
thf(zip_derived_cl545_010,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(zip_derived_cl545_011,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(zip_derived_cl671,plain,
! [X0: int] :
( ( times_times_int @ zero_zero_int @ X0 )
= zero_zero_int ),
inference(demod,[status(thm)],[zip_derived_cl96,zip_derived_cl545,zip_derived_cl545]) ).
thf(zip_derived_cl31_012,plain,
! [X0: int,X1: int] :
( ( times_times_int @ X1 @ X0 )
= ( times_times_int @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[fact_25_zmult__commute]) ).
thf(zip_derived_cl682,plain,
! [X0: int] :
( zero_zero_int
= ( times_times_int @ X0 @ zero_zero_int ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl671,zip_derived_cl31]) ).
thf(fact_13_one__power2,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ) ).
thf(zip_derived_cl18,plain,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
inference(cnf,[status(esa)],[fact_13_one__power2]) ).
thf(zip_derived_cl545_013,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(zip_derived_cl547,plain,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) )
= one_one_int ),
inference(demod,[status(thm)],[zip_derived_cl18,zip_derived_cl545]) ).
thf(fact_65_nat__1__add__1,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
thf(zip_derived_cl95,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(cnf,[status(esa)],[fact_65_nat__1__add__1]) ).
thf(zip_derived_cl545_014,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(zip_derived_cl577,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl95,zip_derived_cl545]) ).
thf(zip_derived_cl579,plain,
( ( power_power_int @ one_one_int @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
= one_one_int ),
inference(demod,[status(thm)],[zip_derived_cl547,zip_derived_cl577]) ).
thf(fact_7_not__sum__power2__lt__zero,axiom,
! [X: int,Y: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ).
thf(zip_derived_cl7,plain,
! [X0: int,X1: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ),
inference(cnf,[status(esa)],[fact_7_not__sum__power2__lt__zero]) ).
thf(zip_derived_cl545_015,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(zip_derived_cl545_016,plain,
zero_zero_int = pls,
inference('s_sup+',[status(thm)],[zip_derived_cl157,zip_derived_cl30]) ).
thf(zip_derived_cl555,plain,
! [X0: int,X1: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ) @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ) ) @ zero_zero_int ),
inference(demod,[status(thm)],[zip_derived_cl7,zip_derived_cl545,zip_derived_cl545]) ).
thf(zip_derived_cl577_017,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl95,zip_derived_cl545]) ).
thf(zip_derived_cl577_018,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl95,zip_derived_cl545]) ).
thf(zip_derived_cl582,plain,
! [X0: int,X1: int] :
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X0 @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) @ ( power_power_int @ X1 @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) @ zero_zero_int ),
inference(demod,[status(thm)],[zip_derived_cl555,zip_derived_cl577,zip_derived_cl577]) ).
thf(zip_derived_cl661,plain,
! [X0: int] :
~ ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( power_power_int @ X0 @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) @ zero_zero_int ),
inference('s_sup-',[status(thm)],[zip_derived_cl579,zip_derived_cl582]) ).
thf(zip_derived_cl577_019,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl95,zip_derived_cl545]) ).
thf(zip_derived_cl1273_020,plain,
( ( bit1 @ zero_zero_int )
= one_one_int ),
inference(demod,[status(thm)],[zip_derived_cl1269,zip_derived_cl1163]) ).
thf(zip_derived_cl1276,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ one_one_int ) ) ),
inference(demod,[status(thm)],[zip_derived_cl577,zip_derived_cl1273]) ).
thf(zip_derived_cl1544,plain,
! [X0: int] :
~ ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( power_power_int @ X0 @ ( number_number_of_nat @ ( bit0 @ one_one_int ) ) ) ) @ zero_zero_int ),
inference(demod,[status(thm)],[zip_derived_cl661,zip_derived_cl1276]) ).
thf(zip_derived_cl1863,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl543,zip_derived_cl545,zip_derived_cl1273,zip_derived_cl156,zip_derived_cl545,zip_derived_cl1273,zip_derived_cl30,zip_derived_cl31,zip_derived_cl156,zip_derived_cl682,zip_derived_cl1544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM924_1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6fsWDdOjCv true
% 0.19/0.35 % Computer : n021.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Fri Aug 25 13:42:26 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.19/0.35 % Running portfolio for 300 s
% 0.19/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36 % Number of cores: 8
% 0.21/0.36 % Python version: Python 3.6.8
% 0.21/0.36 % Running in FO mode
% 0.23/0.65 % Total configuration time : 435
% 0.23/0.65 % Estimated wc time : 1092
% 0.23/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.23/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.23/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.23/0.78 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.23/0.79 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 2.44/0.98 % Solved by fo/fo6_bce.sh.
% 2.44/0.98 % BCE start: 159
% 2.44/0.98 % BCE eliminated: 2
% 2.44/0.98 % PE start: 157
% 2.44/0.98 logic: eq
% 2.44/0.98 % PE eliminated: 1
% 2.44/0.98 % done 413 iterations in 0.243s
% 2.44/0.98 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.44/0.98 % SZS output start Refutation
% See solution above
% 2.44/0.98
% 2.44/0.98
% 2.44/0.98 % Terminating...
% 2.99/1.06 % Runner terminated.
% 2.99/1.07 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------