TSTP Solution File: NUM650^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM650^4 : 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.Isosxrw2lP 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 12:43:05 EDT 2023
% Result : Theorem 56.71s 7.71s
% Output : Refutation 56.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 60
% Syntax : Number of formulae : 87 ( 50 unt; 24 typ; 0 def)
% Number of atoms : 273 ( 109 equ; 0 cnn)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 416 ( 51 ~; 8 |; 0 &; 333 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 6 con; 0-3 aty)
% Number of variables : 160 ( 149 ^; 11 !; 0 ?; 160 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk__2_type,type,
sk__2: $i ).
thf(orec3_type,type,
orec3: $o > $o > $o > $o ).
thf(nat_type,type,
nat: $i ).
thf(and3_type,type,
and3: $o > $o > $o > $o ).
thf(is_of_type,type,
is_of: $i > ( $i > $o ) > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(l_some_type,type,
l_some: $i > ( $i > $o ) > $o ).
thf(d_Sep_type,type,
d_Sep: $i > ( $i > $o ) > $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(l_ec_type,type,
l_ec: $o > $o > $o ).
thf(imp_type,type,
imp: $o > $o > $o ).
thf(ec3_type,type,
ec3: $o > $o > $o > $o ).
thf(d_and_type,type,
d_and: $o > $o > $o ).
thf(omega_type,type,
omega: $i ).
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(l_or_type,type,
l_or: $o > $o > $o ).
thf(d_not_type,type,
d_not: $o > $o ).
thf(or3_type,type,
or3: $o > $o > $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_diffprop,axiom,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ) ).
thf(def_nat,axiom,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).
thf('0',plain,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nat]) ).
thf('1',plain,
( nat
= ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
define([status(thm)]) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).
thf('2',plain,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).
thf('3',plain,
( e_is
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
define([status(thm)]) ).
thf('4',plain,
( n_is
= ( e_is @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_is,'1','3']) ).
thf('5',plain,
( n_is
= ( e_is @ nat ) ),
define([status(thm)]) ).
thf('6',plain,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_diffprop,'5','1','3']) ).
thf('7',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('8',plain,
( n_some
= ( l_some @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_some,'1']) ).
thf('9',plain,
( n_some
= ( l_some @ nat ) ),
define([status(thm)]) ).
thf(def_or3,axiom,
( or3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) ) ) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ) ).
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,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_or,'13','11']) ).
thf('15',plain,
( l_or
= ( ^ [V_1: $o] : ( imp @ ( d_not @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('16',plain,
( or3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_or3,'15','13','11']) ).
thf('17',plain,
( or3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( l_or @ V_1 @ ( l_or @ V_2 @ V_3 ) ) ) ),
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('18',plain,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).
thf('19',plain,
( is_of
= ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
define([status(thm)]) ).
thf('20',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,'19']) ).
thf('21',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(satz9a,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( or3 @ ( n_is @ X0 @ X1 ) @ ( n_some @ ( diffprop @ X0 @ X1 ) ) @ ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( in @ X4
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) )
=> ( ( X4 != X6 )
=> ( ~ ( l_some
@ ( d_Sep @ omega
@ ^ [V_3: $i] : ( V_3 != emptyset ) )
@ ^ [V_4: $i] :
( X4
= ( n_pl @ X6 @ V_4 ) ) )
=> ( l_some
@ ( d_Sep @ omega
@ ^ [V_5: $i] : ( V_5 != emptyset ) )
@ ^ [V_6: $i] :
( X6
= ( n_pl @ X4 @ V_6 ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( in @ X4
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) )
=> ( ( X4 != X6 )
=> ( ~ ( l_some
@ ( d_Sep @ omega
@ ^ [V_3: $i] : ( V_3 != emptyset ) )
@ ^ [V_4: $i] :
( X4
= ( n_pl @ X6 @ V_4 ) ) )
=> ( l_some
@ ( d_Sep @ omega
@ ^ [V_5: $i] : ( V_5 != emptyset ) )
@ ^ [V_6: $i] :
( X6
= ( n_pl @ X4 @ V_6 ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl41,plain,
~ ( l_some
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] :
( sk__2
= ( n_pl @ sk__3 @ Y0 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(def_orec3,axiom,
( orec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) ) ) ).
thf(def_ec3,axiom,
( ec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) ) ) ).
thf(def_and3,axiom,
( and3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) ) ) ).
thf(def_d_and,axiom,
( d_and
= ( ^ [X0: $o,X1: $o] : ( d_not @ ( l_ec @ X0 @ X1 ) ) ) ) ).
thf(def_l_ec,axiom,
( l_ec
= ( ^ [X0: $o,X1: $o] : ( imp @ X0 @ ( d_not @ X1 ) ) ) ) ).
thf('22',plain,
( l_ec
= ( ^ [X0: $o,X1: $o] : ( imp @ X0 @ ( d_not @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_ec,'13','11']) ).
thf('23',plain,
( l_ec
= ( ^ [V_1: $o,V_2: $o] : ( imp @ V_1 @ ( d_not @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('24',plain,
( d_and
= ( ^ [X0: $o,X1: $o] : ( d_not @ ( l_ec @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_and,'23','13','11']) ).
thf('25',plain,
( d_and
= ( ^ [V_1: $o,V_2: $o] : ( d_not @ ( l_ec @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('26',plain,
( and3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_and3,'25','23','13','11']) ).
thf('27',plain,
( and3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( d_and @ V_1 @ ( d_and @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('28',plain,
( ec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_ec3,'27','25','23','13','11']) ).
thf('29',plain,
( ec3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( and3 @ ( l_ec @ V_1 @ V_2 ) @ ( l_ec @ V_2 @ V_3 ) @ ( l_ec @ V_3 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('30',plain,
( orec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_orec3,'29','27','17','15','25','23','13','11']) ).
thf('31',plain,
( orec3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( d_and @ ( or3 @ V_1 @ V_2 @ V_3 ) @ ( ec3 @ V_1 @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(satz9,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( orec3 @ ( n_is @ X0 @ X1 )
@ ( n_some
@ ^ [X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) )
@ ( n_some
@ ^ [X2: $i] : ( n_is @ X1 @ ( n_pl @ X0 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
( ( in @ X4
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) )
=> ~ ( ( ( X4 != X6 )
=> ( ~ ( l_some
@ ( d_Sep @ omega
@ ^ [V_3: $i] : ( V_3 != emptyset ) )
@ ^ [V_4: $i] :
( X4
= ( n_pl @ X6 @ V_4 ) ) )
=> ( l_some
@ ( d_Sep @ omega
@ ^ [V_5: $i] : ( V_5 != emptyset ) )
@ ^ [V_6: $i] :
( X6
= ( n_pl @ X4 @ V_6 ) ) ) ) )
=> ( ( ( X4 = X6 )
=> ~ ( l_some
@ ( d_Sep @ omega
@ ^ [V_7: $i] : ( V_7 != emptyset ) )
@ ^ [V_8: $i] :
( X4
= ( n_pl @ X6 @ V_8 ) ) ) )
=> ( ( ( l_some
@ ( d_Sep @ omega
@ ^ [V_9: $i] : ( V_9 != emptyset ) )
@ ^ [V_10: $i] :
( X4
= ( n_pl @ X6 @ V_10 ) ) )
=> ~ ( l_some
@ ( d_Sep @ omega
@ ^ [V_11: $i] : ( V_11 != emptyset ) )
@ ^ [V_12: $i] :
( X6
= ( n_pl @ X4 @ V_12 ) ) ) )
=> ~ ( ( l_some
@ ( d_Sep @ omega
@ ^ [V_13: $i] : ( V_13 != emptyset ) )
@ ^ [V_14: $i] :
( X6
= ( n_pl @ X4 @ V_14 ) ) )
=> ( X4 != X6 ) ) ) ) ) ) ) ).
thf(zip_derived_cl34,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ( X1 = X0 )
| ( l_some
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] :
( X0
= ( n_pl @ X1 @ Y0 ) ) )
| ( l_some
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] :
( X1
= ( n_pl @ X0 @ Y0 ) ) )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl40,plain,
~ ( l_some
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] :
( sk__3
= ( n_pl @ sk__2 @ Y0 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4688,plain,
( ~ ( in @ sk__3
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ( l_some
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] :
( sk__2
= ( n_pl @ sk__3 @ Y0 ) ) )
| ( sk__3 = sk__2 )
| ~ ( in @ sk__2
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl40]) ).
thf(zip_derived_cl42,plain,
( in @ sk__3
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl38,plain,
( in @ sk__2
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4690,plain,
( ( l_some
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] :
( sk__2
= ( n_pl @ sk__3 @ Y0 ) ) )
| ( sk__3 = sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl4688,zip_derived_cl42,zip_derived_cl38]) ).
thf(zip_derived_cl39,plain,
sk__2 != sk__3,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4691,plain,
( l_some
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) )
@ ^ [Y0: $i] :
( sk__2
= ( n_pl @ sk__3 @ Y0 ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl4690,zip_derived_cl39]) ).
thf(zip_derived_cl4957,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl41,zip_derived_cl4691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM650^4 : TPTP v8.1.2. Released v7.1.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Isosxrw2lP true
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 15:20:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in HO mode
% 0.54/0.65 % Total configuration time : 828
% 0.54/0.65 % Estimated wc time : 1656
% 0.54/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.54/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.54/0.69 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.56/0.95 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 56.71/7.71 % Solved by lams/40_c.s.sh.
% 56.71/7.71 % done 408 iterations in 7.012s
% 56.71/7.71 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 56.71/7.71 % SZS output start Refutation
% See solution above
% 56.71/7.71
% 56.71/7.71
% 56.71/7.71 % Terminating...
% 56.91/7.85 % Runner terminated.
% 56.91/7.85 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------