%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM670^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.OdYS3BAi8i true
% Computer : n005.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 Oct 2 04:47:55 PM UTC 2025
% Result : Theorem 162.20s 21.05s
% Output : Refutation 162.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 28
% Syntax : Number of formulae : 48 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 46 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 270 ( 16 ~; 6 |; 0 &; 224 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 103 ( 79 ^; 24 !; 0 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_29_ii_type,type,
d_29_ii: $i > $i > $o ).
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(non_type,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(l_some_type,type,
l_some: $i > ( $i > $o ) > $o ).
thf(sk__79_type,type,
sk__79: $i ).
thf(sk__82_type,type,
sk__82: $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(imp_type,type,
imp: $o > $o > $o ).
thf(sk__81_type,type,
sk__81: $i ).
thf(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(diffprop_type,type,
diffprop: $i > $i > $i > $o ).
thf(sk__80_type,type,
sk__80: $i ).
thf(n_some_type,type,
n_some: ( $i > $o ) > $o ).
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_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(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('4',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('5',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('6',plain,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_imp]) ).
thf('7',plain,
( imp
= ( ^ [V_1: $o,V_2: $o] :
( V_1
=> V_2 ) ) ),
define([status(thm)]) ).
thf('8',plain,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_not,'7']) ).
thf('9',plain,
( d_not
= ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
define([status(thm)]) ).
thf('10',plain,
( non
= ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_non,'9','7']) ).
thf('11',plain,
( non
= ( ^ [V_1: $i,V_2: $i > $o,V_3: $i] : ( d_not @ ( 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('12',plain,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).
thf('13',plain,
( is_of
= ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
define([status(thm)]) ).
thf('14',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,'13']) ).
thf('15',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('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,'11','9','7','15','13']) ).
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','11','9','7','15','13']) ).
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,'5','19','3','1','17','11','9','7','15','13']) ).
thf('21',plain,
( d_29_ii
= ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(satz19a,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] :
( ( d_29_ii @ X0 @ X1 )
=> ( d_29_ii @ ( n_pl @ X0 @ X2 ) @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( ~ ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X10 ) ) )
=> ~ ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( ( n_pl @ X4 @ X8 )
!= ( n_pl @ ( n_pl @ X6 @ X8 ) @ X12 ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( ~ ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X10 ) ) )
=> ~ ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( ( n_pl @ X4 @ X8 )
!= ( n_pl @ ( n_pl @ X6 @ X8 ) @ X12 ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl327,plain,
( sk__79
= ( n_pl @ sk__80 @ sk__82 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl324,plain,
in @ sk__81 @ nat,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl328,plain,
in @ sk__80 @ nat,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl326,plain,
in @ sk__82 @ nat,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(satz5,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 @ ( n_pl @ X0 @ X1 ) @ X2 ) @ ( n_pl @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( ( n_pl @ ( n_pl @ X4 @ X6 ) @ X8 )
= ( n_pl @ X4 @ ( n_pl @ X6 @ X8 ) ) ) ) ) ) ).
thf(zip_derived_cl206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ nat )
| ( ( n_pl @ ( n_pl @ X1 @ X0 ) @ X2 )
= ( n_pl @ X1 @ ( n_pl @ X0 @ X2 ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl325,plain,
! [X0: $i] :
( ( ( n_pl @ sk__79 @ sk__81 )
!= ( n_pl @ ( n_pl @ sk__80 @ sk__81 ) @ X0 ) )
| ~ ( in @ X0 @ nat ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(satz6,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ( ( n_pl @ X4 @ X6 )
= ( n_pl @ X6 @ X4 ) ) ) ) ).
thf(zip_derived_cl207,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ nat )
| ( ( n_pl @ X1 @ X0 )
= ( n_pl @ X0 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl27839,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl327,zip_derived_cl324,zip_derived_cl328,zip_derived_cl326,zip_derived_cl206,zip_derived_cl325,zip_derived_cl207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM670^4 : TPTP v9.2.0. 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.OdYS3BAi8i true
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 16:32:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.57/0.67 % Total configuration time : 828
% 0.57/0.67 % Estimated wc time : 1656
% 0.57/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.58/0.79 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 29.60/4.35 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 162.20/21.05 % Solved by lams/40_noforms.sh.
% 162.20/21.05 % done 1729 iterations in 20.236s
% 162.20/21.05 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 162.20/21.05 % SZS output start Refutation
% See solution above
% 162.20/21.05
% 162.20/21.05
% 162.20/21.05 % Terminating...
% 162.20/21.14 % Runner terminated.
% 162.20/21.15 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------