TSTP Solution File: NUM769^4 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM769^4 : 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.HQ3KaDkAEQ true
% Computer : n004.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 12:44:03 EDT 2023
% Result : Theorem 151.70s 20.26s
% Output : Refutation 151.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 55
% Syntax : Number of formulae : 76 ( 45 unt; 25 typ; 0 def)
% Number of atoms : 164 ( 52 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 360 ( 12 ~; 4 |; 0 &; 324 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 6 con; 0-3 aty)
% Number of variables : 98 ( 83 ^; 15 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_29_ii_type,type,
d_29_ii: $i > $i > $o ).
thf(nat_type,type,
nat: $i ).
thf(d_367_w_type,type,
d_367_w: $i > $i > $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__192_type,type,
sk__192: $i ).
thf(n_pf_type,type,
n_pf: $i > $i > $i ).
thf(sk__193_type,type,
sk__193: $i ).
thf(sk__194_type,type,
sk__194: $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(imp_type,type,
imp: $o > $o > $o ).
thf(frac_type,type,
frac: $i ).
thf(n_ts_type,type,
n_ts: $i > $i > $i ).
thf(n_eq_type,type,
n_eq: $i > $i > $o ).
thf(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(diffprop_type,type,
diffprop: $i > $i > $i > $o ).
thf(num_type,type,
num: $i > $i ).
thf(n_some_type,type,
n_some: ( $i > $o ) > $o ).
thf(moref_type,type,
moref: $i > $i > $o ).
thf(d_not_type,type,
d_not: $o > $o ).
thf(den_type,type,
den: $i > $i ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf(n_pl_type,type,
n_pl: $i > $i > $i ).
thf(def_moref,axiom,
( moref
= ( ^ [X0: $i,X1: $i] : ( d_29_ii @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ) ).
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('22',plain,
( moref
= ( ^ [X0: $i,X1: $i] : ( d_29_ii @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_moref,'21','5','19','3','1','17','11','9','7','15','13']) ).
thf('23',plain,
( moref
= ( ^ [V_1: $i,V_2: $i] : ( d_29_ii @ ( n_ts @ ( num @ V_1 ) @ ( den @ V_2 ) ) @ ( n_ts @ ( num @ V_2 ) @ ( den @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X0: $i,X1: $i] : ( n_is @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ) ).
thf('24',plain,
( n_eq
= ( ^ [X0: $i,X1: $i] : ( n_is @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_eq,'3','1']) ).
thf('25',plain,
( n_eq
= ( ^ [V_1: $i,V_2: $i] : ( n_is @ ( n_ts @ ( num @ V_1 ) @ ( den @ V_2 ) ) @ ( n_ts @ ( num @ V_2 ) @ ( den @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(satz67d,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ frac )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( ( moref @ X0 @ X1 )
=> ( n_eq @ X0 @ ( n_pf @ X1 @ ( d_367_w @ X0 @ X1 ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( in @ X4 @ frac )
=> ! [X6: $i] :
( ( in @ X6 @ frac )
=> ( ~ ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( ( n_ts @ ( num @ X4 ) @ ( den @ X6 ) )
!= ( n_pl @ ( n_ts @ ( num @ X6 ) @ ( den @ X4 ) ) @ X8 ) ) )
=> ( ( n_ts @ ( num @ X4 ) @ ( den @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) )
= ( n_ts @ ( num @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) @ ( den @ X4 ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( in @ X4 @ frac )
=> ! [X6: $i] :
( ( in @ X6 @ frac )
=> ( ~ ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( ( n_ts @ ( num @ X4 ) @ ( den @ X6 ) )
!= ( n_pl @ ( n_ts @ ( num @ X6 ) @ ( den @ X4 ) ) @ X8 ) ) )
=> ( ( n_ts @ ( num @ X4 ) @ ( den @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) )
= ( n_ts @ ( num @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) @ ( den @ X4 ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl759,plain,
( ( n_ts @ ( num @ sk__192 ) @ ( den @ ( n_pf @ sk__193 @ ( d_367_w @ sk__192 @ sk__193 ) ) ) )
!= ( n_ts @ ( num @ ( n_pf @ sk__193 @ ( d_367_w @ sk__192 @ sk__193 ) ) ) @ ( den @ sk__192 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl760,plain,
in @ sk__193 @ frac,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl756,plain,
in @ sk__192 @ frac,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl757,plain,
in @ sk__194 @ nat,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl758,plain,
( ( n_ts @ ( num @ sk__192 ) @ ( den @ sk__193 ) )
= ( n_pl @ ( n_ts @ ( num @ sk__193 ) @ ( den @ sk__192 ) ) @ sk__194 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(k_satz67c,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ frac )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( ( moref @ X0 @ X1 )
=> ( n_eq @ ( n_pf @ X1 @ ( d_367_w @ X0 @ X1 ) ) @ X0 ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
( ( in @ X4 @ frac )
=> ! [X6: $i] :
( ( in @ X6 @ frac )
=> ( ~ ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( ( n_ts @ ( num @ X4 ) @ ( den @ X6 ) )
!= ( n_pl @ ( n_ts @ ( num @ X6 ) @ ( den @ X4 ) ) @ X8 ) ) )
=> ( ( n_ts @ ( num @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) @ ( den @ X4 ) )
= ( n_ts @ ( num @ X4 ) @ ( den @ ( n_pf @ X6 @ ( d_367_w @ X4 @ X6 ) ) ) ) ) ) ) ) ).
thf(zip_derived_cl755,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ frac )
| ( ( n_ts @ ( num @ ( n_pf @ X0 @ ( d_367_w @ X1 @ X0 ) ) ) @ ( den @ X1 ) )
= ( n_ts @ ( num @ X1 ) @ ( den @ ( n_pf @ X0 @ ( d_367_w @ X1 @ X0 ) ) ) ) )
| ( ( n_ts @ ( num @ X1 ) @ ( den @ X0 ) )
!= ( n_pl @ ( n_ts @ ( num @ X0 ) @ ( den @ X1 ) ) @ X2 ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X1 @ frac ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl26502,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl759,zip_derived_cl760,zip_derived_cl756,zip_derived_cl757,zip_derived_cl758,zip_derived_cl755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM769^4 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HQ3KaDkAEQ true
% 0.14/0.35 % Computer : n004.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 08:19:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.69 % Total configuration time : 828
% 0.22/0.69 % Estimated wc time : 1656
% 0.22/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.79 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.51/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.51/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.51/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.51/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.51/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 151.70/20.26 % Solved by lams/40_noforms.sh.
% 151.70/20.26 % done 1407 iterations in 19.433s
% 151.70/20.26 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 151.70/20.26 % SZS output start Refutation
% See solution above
% 151.70/20.26
% 151.70/20.26
% 151.70/20.26 % Terminating...
% 152.09/20.33 % Runner terminated.
% 152.09/20.35 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------