%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU820^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.hsI5xjD2ic true
% Computer : n028.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 04:56:40 PM UTC 2025
% Result : Theorem 0.52s 0.81s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 45 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 215 ( 45 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 457 ( 27 ~; 29 |; 30 &; 295 @)
% ( 0 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 103 ( 16 ^; 82 !; 5 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk__22_type,type,
sk__22: $i ).
thf(powersetE1_type,type,
powersetE1: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(sk__21_type,type,
sk__21: $i ).
thf(sk__15_type,type,
sk__15: $i ).
thf(sk__20_type,type,
sk__20: $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subsetemptysetimpeq_type,type,
subsetemptysetimpeq: $o ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(sk__16_type,type,
sk__16: $i ).
thf(vacuousDall_type,type,
vacuousDall: $o ).
thf(nonempty_type,type,
nonempty: $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(wellorderedByIn_type,type,
wellorderedByIn: $i > $o ).
thf(stricttotalorderedByIn_type,type,
stricttotalorderedByIn: $i > $o ).
thf(transitiveset_type,type,
transitiveset: $i > $o ).
thf(ordinal,axiom,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ) ).
thf(wellorderedByIn,axiom,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( ( nonempty @ X )
=> ? [Xx: $i] :
( ! [Y: $i] :
( ( in @ Y @ X )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) )
& ( in @ Xx @ X ) ) ) ) ) ) ) ).
thf(stricttotalorderedByIn,axiom,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( ( in @ Xx @ X )
& ( in @ X @ Y ) )
=> ( in @ Xx @ Y ) ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( X = Y )
| ( in @ X @ Y )
| ( in @ Y @ X ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ~ ( in @ X @ X ) ) ) ) ) ).
thf('0',plain,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( ( in @ Xx @ X )
& ( in @ X @ Y ) )
=> ( in @ Xx @ Y ) ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( X = Y )
| ( in @ X @ Y )
| ( in @ Y @ X ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ~ ( in @ X @ X ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[stricttotalorderedByIn]) ).
thf('1',plain,
( stricttotalorderedByIn
= ( ^ [V_1: $i] :
( ! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ! [X6: $i] :
( ( in @ X6 @ V_1 )
=> ! [X8: $i] :
( ( in @ X8 @ V_1 )
=> ( ( ( in @ X4 @ X6 )
& ( in @ X6 @ X8 ) )
=> ( in @ X4 @ X8 ) ) ) ) )
& ! [X10: $i] :
( ( in @ X10 @ V_1 )
=> ! [X12: $i] :
( ( in @ X12 @ V_1 )
=> ( ( X10 = X12 )
| ( in @ X10 @ X12 )
| ( in @ X12 @ X10 ) ) ) )
& ! [X14: $i] :
( ( in @ X14 @ V_1 )
=> ~ ( in @ X14 @ X14 ) ) ) ) ),
define([status(thm)]) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
thf('2',plain,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[nonempty]) ).
thf('3',plain,
( nonempty
= ( ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
define([status(thm)]) ).
thf('4',plain,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( ( nonempty @ X )
=> ? [Xx: $i] :
( ! [Y: $i] :
( ( in @ Y @ X )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) )
& ( in @ Xx @ X ) ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[wellorderedByIn,'1','3']) ).
thf('5',plain,
( wellorderedByIn
= ( ^ [V_1: $i] :
( ( stricttotalorderedByIn @ V_1 )
& ! [X4: $i] :
( ( in @ X4 @ ( powerset @ V_1 ) )
=> ( ( nonempty @ X4 )
=> ? [X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 = X8 )
| ( in @ X6 @ X8 ) ) )
& ( in @ X6 @ X4 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf('6',plain,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ordinal,'5','1','3']) ).
thf('7',plain,
( ordinal
= ( ^ [V_1: $i] :
( ( transitiveset @ V_1 )
& ( wellorderedByIn @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(transitiveset,axiom,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ) ).
thf('8',plain,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[transitiveset]) ).
thf('9',plain,
( transitiveset
= ( ^ [V_1: $i] :
! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ( subset @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(powersetE1,axiom,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ) ).
thf('10',plain,
( powersetE1
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ( subset @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ) ).
thf('11',plain,
( subsetemptysetimpeq
= ( ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ) ),
define([status(thm)]) ).
thf(vacuousDall,axiom,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ) ).
thf('12',plain,
( vacuousDall
= ( ! [X4: $i > $o,X6: $i] :
( ( in @ X6 @ emptyset )
=> ( X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(emptysetOrdinal,conjecture,
( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i > $o,X6: $i] :
( ( in @ X6 @ emptyset )
=> ( X4 @ X6 ) )
=> ( ! [X8: $i] :
( ( subset @ X8 @ emptyset )
=> ( X8 = emptyset ) )
=> ( ! [X10: $i,X12: $i] :
( ( in @ X12 @ ( powerset @ X10 ) )
=> ( subset @ X12 @ X10 ) )
=> ( ! [X14: $i] :
( ( in @ X14 @ emptyset )
=> ( subset @ X14 @ emptyset ) )
& ! [X16: $i] :
( ( in @ X16 @ emptyset )
=> ! [X18: $i] :
( ( in @ X18 @ emptyset )
=> ! [X20: $i] :
( ( in @ X20 @ emptyset )
=> ( ( ( in @ X16 @ X18 )
& ( in @ X18 @ X20 ) )
=> ( in @ X16 @ X20 ) ) ) ) )
& ! [X22: $i] :
( ( in @ X22 @ emptyset )
=> ! [X24: $i] :
( ( in @ X24 @ emptyset )
=> ( ( X22 = X24 )
| ( in @ X22 @ X24 )
| ( in @ X24 @ X22 ) ) ) )
& ! [X26: $i] :
( ( in @ X26 @ emptyset )
=> ~ ( in @ X26 @ X26 ) )
& ! [X28: $i] :
( ( in @ X28 @ ( powerset @ emptyset ) )
=> ( ( X28 != emptyset )
=> ? [X30: $i] :
( ! [X32: $i] :
( ( in @ X32 @ X28 )
=> ( ( X30 = X32 )
| ( in @ X30 @ X32 ) ) )
& ( in @ X30 @ X28 ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i > $o,X6: $i] :
( ( in @ X6 @ emptyset )
=> ( X4 @ X6 ) )
=> ( ! [X8: $i] :
( ( subset @ X8 @ emptyset )
=> ( X8 = emptyset ) )
=> ( ! [X10: $i,X12: $i] :
( ( in @ X12 @ ( powerset @ X10 ) )
=> ( subset @ X12 @ X10 ) )
=> ( ! [X14: $i] :
( ( in @ X14 @ emptyset )
=> ( subset @ X14 @ emptyset ) )
& ! [X16: $i] :
( ( in @ X16 @ emptyset )
=> ! [X18: $i] :
( ( in @ X18 @ emptyset )
=> ! [X20: $i] :
( ( in @ X20 @ emptyset )
=> ( ( ( in @ X16 @ X18 )
& ( in @ X18 @ X20 ) )
=> ( in @ X16 @ X20 ) ) ) ) )
& ! [X22: $i] :
( ( in @ X22 @ emptyset )
=> ! [X24: $i] :
( ( in @ X24 @ emptyset )
=> ( ( X22 = X24 )
| ( in @ X22 @ X24 )
| ( in @ X24 @ X22 ) ) ) )
& ! [X26: $i] :
( ( in @ X26 @ emptyset )
=> ~ ( in @ X26 @ X26 ) )
& ! [X28: $i] :
( ( in @ X28 @ ( powerset @ emptyset ) )
=> ( ( X28 != emptyset )
=> ? [X30: $i] :
( ! [X32: $i] :
( ( in @ X32 @ X28 )
=> ( ( X30 = X32 )
| ( in @ X30 @ X32 ) ) )
& ( in @ X30 @ X28 ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl602,plain,
! [X5: $i] :
( ( X5 = emptyset )
| ~ ( subset @ X5 @ emptyset ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl302,plain,
( ( in @ sk__15 @ emptyset )
| ( in @ sk__16 @ emptyset )
| ( in @ sk__20 @ emptyset )
| ( in @ sk__21 @ emptyset )
| ( in @ sk__22 @ ( powerset @ emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl0,plain,
! [X0: $i > $o,X1: $i] :
( ( X0 @ X1 )
| ~ ( in @ X1 @ emptyset ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl603,plain,
! [X0: $o,X1: $i] :
( ( ^ [Y0: $i] : X0
@ X1 )
| ~ ( in @ X1 @ emptyset ) ),
inference(prune_arg_fun,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl604,plain,
! [X0: $o,X1: $i] :
( X0
| ~ ( in @ X1 @ emptyset ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl603]) ).
thf(zip_derived_cl611,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference(ho_elim_pred,[status(thm)],[zip_derived_cl604]) ).
thf(zip_derived_cl611_001,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference(ho_elim_pred,[status(thm)],[zip_derived_cl604]) ).
thf(zip_derived_cl611_002,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference(ho_elim_pred,[status(thm)],[zip_derived_cl604]) ).
thf(zip_derived_cl611_003,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference(ho_elim_pred,[status(thm)],[zip_derived_cl604]) ).
thf(zip_derived_cl899,plain,
in @ sk__22 @ ( powerset @ emptyset ),
inference(demod,[status(thm)],[zip_derived_cl302,zip_derived_cl611,zip_derived_cl611,zip_derived_cl611,zip_derived_cl611]) ).
thf(zip_derived_cl1,plain,
! [X2: $i,X3: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ X2 @ ( powerset @ X3 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl900,plain,
subset @ sk__22 @ emptyset,
inference('sup-',[status(thm)],[zip_derived_cl899,zip_derived_cl1]) ).
thf(zip_derived_cl905,plain,
sk__22 = emptyset,
inference('sup+',[status(thm)],[zip_derived_cl602,zip_derived_cl900]) ).
thf(zip_derived_cl306,plain,
( ( in @ sk__15 @ emptyset )
| ( in @ sk__16 @ emptyset )
| ( in @ sk__20 @ emptyset )
| ( in @ sk__21 @ emptyset )
| ( sk__22 != emptyset ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl611_004,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference(ho_elim_pred,[status(thm)],[zip_derived_cl604]) ).
thf(zip_derived_cl611_005,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference(ho_elim_pred,[status(thm)],[zip_derived_cl604]) ).
thf(zip_derived_cl611_006,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference(ho_elim_pred,[status(thm)],[zip_derived_cl604]) ).
thf(zip_derived_cl615,plain,
( ( in @ sk__16 @ emptyset )
| ( sk__22 != emptyset ) ),
inference(demod,[status(thm)],[zip_derived_cl306,zip_derived_cl611,zip_derived_cl611,zip_derived_cl611]) ).
thf(zip_derived_cl611_007,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference(ho_elim_pred,[status(thm)],[zip_derived_cl604]) ).
thf(zip_derived_cl620,plain,
sk__22 != emptyset,
inference(clc,[status(thm)],[zip_derived_cl615,zip_derived_cl611]) ).
thf(zip_derived_cl908,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl905,zip_derived_cl620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU820^2 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.hsI5xjD2ic true
% 0.13/0.36 % Computer : n028.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Oct 1 16:13:08 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.37 % Python version: Python 3.6.8
% 0.13/0.37 % Running in HO mode
% 0.50/0.65 % Total configuration time : 828
% 0.50/0.65 % Estimated wc time : 1656
% 0.50/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.50/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.50/0.71 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.50/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.50/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.50/0.72 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.50/0.73 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.50/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.50/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.52/0.81 % Solved by lams/40_c.s.sh.
% 0.52/0.81 % done 111 iterations in 0.080s
% 0.52/0.81 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.52/0.81 % SZS output start Refutation
% See solution above
% 0.52/0.81
% 0.52/0.81
% 0.52/0.81 % Terminating...
% 1.60/0.86 % Runner terminated.
% 1.60/0.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------