%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU673^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CVWuU44HER 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 Oct 2 04:55:41 PM UTC 2025
% Result : Theorem 0.53s 0.80s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 41 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 33 equ; 0 cnn)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 553 ( 23 ~; 18 |; 18 &; 456 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 9 con; 0-3 aty)
% Number of variables : 141 ( 60 ^; 70 !; 11 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
thf(singleton_type,type,
singleton: $i > $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(funcImageSingleton_type,type,
funcImageSingleton: $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(sk__14_type,type,
sk__14: $i > $i ).
thf(ex1_type,type,
ex1: $i > ( $i > $o ) > $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(sk__11_type,type,
sk__11: $i ).
thf(sk__10_type,type,
sk__10: $i ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(sk__12_type,type,
sk__12: $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf(theprop_type,type,
theprop: $o ).
thf(sk__13_type,type,
sk__13: $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
thf('0',plain,
( funcImageSingleton
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(func,axiom,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
thf(breln,axiom,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf('1',plain,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln]) ).
thf('2',plain,
( breln
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(ex1,axiom,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
thf(singleton,axiom,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ) ).
thf('3',plain,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[singleton]) ).
thf('4',plain,
( singleton
= ( ^ [V_1: $i] :
? [X4: $i] :
( ( V_1
= ( setadjoin @ X4 @ emptyset ) )
& ( in @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('5',plain,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ex1,'4']) ).
thf('6',plain,
( ex1
= ( ^ [V_1: $i,V_2: $i > $o] :
( singleton
@ ( dsetconstr @ V_1
@ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
define([status(thm)]) ).
thf('7',plain,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[func,'2','6','4']) ).
thf('8',plain,
( func
= ( ^ [V_1: $i,V_2: $i,V_3: $i] :
( ( breln @ V_1 @ V_2 @ V_3 )
& ! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ( ex1 @ V_2
@ ^ [V_4: $i] : ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ),
define([status(thm)]) ).
thf(theprop,axiom,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ) ).
thf('9',plain,
( theprop
= ( ! [X4: $i] :
( ( singleton @ X4 )
=> ( in @ ( setunion @ X4 ) @ X4 ) ) ) ),
define([status(thm)]) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ) ).
thf('10',plain,
( dsetconstrEL
= ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( in @ X8 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(apProp,conjecture,
( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( in @ X8 @ X4 ) )
=> ( ! [X10: $i] :
( ? [X12: $i] :
( ( X10
= ( setadjoin @ X12 @ emptyset ) )
& ( in @ X12 @ X10 ) )
=> ( in @ ( setunion @ X10 ) @ X10 ) )
=> ( ! [X14: $i,X16: $i,X18: $i] :
( ( ( subset @ X18 @ ( cartprod @ X14 @ X16 ) )
& ! [X20: $i] :
( ( in @ X20 @ X14 )
=> ? [X22: $i] :
( ( ( dsetconstr @ X16
@ ^ [V_2: $i] : ( in @ ( kpair @ X20 @ V_2 ) @ X18 ) )
= ( setadjoin @ X22 @ emptyset ) )
& ( in @ X22
@ ( dsetconstr @ X16
@ ^ [V_3: $i] : ( in @ ( kpair @ X20 @ V_3 ) @ X18 ) ) ) ) ) )
=> ! [X24: $i] :
( ( in @ X24 @ X14 )
=> ? [X26: $i] :
( ( ( dsetconstr @ X16
@ ^ [V_4: $i] : ( in @ ( kpair @ X24 @ V_4 ) @ X18 ) )
= ( setadjoin @ X26 @ emptyset ) )
& ( in @ X26
@ ( dsetconstr @ X16
@ ^ [V_5: $i] : ( in @ ( kpair @ X24 @ V_5 ) @ X18 ) ) ) ) ) )
=> ! [X28: $i,X30: $i,X32: $i] :
( ( ( subset @ X32 @ ( cartprod @ X28 @ X30 ) )
& ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ? [X36: $i] :
( ( ( dsetconstr @ X30
@ ^ [V_6: $i] : ( in @ ( kpair @ X34 @ V_6 ) @ X32 ) )
= ( setadjoin @ X36 @ emptyset ) )
& ( in @ X36
@ ( dsetconstr @ X30
@ ^ [V_7: $i] : ( in @ ( kpair @ X34 @ V_7 ) @ X32 ) ) ) ) ) )
=> ! [X38: $i] :
( ( in @ X38 @ X28 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X30
@ ^ [V_8: $i] : ( in @ ( kpair @ X38 @ V_8 ) @ X32 ) ) )
@ X30 ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( in @ X8 @ X4 ) )
=> ( ! [X10: $i] :
( ? [X12: $i] :
( ( X10
= ( setadjoin @ X12 @ emptyset ) )
& ( in @ X12 @ X10 ) )
=> ( in @ ( setunion @ X10 ) @ X10 ) )
=> ( ! [X14: $i,X16: $i,X18: $i] :
( ( ( subset @ X18 @ ( cartprod @ X14 @ X16 ) )
& ! [X20: $i] :
( ( in @ X20 @ X14 )
=> ? [X22: $i] :
( ( ( dsetconstr @ X16
@ ^ [V_2: $i] : ( in @ ( kpair @ X20 @ V_2 ) @ X18 ) )
= ( setadjoin @ X22 @ emptyset ) )
& ( in @ X22
@ ( dsetconstr @ X16
@ ^ [V_3: $i] : ( in @ ( kpair @ X20 @ V_3 ) @ X18 ) ) ) ) ) )
=> ! [X24: $i] :
( ( in @ X24 @ X14 )
=> ? [X26: $i] :
( ( ( dsetconstr @ X16
@ ^ [V_4: $i] : ( in @ ( kpair @ X24 @ V_4 ) @ X18 ) )
= ( setadjoin @ X26 @ emptyset ) )
& ( in @ X26
@ ( dsetconstr @ X16
@ ^ [V_5: $i] : ( in @ ( kpair @ X24 @ V_5 ) @ X18 ) ) ) ) ) )
=> ! [X28: $i,X30: $i,X32: $i] :
( ( ( subset @ X32 @ ( cartprod @ X28 @ X30 ) )
& ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ? [X36: $i] :
( ( ( dsetconstr @ X30
@ ^ [V_6: $i] : ( in @ ( kpair @ X34 @ V_6 ) @ X32 ) )
= ( setadjoin @ X36 @ emptyset ) )
& ( in @ X36
@ ( dsetconstr @ X30
@ ^ [V_7: $i] : ( in @ ( kpair @ X34 @ V_7 ) @ X32 ) ) ) ) ) )
=> ! [X38: $i] :
( ( in @ X38 @ X28 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X30
@ ^ [V_8: $i] : ( in @ ( kpair @ X38 @ V_8 ) @ X32 ) ) )
@ X30 ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10,plain,
! [X9: $i,X10: $i] :
( ( in @ ( setunion @ X9 ) @ X9 )
| ~ ( in @ X10 @ X9 )
| ( X9
!= ( setadjoin @ X10 @ emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl54,plain,
! [X10: $i] :
( ~ ( in @ X10 @ ( setadjoin @ X10 @ emptyset ) )
| ( in @ ( setunion @ ( setadjoin @ X10 @ emptyset ) ) @ ( setadjoin @ X10 @ emptyset ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl7,plain,
! [X8: $i] :
( ( ( dsetconstr @ sk__11
@ ^ [Y0: $i] : ( in @ ( kpair @ X8 @ Y0 ) @ sk__12 ) )
= ( setadjoin @ ( sk__14 @ X8 ) @ emptyset ) )
| ~ ( in @ X8 @ sk__10 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
| ~ ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl19,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
| ~ ( in @ X0 @ ( dsetconstr @ X1 @ X2 ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl20,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ ( setadjoin @ ( sk__14 @ X0 ) @ emptyset ) )
| ~ ( in @ X0 @ sk__10 )
| ( in @ X1 @ sk__11 ) ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl19]) ).
thf(zip_derived_cl55,plain,
! [X0: $i] :
( ~ ( in @ ( sk__14 @ X0 ) @ ( setadjoin @ ( sk__14 @ X0 ) @ emptyset ) )
| ( in @ ( setunion @ ( setadjoin @ ( sk__14 @ X0 ) @ emptyset ) ) @ sk__11 )
| ~ ( in @ X0 @ sk__10 ) ),
inference('sup-',[status(thm)],[zip_derived_cl54,zip_derived_cl20]) ).
thf(zip_derived_cl7_001,plain,
! [X8: $i] :
( ( ( dsetconstr @ sk__11
@ ^ [Y0: $i] : ( in @ ( kpair @ X8 @ Y0 ) @ sk__12 ) )
= ( setadjoin @ ( sk__14 @ X8 ) @ emptyset ) )
| ~ ( in @ X8 @ sk__10 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl8,plain,
! [X8: $i] :
( ( in @ ( sk__14 @ X8 )
@ ( dsetconstr @ sk__11
@ ^ [Y0: $i] : ( in @ ( kpair @ X8 @ Y0 ) @ sk__12 ) ) )
| ~ ( in @ X8 @ sk__10 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl11,plain,
! [X0: $i] :
( ( in @ ( sk__14 @ X0 ) @ ( setadjoin @ ( sk__14 @ X0 ) @ emptyset ) )
| ~ ( in @ X0 @ sk__10 )
| ~ ( in @ X0 @ sk__10 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl12,plain,
! [X0: $i] :
( ~ ( in @ X0 @ sk__10 )
| ( in @ ( sk__14 @ X0 ) @ ( setadjoin @ ( sk__14 @ X0 ) @ emptyset ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl61,plain,
! [X0: $i] :
( ~ ( in @ X0 @ sk__10 )
| ( in @ ( setunion @ ( setadjoin @ ( sk__14 @ X0 ) @ emptyset ) ) @ sk__11 ) ),
inference(clc,[status(thm)],[zip_derived_cl55,zip_derived_cl12]) ).
thf(zip_derived_cl7_002,plain,
! [X8: $i] :
( ( ( dsetconstr @ sk__11
@ ^ [Y0: $i] : ( in @ ( kpair @ X8 @ Y0 ) @ sk__12 ) )
= ( setadjoin @ ( sk__14 @ X8 ) @ emptyset ) )
| ~ ( in @ X8 @ sk__10 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl6,plain,
~ ( in
@ ( setunion
@ ( dsetconstr @ sk__11
@ ^ [Y0: $i] : ( in @ ( kpair @ sk__13 @ Y0 ) @ sk__12 ) ) )
@ sk__11 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl17,plain,
( ~ ( in @ ( setunion @ ( setadjoin @ ( sk__14 @ sk__13 ) @ emptyset ) ) @ sk__11 )
| ~ ( in @ sk__13 @ sk__10 ) ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl6]) ).
thf(zip_derived_cl5,plain,
in @ sk__13 @ sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl18,plain,
~ ( in @ ( setunion @ ( setadjoin @ ( sk__14 @ sk__13 ) @ emptyset ) ) @ sk__11 ),
inference(demod,[status(thm)],[zip_derived_cl17,zip_derived_cl5]) ).
thf(zip_derived_cl62,plain,
~ ( in @ sk__13 @ sk__10 ),
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl18]) ).
thf(zip_derived_cl5_003,plain,
in @ sk__13 @ sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl67,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl62,zip_derived_cl5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU673^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CVWuU44HER true
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Oct 1 16:09:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Running portfolio for 300 s
% 0.11/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.33 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.34 % Running in HO mode
% 0.50/0.63 % Total configuration time : 828
% 0.50/0.63 % Estimated wc time : 1656
% 0.50/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.53/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.53/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.53/0.80 % Solved by lams/40_c.s.sh.
% 0.53/0.80 % done 25 iterations in 0.049s
% 0.53/0.80 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.53/0.80 % SZS output start Refutation
% See solution above
% 0.53/0.80
% 0.53/0.80
% 0.53/0.80 % Terminating...
% 0.53/0.85 % Runner terminated.
% 1.77/0.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------