%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU774^2 : 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.ZV381HENQZ true
% Computer : n010.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 04:56:17 PM UTC 2025
% Result : Theorem 0.52s 1.02s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of formulae : 162 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 486 ( 86 equ; 0 cnn)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 2698 ( 149 ~; 235 |; 0 &;2241 @)
% ( 0 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 166 ( 15 ^; 151 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(eqbreln_type,type,
eqbreln: $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(sk__9_type,type,
sk__9: $i ).
thf(sk__10_type,type,
sk__10: $i ).
thf(sk__14_type,type,
sk__14: $i > $i > $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(sk__8_type,type,
sk__8: $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(sk__13_type,type,
sk__13: $i > $i > $i > $i > $i ).
thf(sk__12_type,type,
sk__12: $i > $i > $i > $i > $i ).
thf(breln1_type,type,
breln1: $i > $i > $o ).
thf(sk__11_type,type,
sk__11: $i > $i > $i > $i > $i ).
thf(breln1,axiom,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
thf(breln,axiom,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf('0',plain,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln]) ).
thf('1',plain,
( breln
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('2',plain,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln1,'1']) ).
thf('3',plain,
( breln1
= ( ^ [V_1: $i,V_2: $i] : ( breln @ V_1 @ V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf(eqbreln,axiom,
( eqbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ) ).
thf('4',plain,
( eqbreln
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( breln @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( breln @ X4 @ X6 @ X10 )
=> ( ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X6 )
=> ( ( in @ ( kpair @ X12 @ X14 ) @ X8 )
=> ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) )
=> ( ! [X16: $i] :
( ( in @ X16 @ X4 )
=> ! [X18: $i] :
( ( in @ X18 @ X6 )
=> ( ( in @ ( kpair @ X16 @ X18 ) @ X10 )
=> ( in @ ( kpair @ X16 @ X18 ) @ X8 ) ) ) )
=> ( X8 = X10 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(eqbreln1,conjecture,
( eqbreln
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ! [X10: $i] :
( ( subset @ X10 @ ( cartprod @ X4 @ X6 ) )
=> ( ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X6 )
=> ( ( in @ ( kpair @ X12 @ X14 ) @ X8 )
=> ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) )
=> ( ! [X16: $i] :
( ( in @ X16 @ X4 )
=> ! [X18: $i] :
( ( in @ X18 @ X6 )
=> ( ( in @ ( kpair @ X16 @ X18 ) @ X10 )
=> ( in @ ( kpair @ X16 @ X18 ) @ X8 ) ) ) )
=> ( X8 = X10 ) ) ) ) )
=> ! [X20: $i,X22: $i] :
( ( subset @ X22 @ ( cartprod @ X20 @ X20 ) )
=> ! [X24: $i] :
( ( subset @ X24 @ ( cartprod @ X20 @ X20 ) )
=> ( ! [X26: $i] :
( ( in @ X26 @ X20 )
=> ! [X28: $i] :
( ( in @ X28 @ X20 )
=> ( ( in @ ( kpair @ X26 @ X28 ) @ X22 )
=> ( in @ ( kpair @ X26 @ X28 ) @ X24 ) ) ) )
=> ( ! [X30: $i] :
( ( in @ X30 @ X20 )
=> ! [X32: $i] :
( ( in @ X32 @ X20 )
=> ( ( in @ ( kpair @ X30 @ X32 ) @ X24 )
=> ( in @ ( kpair @ X30 @ X32 ) @ X22 ) ) ) )
=> ( X22 = X24 ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ! [X10: $i] :
( ( subset @ X10 @ ( cartprod @ X4 @ X6 ) )
=> ( ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X6 )
=> ( ( in @ ( kpair @ X12 @ X14 ) @ X8 )
=> ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) )
=> ( ! [X16: $i] :
( ( in @ X16 @ X4 )
=> ! [X18: $i] :
( ( in @ X18 @ X6 )
=> ( ( in @ ( kpair @ X16 @ X18 ) @ X10 )
=> ( in @ ( kpair @ X16 @ X18 ) @ X8 ) ) ) )
=> ( X8 = X10 ) ) ) ) )
=> ! [X20: $i,X22: $i] :
( ( subset @ X22 @ ( cartprod @ X20 @ X20 ) )
=> ! [X24: $i] :
( ( subset @ X24 @ ( cartprod @ X20 @ X20 ) )
=> ( ! [X26: $i] :
( ( in @ X26 @ X20 )
=> ! [X28: $i] :
( ( in @ X28 @ X20 )
=> ( ( in @ ( kpair @ X26 @ X28 ) @ X22 )
=> ( in @ ( kpair @ X26 @ X28 ) @ X24 ) ) ) )
=> ( ! [X30: $i] :
( ( in @ X30 @ X20 )
=> ! [X32: $i] :
( ( in @ X32 @ X20 )
=> ( ( in @ ( kpair @ X30 @ X32 ) @ X24 )
=> ( in @ ( kpair @ X30 @ X32 ) @ X22 ) ) ) )
=> ( X22 = X24 ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl19,plain,
! [X6: $i,X7: $i] :
( ~ ( in @ X6 @ sk__8 )
| ( in @ ( kpair @ X7 @ X6 ) @ sk__10 )
| ~ ( in @ ( kpair @ X7 @ X6 ) @ sk__9 )
| ~ ( in @ X7 @ sk__8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl17,plain,
! [X4: $i,X5: $i] :
( ~ ( in @ X4 @ sk__8 )
| ( in @ ( kpair @ X5 @ X4 ) @ sk__9 )
| ~ ( in @ ( kpair @ X5 @ X4 ) @ sk__10 )
| ~ ( in @ X5 @ sk__8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl20,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl5,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( kpair @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) ) @ X0 )
| ( X3 = X0 )
| ( in @ ( kpair @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) ) @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl153,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ X0 @ sk__8 @ sk__8 ) ) @ X0 )
| ( X0 = sk__10 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ X0 @ sk__8 @ sk__8 ) ) @ sk__10 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl5]) ).
thf(zip_derived_cl212,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( sk__9 = sk__10 )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl153]) ).
thf(zip_derived_cl18,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl215,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl212,zip_derived_cl18]) ).
thf(zip_derived_cl17_001,plain,
! [X4: $i,X5: $i] :
( ~ ( in @ X4 @ sk__8 )
| ( in @ ( kpair @ X5 @ X4 ) @ sk__9 )
| ~ ( in @ ( kpair @ X5 @ X4 ) @ sk__10 )
| ~ ( in @ X5 @ sk__8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl217,plain,
( ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl215,zip_derived_cl17]) ).
thf(zip_derived_cl20_002,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_003,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ X1 )
| ( X3 = X0 )
| ( in @ ( kpair @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) ) @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl45,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ X0 @ sk__8 @ sk__8 ) ) @ X0 )
| ( X0 = sk__10 )
| ( in @ ( sk__13 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl1]) ).
thf(zip_derived_cl106,plain,
( ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl45]) ).
thf(zip_derived_cl18_004,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl109,plain,
( ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl106,zip_derived_cl18]) ).
thf(zip_derived_cl19_005,plain,
! [X6: $i,X7: $i] :
( ~ ( in @ X6 @ sk__8 )
| ( in @ ( kpair @ X7 @ X6 ) @ sk__10 )
| ~ ( in @ ( kpair @ X7 @ X6 ) @ sk__9 )
| ~ ( in @ X7 @ sk__8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl2,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ X1 )
| ( X3 = X0 )
| ~ ( in @ ( kpair @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) ) @ X0 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl81,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( sk__11 @ sk__10 @ X2 @ X1 @ X0 ) @ sk__8 )
| ~ ( in @ ( kpair @ ( sk__11 @ sk__10 @ X2 @ X1 @ X0 ) @ ( sk__12 @ sk__10 @ X2 @ X1 @ X0 ) ) @ sk__9 )
| ~ ( in @ ( sk__12 @ sk__10 @ X2 @ X1 @ X0 ) @ sk__8 )
| ~ ( subset @ X2 @ ( cartprod @ X0 @ X1 ) )
| ( X2 = sk__10 )
| ( in @ ( sk__13 @ sk__10 @ X2 @ X1 @ X0 ) @ X0 )
| ~ ( subset @ sk__10 @ ( cartprod @ X0 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl2]) ).
thf(zip_derived_cl268,plain,
( ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ~ ( subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ) )
| ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl109,zip_derived_cl81]) ).
thf(zip_derived_cl16_006,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl20_007,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl273,plain,
( ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(demod,[status(thm)],[zip_derived_cl268,zip_derived_cl16,zip_derived_cl20]) ).
thf(zip_derived_cl274,plain,
( ~ ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(simplify,[status(thm)],[zip_derived_cl273]) ).
thf(zip_derived_cl18_008,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl275,plain,
( ~ ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl274,zip_derived_cl18]) ).
thf(zip_derived_cl20_009,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_010,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ X1 )
| ( X3 = X0 )
| ( in @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ X1 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl29,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__11 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 )
| ( X0 = sk__10 )
| ( in @ ( sk__13 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl0]) ).
thf(zip_derived_cl34,plain,
( ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl29]) ).
thf(zip_derived_cl18_011,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl37,plain,
( ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl34,zip_derived_cl18]) ).
thf(zip_derived_cl281,plain,
( ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(clc,[status(thm)],[zip_derived_cl275,zip_derived_cl37]) ).
thf(zip_derived_cl20_012,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_013,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl3,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ X1 )
| ( X3 = X0 )
| ( in @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) @ X2 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl49,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__12 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 )
| ( X0 = sk__10 )
| ( in @ ( sk__13 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl3]) ).
thf(zip_derived_cl64,plain,
( ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl49]) ).
thf(zip_derived_cl18_014,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl67,plain,
( ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl64,zip_derived_cl18]) ).
thf(zip_derived_cl282,plain,
in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference(clc,[status(thm)],[zip_derived_cl281,zip_derived_cl67]) ).
thf(zip_derived_cl395,plain,
( ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(demod,[status(thm)],[zip_derived_cl217,zip_derived_cl282]) ).
thf(zip_derived_cl20_015,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_016,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) @ X2 )
| ( X3 = X0 )
| ( in @ ( kpair @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) ) @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl121,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ X0 @ sk__8 @ sk__8 ) ) @ X0 )
| ( X0 = sk__10 )
| ( in @ ( sk__14 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl13]) ).
thf(zip_derived_cl160,plain,
( ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl121]) ).
thf(zip_derived_cl18_017,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl163,plain,
( ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl160,zip_derived_cl18]) ).
thf(zip_derived_cl396,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 ) ),
inference(clc,[status(thm)],[zip_derived_cl395,zip_derived_cl163]) ).
thf(zip_derived_cl9,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ ( kpair @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) ) @ X3 )
| ( X3 = X0 )
| ( in @ ( kpair @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) ) @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl399,plain,
( ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ( sk__9 = sk__10 )
| ~ ( subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl396,zip_derived_cl9]) ).
thf(zip_derived_cl20_018,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_019,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl409,plain,
( ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ( sk__9 = sk__10 ) ),
inference(demod,[status(thm)],[zip_derived_cl399,zip_derived_cl20,zip_derived_cl16]) ).
thf(zip_derived_cl410,plain,
( ( sk__9 = sk__10 )
| ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 ) ),
inference(simplify,[status(thm)],[zip_derived_cl409]) ).
thf(zip_derived_cl18_020,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl411,plain,
in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl410,zip_derived_cl18]) ).
thf(zip_derived_cl19_021,plain,
! [X6: $i,X7: $i] :
( ~ ( in @ X6 @ sk__8 )
| ( in @ ( kpair @ X7 @ X6 ) @ sk__10 )
| ~ ( in @ ( kpair @ X7 @ X6 ) @ sk__9 )
| ~ ( in @ X7 @ sk__8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl6,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( kpair @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) ) @ X0 )
| ( X3 = X0 )
| ~ ( in @ ( kpair @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) ) @ X0 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl125,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( sk__11 @ sk__10 @ X2 @ X1 @ X0 ) @ sk__8 )
| ~ ( in @ ( kpair @ ( sk__11 @ sk__10 @ X2 @ X1 @ X0 ) @ ( sk__12 @ sk__10 @ X2 @ X1 @ X0 ) ) @ sk__9 )
| ~ ( in @ ( sk__12 @ sk__10 @ X2 @ X1 @ X0 ) @ sk__8 )
| ~ ( subset @ X2 @ ( cartprod @ X0 @ X1 ) )
| ( X2 = sk__10 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ X2 @ X1 @ X0 ) @ ( sk__14 @ sk__10 @ X2 @ X1 @ X0 ) ) @ sk__10 )
| ~ ( subset @ sk__10 @ ( cartprod @ X0 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl6]) ).
thf(zip_derived_cl477,plain,
( ~ ( subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( sk__9 = sk__10 )
| ~ ( subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ) )
| ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl411,zip_derived_cl125]) ).
thf(zip_derived_cl16_022,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl20_023,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl20_024,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_025,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl7,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( kpair @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) ) @ X0 )
| ( X3 = X0 )
| ( in @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) @ X2 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl117,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__12 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 )
| ( X0 = sk__10 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ X0 @ sk__8 @ sk__8 ) ) @ sk__10 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl7]) ).
thf(zip_derived_cl176,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( sk__9 = sk__10 )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl117]) ).
thf(zip_derived_cl18_026,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl179,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl176,zip_derived_cl18]) ).
thf(zip_derived_cl17_027,plain,
! [X4: $i,X5: $i] :
( ~ ( in @ X4 @ sk__8 )
| ( in @ ( kpair @ X5 @ X4 ) @ sk__9 )
| ~ ( in @ ( kpair @ X5 @ X4 ) @ sk__10 )
| ~ ( in @ X5 @ sk__8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl181,plain,
( ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl179,zip_derived_cl17]) ).
thf(zip_derived_cl282_028,plain,
in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference(clc,[status(thm)],[zip_derived_cl281,zip_derived_cl67]) ).
thf(zip_derived_cl357,plain,
( ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(demod,[status(thm)],[zip_derived_cl181,zip_derived_cl282]) ).
thf(zip_derived_cl20_029,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_030,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl15,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) @ X2 )
| ( X3 = X0 )
| ( in @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) @ X2 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl57,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__12 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 )
| ( X0 = sk__10 )
| ( in @ ( sk__14 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl15]) ).
thf(zip_derived_cl94,plain,
( ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl57]) ).
thf(zip_derived_cl18_031,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl97,plain,
( ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl94,zip_derived_cl18]) ).
thf(zip_derived_cl358,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(clc,[status(thm)],[zip_derived_cl357,zip_derived_cl97]) ).
thf(zip_derived_cl11,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ ( kpair @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) ) @ X3 )
| ( X3 = X0 )
| ( in @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) @ X2 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl359,plain,
( ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ~ ( subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl358,zip_derived_cl11]) ).
thf(zip_derived_cl20_032,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_033,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl367,plain,
( ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 ) ),
inference(demod,[status(thm)],[zip_derived_cl359,zip_derived_cl20,zip_derived_cl16]) ).
thf(zip_derived_cl368,plain,
( ( sk__9 = sk__10 )
| ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(simplify,[status(thm)],[zip_derived_cl367]) ).
thf(zip_derived_cl18_034,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl369,plain,
in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl368,zip_derived_cl18]) ).
thf(zip_derived_cl20_035,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_036,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( kpair @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) ) @ X0 )
| ( X3 = X0 )
| ( in @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ X1 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl111,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__11 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 )
| ( X0 = sk__10 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ X0 @ sk__8 @ sk__8 ) ) @ sk__10 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl4]) ).
thf(zip_derived_cl138,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( sk__9 = sk__10 )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl111]) ).
thf(zip_derived_cl18_037,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl141,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl138,zip_derived_cl18]) ).
thf(zip_derived_cl17_038,plain,
! [X4: $i,X5: $i] :
( ~ ( in @ X4 @ sk__8 )
| ( in @ ( kpair @ X5 @ X4 ) @ sk__9 )
| ~ ( in @ ( kpair @ X5 @ X4 ) @ sk__10 )
| ~ ( in @ X5 @ sk__8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl143,plain,
( ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl141,zip_derived_cl17]) ).
thf(zip_derived_cl282_039,plain,
in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference(clc,[status(thm)],[zip_derived_cl281,zip_derived_cl67]) ).
thf(zip_derived_cl291,plain,
( ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(demod,[status(thm)],[zip_derived_cl143,zip_derived_cl282]) ).
thf(zip_derived_cl20_040,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_041,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl12,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) @ X2 )
| ( X3 = X0 )
| ( in @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ X1 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl53,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__11 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 )
| ( X0 = sk__10 )
| ( in @ ( sk__14 @ sk__10 @ X0 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl12]) ).
thf(zip_derived_cl76,plain,
( ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl53]) ).
thf(zip_derived_cl18_042,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl79,plain,
( ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl76,zip_derived_cl18]) ).
thf(zip_derived_cl292,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(clc,[status(thm)],[zip_derived_cl291,zip_derived_cl79]) ).
thf(zip_derived_cl8,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ ( kpair @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) ) @ X3 )
| ( X3 = X0 )
| ( in @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ X1 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl296,plain,
( ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ~ ( subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl292,zip_derived_cl8]) ).
thf(zip_derived_cl20_043,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_044,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl307,plain,
( ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 ) ),
inference(demod,[status(thm)],[zip_derived_cl296,zip_derived_cl20,zip_derived_cl16]) ).
thf(zip_derived_cl308,plain,
( ( sk__9 = sk__10 )
| ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference(simplify,[status(thm)],[zip_derived_cl307]) ).
thf(zip_derived_cl18_045,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl309,plain,
in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl308,zip_derived_cl18]) ).
thf(zip_derived_cl479,plain,
( ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( sk__9 = sk__10 ) ),
inference(demod,[status(thm)],[zip_derived_cl477,zip_derived_cl16,zip_derived_cl20,zip_derived_cl369,zip_derived_cl309]) ).
thf(zip_derived_cl18_046,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl480,plain,
in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl479,zip_derived_cl18]) ).
thf(zip_derived_cl484,plain,
( ~ ( in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup+',[status(thm)],[zip_derived_cl17,zip_derived_cl480]) ).
thf(zip_derived_cl282_047,plain,
in @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference(clc,[status(thm)],[zip_derived_cl281,zip_derived_cl67]) ).
thf(zip_derived_cl411_048,plain,
in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl410,zip_derived_cl18]) ).
thf(zip_derived_cl19_049,plain,
! [X6: $i,X7: $i] :
( ~ ( in @ X6 @ sk__8 )
| ( in @ ( kpair @ X7 @ X6 ) @ sk__10 )
| ~ ( in @ ( kpair @ X7 @ X6 ) @ sk__9 )
| ~ ( in @ X7 @ sk__8 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl14,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ( in @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) @ X2 )
| ( X3 = X0 )
| ~ ( in @ ( kpair @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) ) @ X0 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl115,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( sk__11 @ sk__10 @ X2 @ X1 @ X0 ) @ sk__8 )
| ~ ( in @ ( kpair @ ( sk__11 @ sk__10 @ X2 @ X1 @ X0 ) @ ( sk__12 @ sk__10 @ X2 @ X1 @ X0 ) ) @ sk__9 )
| ~ ( in @ ( sk__12 @ sk__10 @ X2 @ X1 @ X0 ) @ sk__8 )
| ~ ( subset @ X2 @ ( cartprod @ X0 @ X1 ) )
| ( X2 = sk__10 )
| ( in @ ( sk__14 @ sk__10 @ X2 @ X1 @ X0 ) @ X1 )
| ~ ( subset @ sk__10 @ ( cartprod @ X0 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl14]) ).
thf(zip_derived_cl471,plain,
( ~ ( subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ) )
| ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 )
| ~ ( subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ) )
| ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl411,zip_derived_cl115]) ).
thf(zip_derived_cl16_050,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl20_051,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl369_052,plain,
in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl368,zip_derived_cl18]) ).
thf(zip_derived_cl309_053,plain,
in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl308,zip_derived_cl18]) ).
thf(zip_derived_cl473,plain,
( ( in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ( sk__9 = sk__10 ) ),
inference(demod,[status(thm)],[zip_derived_cl471,zip_derived_cl16,zip_derived_cl20,zip_derived_cl369,zip_derived_cl309]) ).
thf(zip_derived_cl18_054,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl474,plain,
in @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl473,zip_derived_cl18]) ).
thf(zip_derived_cl487,plain,
in @ ( kpair @ ( sk__13 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__14 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9,
inference(demod,[status(thm)],[zip_derived_cl484,zip_derived_cl282,zip_derived_cl474]) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ ( kpair @ ( sk__13 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__14 @ X0 @ X3 @ X2 @ X1 ) ) @ X3 )
| ( X3 = X0 )
| ~ ( in @ ( kpair @ ( sk__11 @ X0 @ X3 @ X2 @ X1 ) @ ( sk__12 @ X0 @ X3 @ X2 @ X1 ) ) @ X0 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl492,plain,
( ~ ( subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ) )
| ~ ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( sk__9 = sk__10 )
| ~ ( subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl487,zip_derived_cl10]) ).
thf(zip_derived_cl20_055,plain,
subset @ sk__9 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl16_056,plain,
subset @ sk__10 @ ( cartprod @ sk__8 @ sk__8 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl501,plain,
( ~ ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 )
| ( sk__9 = sk__10 ) ),
inference(demod,[status(thm)],[zip_derived_cl492,zip_derived_cl20,zip_derived_cl16]) ).
thf(zip_derived_cl18_057,plain,
sk__9 != sk__10,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl502,plain,
~ ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__10 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl501,zip_derived_cl18]) ).
thf(zip_derived_cl515,plain,
( ~ ( in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 )
| ~ ( in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9 )
| ~ ( in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl502]) ).
thf(zip_derived_cl309_058,plain,
in @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl308,zip_derived_cl18]) ).
thf(zip_derived_cl411_059,plain,
in @ ( kpair @ ( sk__11 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) ) @ sk__9,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl410,zip_derived_cl18]) ).
thf(zip_derived_cl369_060,plain,
in @ ( sk__12 @ sk__10 @ sk__9 @ sk__8 @ sk__8 ) @ sk__8,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl368,zip_derived_cl18]) ).
thf(zip_derived_cl517,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl515,zip_derived_cl309,zip_derived_cl411,zip_derived_cl369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU774^2 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ZV381HENQZ true
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 1 16:12:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % 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
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.51/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.52/1.02 % Solved by lams/40_c.s.sh.
% 0.52/1.02 % done 168 iterations in 0.255s
% 0.52/1.02 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.52/1.02 % SZS output start Refutation
% See solution above
% 0.52/1.02
% 0.52/1.02
% 0.52/1.02 % Terminating...
% 0.59/1.14 % Runner terminated.
% 0.59/1.15 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------