TSTP Solution File: GRP774+1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP774+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lcIKR7KggB true
% Computer : n007.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 01:53:15 EDT 2023
% Result : Theorem 258.32s 37.85s
% Output : Refutation 258.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 10
% Syntax : Number of formulae : 504 ( 487 unt; 6 typ; 0 def)
% Number of atoms : 513 ( 495 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 5378 ( 15 ~; 9 |; 3 &;5348 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 988 ( 0 ^; 988 !; 0 ?; 988 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i ).
thf(d_type,type,
d: $i > $i > $o ).
thf(sk__1_type,type,
sk__1: $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(sk__3_type,type,
sk__3: $i ).
thf(sk__type,type,
sk_: $i ).
thf(sos01,axiom,
! [C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ C )
= ( product @ A @ ( product @ B @ C ) ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(sos02,axiom,
! [A: $i] :
( ( product @ A @ A )
= A ) ).
thf(zip_derived_cl1,plain,
! [X0: $i] :
( ( product @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[sos02]) ).
thf(zip_derived_cl0_001,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl29,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X2 @ X1 ) @ X0 )
= ( product @ ( product @ X2 @ X1 ) @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl10]) ).
thf(zip_derived_cl0_002,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_003,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl32,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1_004,plain,
! [X0: $i] :
( ( product @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[sos02]) ).
thf(zip_derived_cl0_005,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1_006,plain,
! [X0: $i] :
( ( product @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[sos02]) ).
thf(zip_derived_cl0_007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl9,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X2 @ X1 ) @ X0 )
= ( product @ ( product @ X2 @ X1 ) @ ( product @ X0 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl9]) ).
thf(zip_derived_cl0_008,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl76,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X2 @ X1 ) @ ( product @ X0 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl66,zip_derived_cl0]) ).
thf(zip_derived_cl780,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ X0 @ X0 ) )
= ( product @ ( product @ X1 @ X0 ) @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl76]) ).
thf(zip_derived_cl1_009,plain,
! [X0: $i] :
( ( product @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[sos02]) ).
thf(zip_derived_cl847,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ ( product @ X1 @ X0 ) @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl780,zip_derived_cl1]) ).
thf(zip_derived_cl932,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) )
= ( product @ ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) @ ( product @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl32,zip_derived_cl847]) ).
thf(zip_derived_cl32_010,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl32_011,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl0_012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_013,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_014,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_015,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl9_016,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl9]) ).
thf(zip_derived_cl0_017,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_018,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl975,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl932,zip_derived_cl32,zip_derived_cl32,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl58,zip_derived_cl0,zip_derived_cl0]) ).
thf(goals,conjecture,
! [X2: $i,X3: $i,X4: $i,X5: $i] :
( ( ( d @ X2 @ X3 )
& ( d @ X4 @ X5 ) )
=> ( d @ ( product @ X2 @ X4 ) @ ( product @ X3 @ X5 ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [X2: $i,X3: $i,X4: $i,X5: $i] :
( ( ( d @ X2 @ X3 )
& ( d @ X4 @ X5 ) )
=> ( d @ ( product @ X2 @ X4 ) @ ( product @ X3 @ X5 ) ) ),
inference('cnf.neg',[status(esa)],[goals]) ).
thf(zip_derived_cl6,plain,
d @ sk__2 @ sk__3,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(sos03,axiom,
! [X0: $i,X1: $i] :
( ( d @ X0 @ X1 )
<=> ( ( ( product @ X0 @ ( product @ X1 @ X0 ) )
= X0 )
& ( ( product @ X1 @ ( product @ X0 @ X1 ) )
= X1 ) ) ) ).
thf(zip_derived_cl3,plain,
! [X0: $i,X1: $i] :
( ( ( product @ X0 @ ( product @ X1 @ X0 ) )
= X0 )
| ~ ( d @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[sos03]) ).
thf(zip_derived_cl17,plain,
( ( product @ sk__3 @ ( product @ sk__2 @ sk__3 ) )
= sk__3 ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl3]) ).
thf(zip_derived_cl10_019,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl76_020,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X2 @ X1 ) @ ( product @ X0 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl66,zip_derived_cl0]) ).
thf(zip_derived_cl751,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl76]) ).
thf(zip_derived_cl1151,plain,
( ( product @ sk__3 @ ( product @ sk__2 @ sk__3 ) )
= ( product @ ( product @ sk__3 @ sk__2 ) @ sk__3 ) ),
inference('sup+',[status(thm)],[zip_derived_cl17,zip_derived_cl751]) ).
thf(zip_derived_cl17_021,plain,
( ( product @ sk__3 @ ( product @ sk__2 @ sk__3 ) )
= sk__3 ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl3]) ).
thf(zip_derived_cl1213,plain,
( sk__3
= ( product @ ( product @ sk__3 @ sk__2 ) @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl1151,zip_derived_cl17]) ).
thf(zip_derived_cl0_022,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1359,plain,
! [X0: $i] :
( ( product @ sk__3 @ X0 )
= ( product @ ( product @ sk__3 @ sk__2 ) @ ( product @ sk__3 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1213,zip_derived_cl0]) ).
thf(zip_derived_cl32_023,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1604,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ ( product @ sk__3 @ sk__2 ) @ ( product @ sk__3 @ X0 ) ) )
= ( product @ X1 @ ( product @ ( product @ sk__3 @ sk__2 ) @ ( product @ X1 @ ( product @ sk__3 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1359,zip_derived_cl32]) ).
thf(zip_derived_cl1359_024,plain,
! [X0: $i] :
( ( product @ sk__3 @ X0 )
= ( product @ ( product @ sk__3 @ sk__2 ) @ ( product @ sk__3 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1213,zip_derived_cl0]) ).
thf(zip_derived_cl0_025,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1649,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__3 @ X0 ) )
= ( product @ X1 @ ( product @ sk__3 @ ( product @ sk__2 @ ( product @ X1 @ ( product @ sk__3 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1604,zip_derived_cl1359,zip_derived_cl0]) ).
thf(zip_derived_cl8686,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ sk__3 ) ) ) ) )
= ( product @ X0 @ ( product @ sk__3 @ ( product @ sk__2 @ ( product @ X0 @ sk__3 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl975,zip_derived_cl1649]) ).
thf(zip_derived_cl1213_026,plain,
( sk__3
= ( product @ ( product @ sk__3 @ sk__2 ) @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl1151,zip_derived_cl17]) ).
thf(zip_derived_cl32_027,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1364,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ ( product @ sk__3 @ sk__2 ) @ sk__3 ) )
= ( product @ X0 @ ( product @ ( product @ sk__3 @ sk__2 ) @ ( product @ X0 @ sk__3 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1213,zip_derived_cl32]) ).
thf(zip_derived_cl1213_028,plain,
( sk__3
= ( product @ ( product @ sk__3 @ sk__2 ) @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl1151,zip_derived_cl17]) ).
thf(zip_derived_cl0_029,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1376,plain,
! [X0: $i] :
( ( product @ X0 @ sk__3 )
= ( product @ X0 @ ( product @ sk__3 @ ( product @ sk__2 @ ( product @ X0 @ sk__3 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1364,zip_derived_cl1213,zip_derived_cl0]) ).
thf(zip_derived_cl8764,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ sk__3 ) ) ) ) )
= ( product @ X0 @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl8686,zip_derived_cl1376]) ).
thf(zip_derived_cl32_030,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl8928,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ sk__3 ) ) ) )
= ( product @ sk__3 @ ( product @ X0 @ sk__3 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8764,zip_derived_cl32]) ).
thf(zip_derived_cl6_031,plain,
d @ sk__2 @ sk__3,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2,plain,
! [X0: $i,X1: $i] :
( ( ( product @ X0 @ ( product @ X1 @ X0 ) )
= X0 )
| ~ ( d @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[sos03]) ).
thf(zip_derived_cl15,plain,
( ( product @ sk__2 @ ( product @ sk__3 @ sk__2 ) )
= sk__2 ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl2]) ).
thf(zip_derived_cl751_032,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl76]) ).
thf(zip_derived_cl1150,plain,
( ( product @ sk__2 @ ( product @ sk__3 @ sk__2 ) )
= ( product @ ( product @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl15,zip_derived_cl751]) ).
thf(zip_derived_cl15_033,plain,
( ( product @ sk__2 @ ( product @ sk__3 @ sk__2 ) )
= sk__2 ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl2]) ).
thf(zip_derived_cl1212,plain,
( sk__2
= ( product @ ( product @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1150,zip_derived_cl15]) ).
thf(zip_derived_cl0_034,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1335,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl32_035,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1532,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) )
= ( product @ X1 @ ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ X1 @ ( product @ sk__2 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1335,zip_derived_cl32]) ).
thf(zip_derived_cl1335_036,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl0_037,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1577,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__2 @ X0 ) )
= ( product @ X1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X1 @ ( product @ sk__2 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1532,zip_derived_cl1335,zip_derived_cl0]) ).
thf(zip_derived_cl9118,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ sk__3 ) ) )
= ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X0 @ sk__3 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8928,zip_derived_cl1577]) ).
thf(zip_derived_cl751_038,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl76]) ).
thf(zip_derived_cl9573,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X0 @ sk__3 ) ) ) @ X0 ) )
= ( product @ ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ sk__3 ) ) ) @ ( product @ X0 @ ( product @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X0 @ sk__3 ) ) ) @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9118,zip_derived_cl751]) ).
thf(zip_derived_cl0_039,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_040,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_041,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl9_042,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_043,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_044,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_045,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl9_046,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_048,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl58_050,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl9]) ).
thf(zip_derived_cl17_051,plain,
( ( product @ sk__3 @ ( product @ sk__2 @ sk__3 ) )
= sk__3 ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl3]) ).
thf(zip_derived_cl0_052,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl48,plain,
! [X0: $i] :
( ( product @ sk__3 @ X0 )
= ( product @ sk__3 @ ( product @ ( product @ sk__2 @ sk__3 ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl17,zip_derived_cl0]) ).
thf(zip_derived_cl0_053,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl50,plain,
! [X0: $i] :
( ( product @ sk__3 @ X0 )
= ( product @ sk__3 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl48,zip_derived_cl0]) ).
thf(zip_derived_cl367,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) ) )
= ( product @ sk__3 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl58,zip_derived_cl50]) ).
thf(zip_derived_cl50_054,plain,
! [X0: $i] :
( ( product @ sk__3 @ X0 )
= ( product @ sk__3 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl48,zip_derived_cl0]) ).
thf(zip_derived_cl485,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) ) )
= ( product @ sk__3 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl367,zip_derived_cl50]) ).
thf(zip_derived_cl9664,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) )
= ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__3 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9573,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl9,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl9,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl485]) ).
thf(zip_derived_cl32_055,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl9754,plain,
! [X0: $i] :
( ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__3 @ X0 ) ) )
= ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9664,zip_derived_cl32]) ).
thf(zip_derived_cl975_056,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl932,zip_derived_cl32,zip_derived_cl32,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl58,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl7,plain,
d @ sk_ @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_057,plain,
! [X0: $i,X1: $i] :
( ( ( product @ X0 @ ( product @ X1 @ X0 ) )
= X0 )
| ~ ( d @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[sos03]) ).
thf(zip_derived_cl14,plain,
( ( product @ sk_ @ ( product @ sk__1 @ sk_ ) )
= sk_ ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl2]) ).
thf(zip_derived_cl751_058,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl76]) ).
thf(zip_derived_cl1148,plain,
( ( product @ sk_ @ ( product @ sk__1 @ sk_ ) )
= ( product @ ( product @ sk_ @ sk__1 ) @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl751]) ).
thf(zip_derived_cl14_059,plain,
( ( product @ sk_ @ ( product @ sk__1 @ sk_ ) )
= sk_ ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl2]) ).
thf(zip_derived_cl1210,plain,
( sk_
= ( product @ ( product @ sk_ @ sk__1 ) @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl1148,zip_derived_cl14]) ).
thf(zip_derived_cl0_060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1287,plain,
! [X0: $i] :
( ( product @ sk_ @ X0 )
= ( product @ ( product @ sk_ @ sk__1 ) @ ( product @ sk_ @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1210,zip_derived_cl0]) ).
thf(zip_derived_cl32_061,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1388,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ ( product @ sk_ @ sk__1 ) @ ( product @ sk_ @ X0 ) ) )
= ( product @ X1 @ ( product @ ( product @ sk_ @ sk__1 ) @ ( product @ X1 @ ( product @ sk_ @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1287,zip_derived_cl32]) ).
thf(zip_derived_cl1287_062,plain,
! [X0: $i] :
( ( product @ sk_ @ X0 )
= ( product @ ( product @ sk_ @ sk__1 ) @ ( product @ sk_ @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1210,zip_derived_cl0]) ).
thf(zip_derived_cl0_063,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1433,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk_ @ X0 ) )
= ( product @ X1 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X1 @ ( product @ sk_ @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1388,zip_derived_cl1287,zip_derived_cl0]) ).
thf(zip_derived_cl4860,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) ) )
= ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl975,zip_derived_cl1433]) ).
thf(zip_derived_cl1210_064,plain,
( sk_
= ( product @ ( product @ sk_ @ sk__1 ) @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl1148,zip_derived_cl14]) ).
thf(zip_derived_cl32_065,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1292,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ ( product @ sk_ @ sk__1 ) @ sk_ ) )
= ( product @ X0 @ ( product @ ( product @ sk_ @ sk__1 ) @ ( product @ X0 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1210,zip_derived_cl32]) ).
thf(zip_derived_cl1210_066,plain,
( sk_
= ( product @ ( product @ sk_ @ sk__1 ) @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl1148,zip_derived_cl14]) ).
thf(zip_derived_cl0_067,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1304,plain,
! [X0: $i] :
( ( product @ X0 @ sk_ )
= ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1292,zip_derived_cl1210,zip_derived_cl0]) ).
thf(zip_derived_cl4915,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) ) )
= ( product @ X0 @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl4860,zip_derived_cl1304]) ).
thf(zip_derived_cl32_068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl5048,plain,
! [X0: $i] :
( ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) )
= ( product @ sk_ @ ( product @ X0 @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4915,zip_derived_cl32]) ).
thf(zip_derived_cl7_069,plain,
d @ sk_ @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3_070,plain,
! [X0: $i,X1: $i] :
( ( ( product @ X0 @ ( product @ X1 @ X0 ) )
= X0 )
| ~ ( d @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[sos03]) ).
thf(zip_derived_cl16,plain,
( ( product @ sk__1 @ ( product @ sk_ @ sk__1 ) )
= sk__1 ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl3]) ).
thf(zip_derived_cl751_071,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl76]) ).
thf(zip_derived_cl1149,plain,
( ( product @ sk__1 @ ( product @ sk_ @ sk__1 ) )
= ( product @ ( product @ sk__1 @ sk_ ) @ sk__1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl16,zip_derived_cl751]) ).
thf(zip_derived_cl16_072,plain,
( ( product @ sk__1 @ ( product @ sk_ @ sk__1 ) )
= sk__1 ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl3]) ).
thf(zip_derived_cl1211,plain,
( sk__1
= ( product @ ( product @ sk__1 @ sk_ ) @ sk__1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1149,zip_derived_cl16]) ).
thf(zip_derived_cl0_073,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1311,plain,
! [X0: $i] :
( ( product @ sk__1 @ X0 )
= ( product @ ( product @ sk__1 @ sk_ ) @ ( product @ sk__1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1211,zip_derived_cl0]) ).
thf(zip_derived_cl32_074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1460,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ ( product @ sk__1 @ sk_ ) @ ( product @ sk__1 @ X0 ) ) )
= ( product @ X1 @ ( product @ ( product @ sk__1 @ sk_ ) @ ( product @ X1 @ ( product @ sk__1 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1311,zip_derived_cl32]) ).
thf(zip_derived_cl1311_075,plain,
! [X0: $i] :
( ( product @ sk__1 @ X0 )
= ( product @ ( product @ sk__1 @ sk_ ) @ ( product @ sk__1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1211,zip_derived_cl0]) ).
thf(zip_derived_cl0_076,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1505,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__1 @ X0 ) )
= ( product @ X1 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ X1 @ ( product @ sk__1 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1460,zip_derived_cl1311,zip_derived_cl0]) ).
thf(zip_derived_cl6002,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) )
= ( product @ X0 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ X0 @ sk_ ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5048,zip_derived_cl1505]) ).
thf(zip_derived_cl1335_077,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl76_078,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X2 @ X1 ) @ ( product @ X0 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl66,zip_derived_cl0]) ).
thf(zip_derived_cl1550,plain,
! [X0: $i] :
( ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__2 @ sk__3 ) ) )
= ( product @ ( product @ sk__2 @ X0 ) @ ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__2 @ sk__3 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1335,zip_derived_cl76]) ).
thf(zip_derived_cl6237,plain,
( ( product @ sk__2 @ ( product @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__2 @ sk_ ) ) ) @ ( product @ sk__2 @ sk__3 ) ) )
= ( product @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ sk_ ) ) ) @ ( product @ sk__2 @ ( product @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__2 @ sk_ ) ) ) @ ( product @ sk__2 @ sk__3 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6002,zip_derived_cl1550]) ).
thf(zip_derived_cl0_079,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_081,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl32_082,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl0_083,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_084,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_085,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl32_086,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl0_087,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_088,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl58_090,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl9]) ).
thf(zip_derived_cl14_091,plain,
( ( product @ sk_ @ ( product @ sk__1 @ sk_ ) )
= sk_ ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl2]) ).
thf(zip_derived_cl0_092,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl36,plain,
! [X0: $i] :
( ( product @ sk_ @ X0 )
= ( product @ sk_ @ ( product @ ( product @ sk__1 @ sk_ ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl0]) ).
thf(zip_derived_cl0_093,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl38,plain,
! [X0: $i] :
( ( product @ sk_ @ X0 )
= ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk_ @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl36,zip_derived_cl0]) ).
thf(zip_derived_cl363,plain,
! [X0: $i] :
( ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ sk_ @ X0 ) ) ) )
= ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk_ @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl58,zip_derived_cl38]) ).
thf(zip_derived_cl38_094,plain,
! [X0: $i] :
( ( product @ sk_ @ X0 )
= ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk_ @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl36,zip_derived_cl0]) ).
thf(zip_derived_cl481,plain,
! [X0: $i] :
( ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ sk_ @ X0 ) ) ) )
= ( product @ sk_ @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl363,zip_derived_cl38]) ).
thf(zip_derived_cl0_095,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl548,plain,
! [X0: $i,X1: $i] :
( ( product @ ( product @ sk_ @ X0 ) @ X1 )
= ( product @ sk_ @ ( product @ ( product @ X0 @ ( product @ sk__1 @ ( product @ sk_ @ X0 ) ) ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl481,zip_derived_cl0]) ).
thf(zip_derived_cl0_096,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_097,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_098,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_099,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl597,plain,
! [X0: $i,X1: $i] :
( ( product @ sk_ @ ( product @ X0 @ X1 ) )
= ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ X0 @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl548,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl6320,plain,
( ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__2 @ sk__3 ) ) ) )
= ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__2 @ sk__3 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6237,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl32,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl32,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl597]) ).
thf(zip_derived_cl10_100,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl32_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( product @ ( product @ X3 @ X2 ) @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X3 @ X2 ) @ ( product @ X1 @ ( product @ X3 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl32]) ).
thf(zip_derived_cl0_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( product @ X3 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) )
= ( product @ ( product @ X3 @ X2 ) @ ( product @ X1 @ ( product @ X3 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl272,zip_derived_cl0]) ).
thf(zip_derived_cl13544,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) )
= ( product @ ( product @ X1 @ X2 ) @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl303]) ).
thf(zip_derived_cl23293,plain,
! [X0: $i] :
( ( product @ sk__2 @ ( product @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__2 @ sk__3 ) ) ) ) @ ( product @ sk__2 @ X0 ) ) )
= ( product @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__2 @ sk__3 ) ) ) ) @ ( product @ sk__2 @ ( product @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__2 @ sk__3 ) ) ) ) @ ( product @ sk__2 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6320,zip_derived_cl13544]) ).
thf(zip_derived_cl0_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1335_107,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl0_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1335_111,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl0_112,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1335_115,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl5048_116,plain,
! [X0: $i] :
( ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) )
= ( product @ sk_ @ ( product @ X0 @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4915,zip_derived_cl32]) ).
thf(zip_derived_cl0_117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl5174,plain,
! [X0: $i,X1: $i] :
( ( product @ ( product @ sk_ @ ( product @ X0 @ sk_ ) ) @ X1 )
= ( product @ sk_ @ ( product @ ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5048,zip_derived_cl0]) ).
thf(zip_derived_cl0_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl5243,plain,
! [X0: $i,X1: $i] :
( ( product @ sk_ @ ( product @ X0 @ ( product @ sk_ @ X1 ) ) )
= ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5174,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl32_123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl23756,plain,
! [X0: $i] :
( ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__2 @ X0 ) ) ) ) )
= ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__2 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl23293,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1335,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1335,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1335,zip_derived_cl5243,zip_derived_cl32]) ).
thf(zip_derived_cl26812,plain,
( ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__3 @ sk_ ) ) ) ) )
= ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__3 @ sk_ ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9754,zip_derived_cl23756]) ).
thf(zip_derived_cl975_124,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl932,zip_derived_cl32,zip_derived_cl32,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl58,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1505_125,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__1 @ X0 ) )
= ( product @ X1 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ X1 @ ( product @ sk__1 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1460,zip_derived_cl1311,zip_derived_cl0]) ).
thf(zip_derived_cl5997,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ sk__1 ) ) ) ) )
= ( product @ X0 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ X0 @ sk__1 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl975,zip_derived_cl1505]) ).
thf(zip_derived_cl1211_126,plain,
( sk__1
= ( product @ ( product @ sk__1 @ sk_ ) @ sk__1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1149,zip_derived_cl16]) ).
thf(zip_derived_cl32_127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1316,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ ( product @ sk__1 @ sk_ ) @ sk__1 ) )
= ( product @ X0 @ ( product @ ( product @ sk__1 @ sk_ ) @ ( product @ X0 @ sk__1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1211,zip_derived_cl32]) ).
thf(zip_derived_cl1211_128,plain,
( sk__1
= ( product @ ( product @ sk__1 @ sk_ ) @ sk__1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1149,zip_derived_cl16]) ).
thf(zip_derived_cl0_129,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1328,plain,
! [X0: $i] :
( ( product @ X0 @ sk__1 )
= ( product @ X0 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ X0 @ sk__1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1316,zip_derived_cl1211,zip_derived_cl0]) ).
thf(zip_derived_cl6062,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ sk__1 ) ) ) ) )
= ( product @ X0 @ sk__1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5997,zip_derived_cl1328]) ).
thf(zip_derived_cl32_130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl6354,plain,
! [X0: $i] :
( ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ sk__1 ) ) ) )
= ( product @ sk__1 @ ( product @ X0 @ sk__1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6062,zip_derived_cl32]) ).
thf(zip_derived_cl1433_131,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk_ @ X0 ) )
= ( product @ X1 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X1 @ ( product @ sk_ @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1388,zip_derived_cl1287,zip_derived_cl0]) ).
thf(zip_derived_cl6530,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ sk__1 ) ) )
= ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ sk__1 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6354,zip_derived_cl1433]) ).
thf(zip_derived_cl1550_132,plain,
! [X0: $i] :
( ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__2 @ sk__3 ) ) )
= ( product @ ( product @ sk__2 @ X0 ) @ ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__2 @ sk__3 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1335,zip_derived_cl76]) ).
thf(zip_derived_cl6848,plain,
( ( product @ sk__2 @ ( product @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk__1 ) ) ) @ ( product @ sk__2 @ sk__3 ) ) )
= ( product @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__2 @ sk__1 ) ) ) @ ( product @ sk__2 @ ( product @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk__1 ) ) ) @ ( product @ sk__2 @ sk__3 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6530,zip_derived_cl1550]) ).
thf(zip_derived_cl0_133,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl32_136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl0_137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_138,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_139,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl32_140,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl0_141,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_142,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl58_144,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl9]) ).
thf(zip_derived_cl16_145,plain,
( ( product @ sk__1 @ ( product @ sk_ @ sk__1 ) )
= sk__1 ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl3]) ).
thf(zip_derived_cl0_146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl44,plain,
! [X0: $i] :
( ( product @ sk__1 @ X0 )
= ( product @ sk__1 @ ( product @ ( product @ sk_ @ sk__1 ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl16,zip_derived_cl0]) ).
thf(zip_derived_cl0_147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl46,plain,
! [X0: $i] :
( ( product @ sk__1 @ X0 )
= ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl44,zip_derived_cl0]) ).
thf(zip_derived_cl361,plain,
! [X0: $i] :
( ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) )
= ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl58,zip_derived_cl46]) ).
thf(zip_derived_cl46_148,plain,
! [X0: $i] :
( ( product @ sk__1 @ X0 )
= ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl44,zip_derived_cl0]) ).
thf(zip_derived_cl479,plain,
! [X0: $i] :
( ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) )
= ( product @ sk__1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl361,zip_derived_cl46]) ).
thf(zip_derived_cl0_149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl489,plain,
! [X0: $i,X1: $i] :
( ( product @ ( product @ sk__1 @ X0 ) @ X1 )
= ( product @ sk__1 @ ( product @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl479,zip_derived_cl0]) ).
thf(zip_derived_cl0_150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_152,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_153,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl535,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__1 @ ( product @ X0 @ X1 ) )
= ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl6932,plain,
( ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk__3 ) ) ) )
= ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ sk__3 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6848,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl32,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl32,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl535]) ).
thf(zip_derived_cl32_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl7660,plain,
( ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ sk__3 ) ) ) )
= ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk__3 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6932,zip_derived_cl32]) ).
thf(zip_derived_cl10_155,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl303_156,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( product @ X3 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) )
= ( product @ ( product @ X3 @ X2 ) @ ( product @ X1 @ ( product @ X3 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl272,zip_derived_cl0]) ).
thf(zip_derived_cl13685,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ ( product @ X1 @ X0 ) ) )
= ( product @ ( product @ X2 @ X1 ) @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl303]) ).
thf(zip_derived_cl10_157,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl14113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X2 @ X1 ) @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl13685,zip_derived_cl10]) ).
thf(zip_derived_cl16492,plain,
( ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk__3 ) ) ) )
= ( product @ ( product @ sk__2 @ sk_ ) @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ sk__3 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7660,zip_derived_cl14113]) ).
thf(zip_derived_cl9_158,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl14113_159,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X2 @ X1 ) @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl13685,zip_derived_cl10]) ).
thf(zip_derived_cl16460,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl14113]) ).
thf(zip_derived_cl65697,plain,
( ( product @ ( product @ sk__2 @ sk_ ) @ ( product @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ sk__3 ) ) ) ) @ ( product @ sk__2 @ sk_ ) ) )
= ( product @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk__3 ) ) ) ) @ ( product @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ sk__3 ) ) ) ) @ ( product @ sk__2 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl16492,zip_derived_cl16460]) ).
thf(zip_derived_cl0_160,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1335_163,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl5048_164,plain,
! [X0: $i] :
( ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) )
= ( product @ sk_ @ ( product @ X0 @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4915,zip_derived_cl32]) ).
thf(zip_derived_cl0_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl10_166,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl9_167,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_168,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1335_171,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl5048_172,plain,
! [X0: $i] :
( ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) )
= ( product @ sk_ @ ( product @ X0 @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4915,zip_derived_cl32]) ).
thf(zip_derived_cl0_173,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_175,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl65795,plain,
( ( product @ sk__2 @ sk_ )
= ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk_ ) ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl65697,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1335,zip_derived_cl5048,zip_derived_cl0,zip_derived_cl10,zip_derived_cl9,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1335,zip_derived_cl5048,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl535_177,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__1 @ ( product @ X0 @ X1 ) )
= ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl89321,plain,
( ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk_ ) ) ) ) )
= ( product @ sk__1 @ ( product @ sk__2 @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl65795,zip_derived_cl535]) ).
thf(zip_derived_cl1287_178,plain,
! [X0: $i] :
( ( product @ sk_ @ X0 )
= ( product @ ( product @ sk_ @ sk__1 ) @ ( product @ sk_ @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1210,zip_derived_cl0]) ).
thf(zip_derived_cl485_179,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) ) )
= ( product @ sk__3 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl367,zip_derived_cl50]) ).
thf(zip_derived_cl0_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl611,plain,
! [X0: $i,X1: $i] :
( ( product @ ( product @ sk__3 @ X0 ) @ X1 )
= ( product @ sk__3 @ ( product @ ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl485,zip_derived_cl0]) ).
thf(zip_derived_cl0_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_183,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl657,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__3 @ ( product @ X0 @ X1 ) )
= ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X0 @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl611,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl4388,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ ( product @ sk_ @ sk__1 ) @ ( product @ sk_ @ X0 ) ) )
= ( product @ sk__3 @ ( product @ ( product @ sk_ @ sk__1 ) @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ X0 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1287,zip_derived_cl657]) ).
thf(zip_derived_cl1287_185,plain,
! [X0: $i] :
( ( product @ sk_ @ X0 )
= ( product @ ( product @ sk_ @ sk__1 ) @ ( product @ sk_ @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1210,zip_derived_cl0]) ).
thf(zip_derived_cl0_186,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl4473,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ sk_ @ X0 ) )
= ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ X0 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4388,zip_derived_cl1287,zip_derived_cl0]) ).
thf(zip_derived_cl89647,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk_ ) ) )
= ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk_ ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89321,zip_derived_cl4473]) ).
thf(zip_derived_cl0_187,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl16460_188,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl14113]) ).
thf(zip_derived_cl17491,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X2 @ X1 ) @ ( product @ X0 @ ( product @ X2 @ X1 ) ) )
= ( product @ ( product @ X2 @ ( product @ X1 @ X0 ) ) @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl16460]) ).
thf(zip_derived_cl0_189,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl17729,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) )
= ( product @ ( product @ X2 @ ( product @ X1 @ X0 ) ) @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl17491,zip_derived_cl0]) ).
thf(zip_derived_cl89878,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ ( product @ sk__1 @ ( product @ sk__2 @ sk_ ) ) @ ( product @ sk__3 @ sk_ ) ) ) )
= ( product @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk_ ) ) ) @ ( product @ ( product @ sk__1 @ ( product @ sk__2 @ sk_ ) ) @ ( product @ sk__3 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89647,zip_derived_cl17729]) ).
thf(zip_derived_cl0_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_191,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_192,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_193,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_194,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_195,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_196,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1433_197,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk_ @ X0 ) )
= ( product @ X1 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X1 @ ( product @ sk_ @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1388,zip_derived_cl1287,zip_derived_cl0]) ).
thf(zip_derived_cl9664_198,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) )
= ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__3 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9573,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl9,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl9,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl485]) ).
thf(zip_derived_cl485_199,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ X0 ) ) ) )
= ( product @ sk__3 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl367,zip_derived_cl50]) ).
thf(zip_derived_cl90023,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__3 @ sk_ ) ) ) ) ) )
= ( product @ sk__3 @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl89878,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1433,zip_derived_cl9664,zip_derived_cl485]) ).
thf(zip_derived_cl1335_200,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl535_201,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__1 @ ( product @ X0 @ X1 ) )
= ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl3635,plain,
! [X0: $i] :
( ( product @ sk__1 @ ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) )
= ( product @ sk__1 @ ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ X0 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1335,zip_derived_cl535]) ).
thf(zip_derived_cl1335_202,plain,
! [X0: $i] :
( ( product @ sk__2 @ X0 )
= ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk__2 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl0_203,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl3713,plain,
! [X0: $i] :
( ( product @ sk__1 @ ( product @ sk__2 @ X0 ) )
= ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ X0 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3635,zip_derived_cl1335,zip_derived_cl0]) ).
thf(zip_derived_cl91666,plain,
( ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk_ @ ( product @ sk__3 @ sk_ ) ) ) )
= ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl90023,zip_derived_cl3713]) ).
thf(zip_derived_cl91813,plain,
( ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ sk_ ) ) ) )
= ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__3 @ sk_ ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl26812,zip_derived_cl91666]) ).
thf(zip_derived_cl17729_204,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) )
= ( product @ ( product @ X2 @ ( product @ X1 @ X0 ) ) @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl17491,zip_derived_cl0]) ).
thf(zip_derived_cl93590,plain,
( ( product @ sk__2 @ ( product @ sk__1 @ ( product @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__3 @ sk_ ) ) ) @ ( product @ sk__2 @ sk__1 ) ) ) )
= ( product @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ sk_ ) ) ) ) @ ( product @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__3 @ sk_ ) ) ) @ ( product @ sk__2 @ sk__1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl91813,zip_derived_cl17729]) ).
thf(zip_derived_cl0_205,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1577_208,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__2 @ X0 ) )
= ( product @ X1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X1 @ ( product @ sk__2 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1532,zip_derived_cl1335,zip_derived_cl0]) ).
thf(zip_derived_cl1328_209,plain,
! [X0: $i] :
( ( product @ X0 @ sk__1 )
= ( product @ X0 @ ( product @ sk__1 @ ( product @ sk_ @ ( product @ X0 @ sk__1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1316,zip_derived_cl1211,zip_derived_cl0]) ).
thf(zip_derived_cl0_210,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1577_213,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__2 @ X0 ) )
= ( product @ X1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X1 @ ( product @ sk__2 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1532,zip_derived_cl1335,zip_derived_cl0]) ).
thf(zip_derived_cl0_214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_216,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_217,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl10_218,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl93738,plain,
( ( product @ sk__2 @ sk__1 )
= ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk__1 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl93590,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1577,zip_derived_cl1328,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1577,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl10]) ).
thf(zip_derived_cl32_219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl94187,plain,
( ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk__1 ) ) ) ) )
= ( product @ sk__1 @ ( product @ sk__2 @ sk__1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl93738,zip_derived_cl32]) ).
thf(zip_derived_cl17729_220,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) )
= ( product @ ( product @ X2 @ ( product @ X1 @ X0 ) ) @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl17491,zip_derived_cl0]) ).
thf(zip_derived_cl94477,plain,
( ( product @ sk__1 @ ( product @ sk__2 @ ( product @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk__1 ) ) ) @ ( product @ sk__1 @ sk__2 ) ) ) )
= ( product @ ( product @ sk__1 @ ( product @ sk__2 @ sk__1 ) ) @ ( product @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk__1 ) ) ) @ ( product @ sk__1 @ sk__2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl94187,zip_derived_cl17729]) ).
thf(zip_derived_cl0_221,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_222,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl16460_223,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl14113]) ).
thf(zip_derived_cl89321_224,plain,
( ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk_ ) ) ) ) )
= ( product @ sk__1 @ ( product @ sk__2 @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl65795,zip_derived_cl535]) ).
thf(zip_derived_cl17729_225,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) )
= ( product @ ( product @ X2 @ ( product @ X1 @ X0 ) ) @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl17491,zip_derived_cl0]) ).
thf(zip_derived_cl89591,plain,
( ( product @ sk__1 @ ( product @ sk__2 @ ( product @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk_ ) ) ) @ ( product @ sk__1 @ sk__2 ) ) ) )
= ( product @ ( product @ sk__1 @ ( product @ sk__2 @ sk_ ) ) @ ( product @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk_ ) ) ) @ ( product @ sk__1 @ sk__2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89321,zip_derived_cl17729]) ).
thf(zip_derived_cl0_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_227,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl6530_229,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ sk__1 ) ) )
= ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ sk__1 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6354,zip_derived_cl1433]) ).
thf(zip_derived_cl751_230,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl76]) ).
thf(zip_derived_cl6796,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ sk__1 ) ) ) @ X0 ) )
= ( product @ ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ sk__1 ) ) ) @ ( product @ X0 @ ( product @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ sk__1 ) ) ) @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6530,zip_derived_cl751]) ).
thf(zip_derived_cl0_231,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_232,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl9_234,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_235,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_237,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl9_238,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_239,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_240,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_241,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl479_242,plain,
! [X0: $i] :
( ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) )
= ( product @ sk__1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl361,zip_derived_cl46]) ).
thf(zip_derived_cl6881,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) )
= ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6796,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl9,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl9,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl479]) ).
thf(zip_derived_cl32_243,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl6965,plain,
! [X0: $i] :
( ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ X0 ) ) )
= ( product @ sk_ @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6881,zip_derived_cl32]) ).
thf(zip_derived_cl0_244,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_245,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_246,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl6965_247,plain,
! [X0: $i] :
( ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ X0 ) ) )
= ( product @ sk_ @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl6881,zip_derived_cl32]) ).
thf(zip_derived_cl0_248,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_249,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl975_250,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl932,zip_derived_cl32,zip_derived_cl32,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl58,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1577_251,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__2 @ X0 ) )
= ( product @ X1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X1 @ ( product @ sk__2 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1532,zip_derived_cl1335,zip_derived_cl0]) ).
thf(zip_derived_cl8118,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__3 @ ( product @ X0 @ sk__2 ) ) ) ) )
= ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X0 @ sk__2 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl975,zip_derived_cl1577]) ).
thf(zip_derived_cl1212_252,plain,
( sk__2
= ( product @ ( product @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1150,zip_derived_cl15]) ).
thf(zip_derived_cl32_253,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl1340,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ ( product @ sk__2 @ sk__3 ) @ sk__2 ) )
= ( product @ X0 @ ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ X0 @ sk__2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl32]) ).
thf(zip_derived_cl1212_254,plain,
( sk__2
= ( product @ ( product @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1150,zip_derived_cl15]) ).
thf(zip_derived_cl0_255,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1352,plain,
! [X0: $i] :
( ( product @ X0 @ sk__2 )
= ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X0 @ sk__2 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1340,zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl8192,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__3 @ ( product @ X0 @ sk__2 ) ) ) ) )
= ( product @ X0 @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl8118,zip_derived_cl1352]) ).
thf(zip_derived_cl32_256,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl8351,plain,
! [X0: $i] :
( ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__3 @ ( product @ X0 @ sk__2 ) ) ) )
= ( product @ sk__2 @ ( product @ X0 @ sk__2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8192,zip_derived_cl32]) ).
thf(zip_derived_cl0_257,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl8491,plain,
! [X0: $i,X1: $i] :
( ( product @ ( product @ sk__2 @ ( product @ X0 @ sk__2 ) ) @ X1 )
= ( product @ sk__2 @ ( product @ ( product @ X0 @ ( product @ sk__3 @ ( product @ X0 @ sk__2 ) ) ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8351,zip_derived_cl0]) ).
thf(zip_derived_cl0_258,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_259,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_260,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_261,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_262,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl8562,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__2 @ X1 ) ) )
= ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8491,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl6881_263,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) )
= ( product @ X0 @ ( product @ sk_ @ ( product @ X0 @ ( product @ sk__1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6796,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl9,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl9,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl479]) ).
thf(zip_derived_cl479_264,plain,
! [X0: $i] :
( ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) )
= ( product @ sk__1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl361,zip_derived_cl46]) ).
thf(zip_derived_cl89735,plain,
( ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ sk__2 ) ) ) ) ) )
= ( product @ sk__1 @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl89591,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl6965,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl6965,zip_derived_cl0,zip_derived_cl0,zip_derived_cl8562,zip_derived_cl6881,zip_derived_cl479]) ).
thf(zip_derived_cl4473_265,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ sk_ @ X0 ) )
= ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ X0 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4388,zip_derived_cl1287,zip_derived_cl0]) ).
thf(zip_derived_cl91086,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ sk__2 ) ) ) )
= ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89735,zip_derived_cl4473]) ).
thf(zip_derived_cl1212_266,plain,
( sk__2
= ( product @ ( product @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1150,zip_derived_cl15]) ).
thf(zip_derived_cl535_267,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__1 @ ( product @ X0 @ X1 ) )
= ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl3641,plain,
( ( product @ sk__1 @ ( product @ ( product @ sk__2 @ sk__3 ) @ sk__2 ) )
= ( product @ sk__1 @ ( product @ ( product @ sk__2 @ sk__3 ) @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1212,zip_derived_cl535]) ).
thf(zip_derived_cl1212_268,plain,
( sk__2
= ( product @ ( product @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1150,zip_derived_cl15]) ).
thf(zip_derived_cl0_269,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl3719,plain,
( ( product @ sk__1 @ sk__2 )
= ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3641,zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl0_270,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_271,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl16460_272,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl14113]) ).
thf(zip_derived_cl91086_273,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ sk__2 ) ) ) )
= ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89735,zip_derived_cl4473]) ).
thf(zip_derived_cl0_274,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_275,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl94621,plain,
( ( product @ sk__1 @ sk__2 )
= ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl94477,zip_derived_cl0,zip_derived_cl0,zip_derived_cl16460,zip_derived_cl91086,zip_derived_cl3719,zip_derived_cl0,zip_derived_cl0,zip_derived_cl16460,zip_derived_cl91086,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl32_276,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl100728,plain,
( ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) ) ) )
= ( product @ sk__2 @ ( product @ sk__1 @ sk__2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl94621,zip_derived_cl32]) ).
thf(zip_derived_cl1649_277,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__3 @ X0 ) )
= ( product @ X1 @ ( product @ sk__3 @ ( product @ sk__2 @ ( product @ X1 @ ( product @ sk__3 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1604,zip_derived_cl1359,zip_derived_cl0]) ).
thf(zip_derived_cl101072,plain,
( ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) ) )
= ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk__2 @ ( product @ sk__1 @ sk__2 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl100728,zip_derived_cl1649]) ).
thf(zip_derived_cl8351_278,plain,
! [X0: $i] :
( ( product @ sk__2 @ ( product @ X0 @ ( product @ sk__3 @ ( product @ X0 @ sk__2 ) ) ) )
= ( product @ sk__2 @ ( product @ X0 @ sk__2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8192,zip_derived_cl32]) ).
thf(zip_derived_cl1649_279,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__3 @ X0 ) )
= ( product @ X1 @ ( product @ sk__3 @ ( product @ sk__2 @ ( product @ X1 @ ( product @ sk__3 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1604,zip_derived_cl1359,zip_derived_cl0]) ).
thf(zip_derived_cl8691,plain,
! [X0: $i] :
( ( product @ X0 @ ( product @ sk__3 @ ( product @ X0 @ sk__2 ) ) )
= ( product @ X0 @ ( product @ sk__3 @ ( product @ sk__2 @ ( product @ X0 @ sk__2 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8351,zip_derived_cl1649]) ).
thf(zip_derived_cl101219,plain,
( ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) ) )
= ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk__1 @ sk__2 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl101072,zip_derived_cl8691]) ).
thf(zip_derived_cl17729_280,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) )
= ( product @ ( product @ X2 @ ( product @ X1 @ X0 ) ) @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl17491,zip_derived_cl0]) ).
thf(zip_derived_cl101604,plain,
( ( product @ sk__1 @ ( product @ sk__3 @ ( product @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) @ ( product @ sk__1 @ sk__3 ) ) ) )
= ( product @ ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk__1 @ sk__2 ) ) ) @ ( product @ ( product @ sk_ @ ( product @ sk__1 @ sk__2 ) ) @ ( product @ sk__1 @ sk__3 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl101219,zip_derived_cl17729]) ).
thf(zip_derived_cl0_281,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_282,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl94187_283,plain,
( ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk__1 ) ) ) ) )
= ( product @ sk__1 @ ( product @ sk__2 @ sk__1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl93738,zip_derived_cl32]) ).
thf(zip_derived_cl4473_284,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ sk_ @ X0 ) )
= ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ sk_ @ X0 ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4388,zip_derived_cl1287,zip_derived_cl0]) ).
thf(zip_derived_cl94533,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk__1 ) ) )
= ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk__1 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl94187,zip_derived_cl4473]) ).
thf(zip_derived_cl16460_285,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ X0 @ X1 ) @ ( product @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl14113]) ).
thf(zip_derived_cl94689,plain,
( ( product @ sk__3 @ ( product @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk__1 ) ) ) @ sk__3 ) )
= ( product @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ sk__1 ) ) ) @ ( product @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ sk__1 ) ) ) @ sk__3 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl94533,zip_derived_cl16460]) ).
thf(zip_derived_cl0_286,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_287,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_288,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_289,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_292,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_293,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_294,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl46_295,plain,
! [X0: $i] :
( ( product @ sk__1 @ X0 )
= ( product @ sk__1 @ ( product @ sk_ @ ( product @ sk__1 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl44,zip_derived_cl0]) ).
thf(zip_derived_cl32_296,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ X0 ) )
= ( product @ X2 @ ( product @ X1 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl94834,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ sk__2 @ ( product @ sk__1 @ sk__3 ) ) ) ) )
= ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ sk__3 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl94689,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl46,zip_derived_cl32]) ).
thf(zip_derived_cl0_297,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_298,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_299,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_300,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl535_301,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__1 @ ( product @ X0 @ X1 ) )
= ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl303_302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( product @ X3 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) )
= ( product @ ( product @ X3 @ X2 ) @ ( product @ X1 @ ( product @ X3 @ ( product @ X2 @ ( product @ X1 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl272,zip_derived_cl0]) ).
thf(zip_derived_cl13650,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__1 @ ( product @ X1 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X1 @ X0 ) ) ) ) )
= ( product @ ( product @ sk__1 @ X1 ) @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X1 @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl535,zip_derived_cl303]) ).
thf(zip_derived_cl535_303,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__1 @ ( product @ X0 @ X1 ) )
= ( product @ sk__1 @ ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ X1 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl489,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl14078,plain,
! [X0: $i,X1: $i] :
( ( product @ sk__1 @ ( product @ X1 @ X0 ) )
= ( product @ ( product @ sk__1 @ X1 ) @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl13650,zip_derived_cl535]) ).
thf(zip_derived_cl8928_304,plain,
! [X0: $i] :
( ( product @ sk__3 @ ( product @ X0 @ ( product @ sk__2 @ ( product @ X0 @ sk__3 ) ) ) )
= ( product @ sk__3 @ ( product @ X0 @ sk__3 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8764,zip_derived_cl32]) ).
thf(zip_derived_cl9_305,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ X0 )
= ( product @ X1 @ ( product @ X0 @ ( product @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl101752,plain,
( ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ sk__3 ) ) ) ) )
= ( product @ sk__1 @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl101604,zip_derived_cl0,zip_derived_cl0,zip_derived_cl94834,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl14078,zip_derived_cl8928,zip_derived_cl9]) ).
thf(zip_derived_cl1433_306,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk_ @ X0 ) )
= ( product @ X1 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X1 @ ( product @ sk_ @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1388,zip_derived_cl1287,zip_derived_cl0]) ).
thf(zip_derived_cl102243,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ sk__3 ) ) ) )
= ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ sk__3 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl101752,zip_derived_cl1433]) ).
thf(zip_derived_cl17729_307,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) )
= ( product @ ( product @ X2 @ ( product @ X1 @ X0 ) ) @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl17491,zip_derived_cl0]) ).
thf(zip_derived_cl103078,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ ( product @ sk__2 @ ( product @ sk__1 @ sk__3 ) ) @ ( product @ sk__3 @ sk_ ) ) ) )
= ( product @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__1 @ sk__3 ) ) ) @ ( product @ ( product @ sk__2 @ ( product @ sk__1 @ sk__3 ) ) @ ( product @ sk__3 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl102243,zip_derived_cl17729]) ).
thf(zip_derived_cl0_308,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_309,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl10_310,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_311,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_312,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl10_313,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_314,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_315,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_316,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1649_317,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__3 @ X0 ) )
= ( product @ X1 @ ( product @ sk__3 @ ( product @ sk__2 @ ( product @ X1 @ ( product @ sk__3 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1604,zip_derived_cl1359,zip_derived_cl0]) ).
thf(zip_derived_cl1304_318,plain,
! [X0: $i] :
( ( product @ X0 @ sk_ )
= ( product @ X0 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X0 @ sk_ ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1292,zip_derived_cl1210,zip_derived_cl0]) ).
thf(zip_derived_cl103225,plain,
( ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__3 @ sk_ ) ) ) ) )
= ( product @ sk__3 @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl103078,zip_derived_cl0,zip_derived_cl0,zip_derived_cl10,zip_derived_cl0,zip_derived_cl0,zip_derived_cl10,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1649,zip_derived_cl1304]) ).
thf(zip_derived_cl1577_319,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk__2 @ X0 ) )
= ( product @ X1 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X1 @ ( product @ sk__2 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1532,zip_derived_cl1335,zip_derived_cl0]) ).
thf(zip_derived_cl103717,plain,
( ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__3 @ sk_ ) ) ) )
= ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__3 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl103225,zip_derived_cl1577]) ).
thf(zip_derived_cl17729_320,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ X2 @ ( product @ X1 @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) )
= ( product @ ( product @ X2 @ ( product @ X1 @ X0 ) ) @ ( product @ X0 @ ( product @ X2 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl17491,zip_derived_cl0]) ).
thf(zip_derived_cl105427,plain,
( ( product @ sk_ @ ( product @ sk__2 @ ( product @ ( product @ sk__1 @ ( product @ sk__3 @ sk_ ) ) @ ( product @ sk_ @ sk__2 ) ) ) )
= ( product @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__3 @ sk_ ) ) ) @ ( product @ ( product @ sk__1 @ ( product @ sk__3 @ sk_ ) ) @ ( product @ sk_ @ sk__2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl103717,zip_derived_cl17729]) ).
thf(zip_derived_cl0_321,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_322,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl10_323,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_325,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl10_326,plain,
! [X0: $i,X1: $i] :
( ( product @ X0 @ X1 )
= ( product @ X0 @ ( product @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_327,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_328,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_329,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl1433_330,plain,
! [X0: $i,X1: $i] :
( ( product @ X1 @ ( product @ sk_ @ X0 ) )
= ( product @ X1 @ ( product @ sk_ @ ( product @ sk__1 @ ( product @ X1 @ ( product @ sk_ @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1388,zip_derived_cl1287,zip_derived_cl0]) ).
thf(zip_derived_cl1352_331,plain,
! [X0: $i] :
( ( product @ X0 @ sk__2 )
= ( product @ X0 @ ( product @ sk__2 @ ( product @ sk__3 @ ( product @ X0 @ sk__2 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1340,zip_derived_cl1212,zip_derived_cl0]) ).
thf(zip_derived_cl105574,plain,
( ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ sk__2 ) ) ) ) )
= ( product @ sk_ @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl105427,zip_derived_cl0,zip_derived_cl0,zip_derived_cl10,zip_derived_cl0,zip_derived_cl0,zip_derived_cl10,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl1433,zip_derived_cl1352]) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: $i] :
( ( d @ X0 @ X1 )
| ( ( product @ X1 @ ( product @ X0 @ X1 ) )
!= X1 )
| ( ( product @ X0 @ ( product @ X1 @ X0 ) )
!= X0 ) ),
inference(cnf,[status(esa)],[sos03]) ).
thf(zip_derived_cl5,plain,
~ ( d @ ( product @ sk_ @ sk__2 ) @ ( product @ sk__1 @ sk__3 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl20,plain,
( ( ( product @ ( product @ sk_ @ sk__2 ) @ ( product @ ( product @ sk__1 @ sk__3 ) @ ( product @ sk_ @ sk__2 ) ) )
!= ( product @ sk_ @ sk__2 ) )
| ( ( product @ ( product @ sk__1 @ sk__3 ) @ ( product @ ( product @ sk_ @ sk__2 ) @ ( product @ sk__1 @ sk__3 ) ) )
!= ( product @ sk__1 @ sk__3 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl5]) ).
thf(zip_derived_cl0_332,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_333,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_334,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl0_335,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product @ ( product @ X0 @ X1 ) @ X2 )
= ( product @ X0 @ ( product @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[sos01]) ).
thf(zip_derived_cl23,plain,
( ( ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ sk__2 ) ) ) ) )
!= ( product @ sk_ @ sk__2 ) )
| ( ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ sk__3 ) ) ) ) )
!= ( product @ sk__1 @ sk__3 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl20,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0]) ).
thf(zip_derived_cl101752_336,plain,
( ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ sk__3 ) ) ) ) )
= ( product @ sk__1 @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl101604,zip_derived_cl0,zip_derived_cl0,zip_derived_cl94834,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl0,zip_derived_cl14078,zip_derived_cl8928,zip_derived_cl9]) ).
thf(zip_derived_cl102100,plain,
( ( ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ sk__2 ) ) ) ) )
!= ( product @ sk_ @ sk__2 ) )
| ( ( product @ sk__1 @ sk__3 )
!= ( product @ sk__1 @ sk__3 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl23,zip_derived_cl101752]) ).
thf(zip_derived_cl102101,plain,
( ( product @ sk_ @ ( product @ sk__2 @ ( product @ sk__1 @ ( product @ sk__3 @ ( product @ sk_ @ sk__2 ) ) ) ) )
!= ( product @ sk_ @ sk__2 ) ),
inference(simplify,[status(thm)],[zip_derived_cl102100]) ).
thf(zip_derived_cl105575,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl105574,zip_derived_cl102101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP774+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lcIKR7KggB true
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 : Mon Aug 28 19:31:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.38/0.71 % Total configuration time : 435
% 0.38/0.71 % Estimated wc time : 1092
% 0.38/0.71 % Estimated cpu time (7 cpus) : 156.0
% 0.40/0.82 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.40/0.83 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.40/0.83 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.40/0.83 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.40/0.83 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.40/0.83 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.40/0.84 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 258.32/37.85 % Solved by fo/fo7.sh.
% 258.32/37.85 % done 991 iterations in 36.931s
% 258.32/37.85 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 258.32/37.85 % SZS output start Refutation
% See solution above
% 258.32/37.86
% 258.32/37.86
% 258.32/37.86 % Terminating...
% 258.32/37.92 % Runner terminated.
% 258.32/37.94 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------