%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP683+1 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Bviyjw8VxC true
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:37:04 PM UTC 2025
% Result : Theorem 24.35s 4.11s
% Output : Refutation 24.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 211 ( 202 unt; 0 typ; 0 def)
% Number of atoms : 220 ( 219 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 2142 ( 17 ~; 7 |; 2 &;2116 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 431 ( 0 ^; 431 !; 0 ?; 431 :)
% Comments :
%------------------------------------------------------------------------------
thf(rd_type,type,
rd: $i > $i > $i ).
thf(mult_type,type,
mult: $i > $i > $i ).
thf(sk__type,type,
sk_: $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(ld_type,type,
ld: $i > $i > $i ).
thf(sk__1_type,type,
sk__1: $i ).
thf(goals,conjecture,
! [X3: $i,X4: $i,X5: $i] :
( ( ( mult @ ( rd @ ( mult @ X3 @ X4 ) @ X4 ) @ X5 )
= ( mult @ X3 @ X5 ) )
& ( ( mult @ X3 @ ( ld @ X4 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ X3 @ X5 ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [X3: $i,X4: $i,X5: $i] :
( ( ( mult @ ( rd @ ( mult @ X3 @ X4 ) @ X4 ) @ X5 )
= ( mult @ X3 @ X5 ) )
& ( ( mult @ X3 @ ( ld @ X4 @ ( mult @ X4 @ X5 ) ) )
= ( mult @ X3 @ X5 ) ) ),
inference('cnf.neg',[status(esa)],[goals]) ).
thf(zip_derived_cl7,plain,
( ( ( mult @ ( rd @ ( mult @ sk_ @ sk__1 ) @ sk__1 ) @ sk__2 )
!= ( mult @ sk_ @ sk__2 ) )
| ( ( mult @ sk_ @ ( ld @ sk__1 @ ( mult @ sk__1 @ sk__2 ) ) )
!= ( mult @ sk_ @ sk__2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(f04,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= ( rd @ ( mult @ A @ B ) @ B ) ) ).
thf(zip_derived_cl3,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f04]) ).
thf(zip_derived_cl9,plain,
( ( ( mult @ ( mult @ ( rd @ sk_ @ sk__1 ) @ sk__1 ) @ sk__2 )
!= ( mult @ sk_ @ sk__2 ) )
| ( ( mult @ sk_ @ ( ld @ sk__1 @ ( mult @ sk__1 @ sk__2 ) ) )
!= ( mult @ sk_ @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl7,zip_derived_cl3]) ).
thf(f01,axiom,
! [A: $i] :
( ( ld @ A @ ( mult @ A @ A ) )
= A ) ).
thf(zip_derived_cl0,plain,
! [X0: $i] :
( ( ld @ X0 @ ( mult @ X0 @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[f01]) ).
thf(f03,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= ( ld @ A @ ( mult @ A @ B ) ) ) ).
thf(zip_derived_cl2,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X0 @ X1 ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[f03]) ).
thf(f02,axiom,
! [A: $i] :
( ( rd @ ( mult @ A @ A ) @ A )
= A ) ).
thf(zip_derived_cl1,plain,
! [X0: $i] :
( ( rd @ ( mult @ X0 @ X0 ) @ X0 )
= X0 ),
inference(cnf,[status(esa)],[f02]) ).
thf(f06,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( rd @ ( mult @ ( mult @ A @ B ) @ ( rd @ C @ D ) ) @ ( rd @ C @ D ) )
= ( mult @ A @ ( rd @ ( mult @ B @ D ) @ D ) ) ) ).
thf(zip_derived_cl5,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( rd @ ( mult @ ( mult @ X0 @ X1 ) @ ( rd @ X3 @ X2 ) ) @ ( rd @ X3 @ X2 ) )
= ( mult @ X0 @ ( rd @ ( mult @ X1 @ X2 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[f06]) ).
thf(zip_derived_cl3_001,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f04]) ).
thf(zip_derived_cl76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( rd @ ( mult @ ( mult @ X0 @ X1 ) @ ( rd @ X3 @ X2 ) ) @ ( rd @ X3 @ X2 ) )
= ( mult @ X0 @ ( mult @ ( rd @ X1 @ X2 ) @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5,zip_derived_cl3]) ).
thf(zip_derived_cl82,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( rd @ ( mult @ ( mult @ X2 @ X1 ) @ ( rd @ ( mult @ X0 @ X0 ) @ X0 ) ) @ X0 )
= ( mult @ X2 @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl76]) ).
thf(zip_derived_cl1_002,plain,
! [X0: $i] :
( ( rd @ ( mult @ X0 @ X0 ) @ X0 )
= X0 ),
inference(cnf,[status(esa)],[f02]) ).
thf(zip_derived_cl3_003,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f04]) ).
thf(zip_derived_cl100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 )
= ( mult @ X2 @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl1,zip_derived_cl3]) ).
thf(zip_derived_cl120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( ld @ X1 @ ( mult @ X1 @ X0 ) ) @ X2 ) @ X2 )
= ( mult @ X1 @ ( mult @ ( rd @ ( ld @ X1 @ X0 ) @ X2 ) @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2,zip_derived_cl100]) ).
thf(zip_derived_cl581,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( mult @ X0 @ ( mult @ ( rd @ ( ld @ X0 @ X0 ) @ X1 ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl120]) ).
thf(f07,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ ( ld @ B @ B ) ) )
= ( rd @ ( mult @ ( rd @ A @ A ) @ B ) @ B ) ) ).
thf(zip_derived_cl6,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) )
= ( rd @ ( mult @ ( rd @ X0 @ X0 ) @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f07]) ).
thf(zip_derived_cl3_004,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f04]) ).
thf(zip_derived_cl1_005,plain,
! [X0: $i] :
( ( rd @ ( mult @ X0 @ X0 ) @ X0 )
= X0 ),
inference(cnf,[status(esa)],[f02]) ).
thf(zip_derived_cl10,plain,
! [X0: $i] :
( ( mult @ ( rd @ X0 @ X0 ) @ X0 )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl1]) ).
thf(zip_derived_cl6_006,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) )
= ( rd @ ( mult @ ( rd @ X0 @ X0 ) @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f07]) ).
thf(zip_derived_cl18,plain,
! [X0: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( ld @ X0 @ X0 ) ) )
= ( rd @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl6]) ).
thf(zip_derived_cl2_007,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X0 @ X1 ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[f03]) ).
thf(zip_derived_cl0_008,plain,
! [X0: $i] :
( ( ld @ X0 @ ( mult @ X0 @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[f01]) ).
thf(zip_derived_cl19,plain,
! [X0: $i] :
( ( ld @ X0 @ X0 )
= ( rd @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl18,zip_derived_cl2,zip_derived_cl0]) ).
thf(zip_derived_cl3_009,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f04]) ).
thf(zip_derived_cl20,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) )
= ( mult @ ( rd @ ( ld @ X0 @ X0 ) @ X1 ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl6,zip_derived_cl19,zip_derived_cl3]) ).
thf(zip_derived_cl2_010,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X0 @ X1 ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[f03]) ).
thf(zip_derived_cl603,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl581,zip_derived_cl20,zip_derived_cl2]) ).
thf(zip_derived_cl690,plain,
( ( ( mult @ ( ld @ sk_ @ ( mult @ sk_ @ ( mult @ sk_ @ ( ld @ sk__1 @ sk__1 ) ) ) ) @ sk__2 )
!= ( mult @ sk_ @ sk__2 ) )
| ( ( mult @ sk_ @ ( ld @ sk__1 @ ( mult @ sk__1 @ sk__2 ) ) )
!= ( mult @ sk_ @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9,zip_derived_cl603]) ).
thf(zip_derived_cl0_011,plain,
! [X0: $i] :
( ( ld @ X0 @ ( mult @ X0 @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[f01]) ).
thf(f05,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ld @ ( ld @ A @ B ) @ ( mult @ ( ld @ A @ B ) @ ( mult @ C @ D ) ) )
= ( mult @ ( ld @ A @ ( mult @ A @ C ) ) @ D ) ) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ld @ ( ld @ X0 @ X3 ) @ ( mult @ ( ld @ X0 @ X3 ) @ ( mult @ X1 @ X2 ) ) )
= ( mult @ ( ld @ X0 @ ( mult @ X0 @ X1 ) ) @ X2 ) ),
inference(cnf,[status(esa)],[f05]) ).
thf(zip_derived_cl1397,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X0 @ ( mult @ X0 @ X0 ) ) @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( ld @ X0 @ ( mult @ X0 @ X2 ) ) @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl4]) ).
thf(zip_derived_cl0_012,plain,
! [X0: $i] :
( ( ld @ X0 @ ( mult @ X0 @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[f01]) ).
thf(zip_derived_cl1434,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( ld @ X0 @ ( mult @ X0 @ X2 ) ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1397,zip_derived_cl0]) ).
thf(zip_derived_cl1455,plain,
( ( ( ld @ sk_ @ ( mult @ sk_ @ ( mult @ ( mult @ sk_ @ ( ld @ sk__1 @ sk__1 ) ) @ sk__2 ) ) )
!= ( mult @ sk_ @ sk__2 ) )
| ( ( mult @ sk_ @ ( ld @ sk__1 @ ( mult @ sk__1 @ sk__2 ) ) )
!= ( mult @ sk_ @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl690,zip_derived_cl1434]) ).
thf(zip_derived_cl0_013,plain,
! [X0: $i] :
( ( ld @ X0 @ ( mult @ X0 @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[f01]) ).
thf(zip_derived_cl1434_014,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( ld @ X0 @ ( mult @ X0 @ X2 ) ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1397,zip_derived_cl0]) ).
thf(zip_derived_cl1496,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl1434_015,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( ld @ X0 @ ( mult @ X0 @ X2 ) ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1397,zip_derived_cl0]) ).
thf(zip_derived_cl1646,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ X1 @ ( mult @ X1 @ ( mult @ ( mult @ X1 @ X0 ) @ X2 ) ) )
= ( mult @ ( mult @ X1 @ X0 ) @ X2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1496,zip_derived_cl1434]) ).
thf(zip_derived_cl2509,plain,
( ( ( mult @ ( mult @ sk_ @ ( ld @ sk__1 @ sk__1 ) ) @ sk__2 )
!= ( mult @ sk_ @ sk__2 ) )
| ( ( mult @ sk_ @ ( ld @ sk__1 @ ( mult @ sk__1 @ sk__2 ) ) )
!= ( mult @ sk_ @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1455,zip_derived_cl1646]) ).
thf(zip_derived_cl1434_016,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( ld @ X0 @ ( mult @ X0 @ X2 ) ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1397,zip_derived_cl0]) ).
thf(zip_derived_cl20_017,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) )
= ( mult @ ( rd @ ( ld @ X0 @ X0 ) @ X1 ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl6,zip_derived_cl19,zip_derived_cl3]) ).
thf(zip_derived_cl3_018,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f04]) ).
thf(zip_derived_cl100_019,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 )
= ( mult @ X2 @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl1,zip_derived_cl3]) ).
thf(zip_derived_cl118,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) @ X0 )
= ( mult @ X1 @ ( mult @ ( rd @ X0 @ X0 ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl100]) ).
thf(zip_derived_cl19_020,plain,
! [X0: $i] :
( ( ld @ X0 @ X0 )
= ( rd @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl18,zip_derived_cl2,zip_derived_cl0]) ).
thf(zip_derived_cl10_021,plain,
! [X0: $i] :
( ( mult @ ( rd @ X0 @ X0 ) @ X0 )
= X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl1]) ).
thf(zip_derived_cl19_022,plain,
! [X0: $i] :
( ( ld @ X0 @ X0 )
= ( rd @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl18,zip_derived_cl2,zip_derived_cl0]) ).
thf(zip_derived_cl21,plain,
! [X0: $i] :
( ( mult @ ( ld @ X0 @ X0 ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl19]) ).
thf(zip_derived_cl131,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) @ X0 )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl118,zip_derived_cl19,zip_derived_cl21]) ).
thf(zip_derived_cl140,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( ld @ X1 @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ) @ X0 )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl20,zip_derived_cl131]) ).
thf(zip_derived_cl1492,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ ( mult @ ( ld @ X0 @ X0 ) @ X0 ) ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1434,zip_derived_cl140]) ).
thf(zip_derived_cl21_023,plain,
! [X0: $i] :
( ( mult @ ( ld @ X0 @ X0 ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl19]) ).
thf(zip_derived_cl1556,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1492,zip_derived_cl21]) ).
thf(zip_derived_cl140_024,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( ld @ X1 @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ) @ X0 )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl20,zip_derived_cl131]) ).
thf(zip_derived_cl4_025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ld @ ( ld @ X0 @ X3 ) @ ( mult @ ( ld @ X0 @ X3 ) @ ( mult @ X1 @ X2 ) ) )
= ( mult @ ( ld @ X0 @ ( mult @ X0 @ X1 ) ) @ X2 ) ),
inference(cnf,[status(esa)],[f05]) ).
thf(zip_derived_cl1408,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ X2 ) @ ( mult @ ( ld @ X1 @ X2 ) @ ( mult @ ( ld @ X0 @ X0 ) @ X0 ) ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl140,zip_derived_cl4]) ).
thf(zip_derived_cl21_026,plain,
! [X0: $i] :
( ( mult @ ( ld @ X0 @ X0 ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl19]) ).
thf(zip_derived_cl1442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ X2 ) @ ( mult @ ( ld @ X1 @ X2 ) @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1408,zip_derived_cl21]) ).
thf(zip_derived_cl1556_027,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1492,zip_derived_cl21]) ).
thf(zip_derived_cl2729,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ X2 ) @ ( mult @ ( ld @ X1 @ X2 ) @ X0 ) )
= ( ld @ X1 @ ( mult @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1442,zip_derived_cl1556]) ).
thf(zip_derived_cl0_028,plain,
! [X0: $i] :
( ( ld @ X0 @ ( mult @ X0 @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[f01]) ).
thf(zip_derived_cl2733,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ ( ld @ X1 @ X0 ) ) )
= ( ld @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl2729,zip_derived_cl0]) ).
thf(zip_derived_cl2_029,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X0 @ X1 ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[f03]) ).
thf(zip_derived_cl2786,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( ld @ X1 @ ( mult @ X1 @ X0 ) ) )
= ( ld @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2733,zip_derived_cl2]) ).
thf(zip_derived_cl2802,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ X1 @ ( mult @ X1 @ X0 ) ) ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1556,zip_derived_cl2786]) ).
thf(zip_derived_cl21_030,plain,
! [X0: $i] :
( ( mult @ ( ld @ X0 @ X0 ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl19]) ).
thf(zip_derived_cl3_031,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f04]) ).
thf(zip_derived_cl603_032,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl581,zip_derived_cl20,zip_derived_cl2]) ).
thf(zip_derived_cl689,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ) )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl3,zip_derived_cl603]) ).
thf(zip_derived_cl716,plain,
! [X0: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( mult @ ( ld @ X0 @ X0 ) @ ( mult @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ X0 ) ) ) )
= ( rd @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl21,zip_derived_cl689]) ).
thf(zip_derived_cl0_033,plain,
! [X0: $i] :
( ( ld @ X0 @ ( mult @ X0 @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[f01]) ).
thf(zip_derived_cl2_034,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X0 @ X1 ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[f03]) ).
thf(zip_derived_cl8,plain,
! [X0: $i] :
( ( mult @ X0 @ X0 )
= ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl2]) ).
thf(zip_derived_cl19_035,plain,
! [X0: $i] :
( ( ld @ X0 @ X0 )
= ( rd @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl18,zip_derived_cl2,zip_derived_cl0]) ).
thf(zip_derived_cl723,plain,
! [X0: $i] :
( ( mult @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ X0 ) )
= ( ld @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl716,zip_derived_cl8,zip_derived_cl19]) ).
thf(zip_derived_cl0_036,plain,
! [X0: $i] :
( ( ld @ X0 @ ( mult @ X0 @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[f01]) ).
thf(zip_derived_cl728,plain,
! [X0: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ X0 ) )
= ( ld @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl723,zip_derived_cl0]) ).
thf(zip_derived_cl1556_037,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1492,zip_derived_cl21]) ).
thf(zip_derived_cl1595,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( mult @ ( ld @ X0 @ X0 ) @ X1 ) )
= ( mult @ ( ld @ X0 @ X0 ) @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl728,zip_derived_cl1556]) ).
thf(zip_derived_cl1556_038,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1492,zip_derived_cl21]) ).
thf(zip_derived_cl1556_039,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1492,zip_derived_cl21]) ).
thf(zip_derived_cl1596,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1595,zip_derived_cl1556,zip_derived_cl1556]) ).
thf(zip_derived_cl1596_040,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1595,zip_derived_cl1556,zip_derived_cl1556]) ).
thf(zip_derived_cl2822,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl2835,plain,
( ( ( mult @ ( mult @ sk_ @ ( ld @ sk__1 @ sk__1 ) ) @ sk__2 )
!= ( mult @ sk_ @ sk__2 ) )
| ( ( mult @ sk_ @ ( ld @ ( ld @ sk__1 @ sk__1 ) @ sk__2 ) )
!= ( mult @ sk_ @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2509,zip_derived_cl2822]) ).
thf(zip_derived_cl1496_041,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl2729_042,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ X2 ) @ ( mult @ ( ld @ X1 @ X2 ) @ X0 ) )
= ( ld @ X1 @ ( mult @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1442,zip_derived_cl1556]) ).
thf(zip_derived_cl2749,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ ( mult @ X1 @ ( mult @ X1 @ X0 ) ) ) @ ( mult @ ( mult @ X1 @ X0 ) @ X2 ) )
= ( ld @ X1 @ ( mult @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1496,zip_derived_cl2729]) ).
thf(zip_derived_cl1496_043,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl2768,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( mult @ X1 @ X0 ) @ ( mult @ ( mult @ X1 @ X0 ) @ X2 ) )
= ( ld @ X1 @ ( mult @ X1 @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2749,zip_derived_cl1496]) ).
thf(zip_derived_cl2822_044,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl4022,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( mult @ X1 @ X0 ) @ ( mult @ ( mult @ X1 @ X0 ) @ X2 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2768,zip_derived_cl2822]) ).
thf(zip_derived_cl2822_045,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl4026,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ X0 )
= ( ld @ ( ld @ ( mult @ X1 @ X2 ) @ ( mult @ X1 @ X2 ) ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl4022,zip_derived_cl2822]) ).
thf(zip_derived_cl689_046,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ) )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl3,zip_derived_cl603]) ).
thf(zip_derived_cl1496_047,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl1634,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X1 @ X1 ) )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl689,zip_derived_cl1496]) ).
thf(zip_derived_cl603_048,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl581,zip_derived_cl20,zip_derived_cl2]) ).
thf(zip_derived_cl1496_049,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl1633,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl603,zip_derived_cl1496]) ).
thf(zip_derived_cl1692,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) @ X0 )
= ( mult @ ( mult @ X1 @ X0 ) @ ( ld @ X0 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1634,zip_derived_cl1633]) ).
thf(zip_derived_cl131_050,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) @ X0 )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl118,zip_derived_cl19,zip_derived_cl21]) ).
thf(zip_derived_cl603_051,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl581,zip_derived_cl20,zip_derived_cl2]) ).
thf(zip_derived_cl697,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( ld @ X1 @ ( mult @ X1 @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ) ) @ X0 )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl131,zip_derived_cl603]) ).
thf(zip_derived_cl1496_052,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl1636,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) @ X0 )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl697,zip_derived_cl1496]) ).
thf(zip_derived_cl1920,plain,
! [X0: $i,X1: $i] :
( ( mult @ X1 @ X0 )
= ( mult @ ( mult @ X1 @ X0 ) @ ( ld @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1692,zip_derived_cl1636]) ).
thf(zip_derived_cl4022_053,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( mult @ X1 @ X0 ) @ ( mult @ ( mult @ X1 @ X0 ) @ X2 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl2768,zip_derived_cl2822]) ).
thf(zip_derived_cl4036,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( mult @ X1 @ X0 ) @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ X0 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1920,zip_derived_cl4022]) ).
thf(zip_derived_cl5586,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ X0 )
= ( ld @ ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ X2 @ X2 ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl4026,zip_derived_cl4036]) ).
thf(zip_derived_cl1556_054,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1492,zip_derived_cl21]) ).
thf(zip_derived_cl2822_055,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl2831,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ X0 )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1556,zip_derived_cl2822]) ).
thf(zip_derived_cl5589,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ X0 @ X0 ) ) @ ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ X0 @ X0 ) ) ) @ X2 )
= ( mult @ ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ X0 @ X0 ) ) ) @ X2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5586,zip_derived_cl2831]) ).
thf(zip_derived_cl5586_056,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ X0 )
= ( ld @ ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ X2 @ X2 ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl4026,zip_derived_cl4036]) ).
thf(zip_derived_cl1556_057,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1492,zip_derived_cl21]) ).
thf(zip_derived_cl2_058,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X0 @ X1 ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[f03]) ).
thf(zip_derived_cl1566,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ) )
= ( ld @ ( ld @ X1 @ X1 ) @ ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1556,zip_derived_cl2]) ).
thf(zip_derived_cl1556_059,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1492,zip_derived_cl21]) ).
thf(zip_derived_cl1605,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ) )
= ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ X1 @ ( mult @ X1 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1566,zip_derived_cl1556]) ).
thf(zip_derived_cl2822_060,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl2_061,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X0 @ X1 ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[f03]) ).
thf(zip_derived_cl2822_062,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl2827,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X0 @ X1 ) )
= ( ld @ ( ld @ X0 @ X0 ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl2822]) ).
thf(zip_derived_cl2876,plain,
! [X0: $i,X1: $i] :
( ( mult @ X1 @ ( ld @ ( ld @ X1 @ X1 ) @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ ( mult @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2822,zip_derived_cl2827]) ).
thf(zip_derived_cl1496_063,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl1596_064,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( ld @ X0 @ ( mult @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1595,zip_derived_cl1556,zip_derived_cl1556]) ).
thf(zip_derived_cl2129,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ ( mult @ X1 @ X0 ) )
= ( ld @ X1 @ ( mult @ X1 @ ( mult @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1496,zip_derived_cl1596]) ).
thf(zip_derived_cl1496_065,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl2149,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ ( mult @ X1 @ X0 ) )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2129,zip_derived_cl1496]) ).
thf(zip_derived_cl2882,plain,
! [X0: $i,X1: $i] :
( ( mult @ X1 @ ( ld @ ( ld @ X1 @ X1 ) @ X0 ) )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2876,zip_derived_cl2149]) ).
thf(zip_derived_cl2822_066,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl2822_067,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl3524,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ X0 )
= ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1605,zip_derived_cl2882,zip_derived_cl2822,zip_derived_cl2822]) ).
thf(zip_derived_cl5586_068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ X0 )
= ( ld @ ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ X2 @ X2 ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl4026,zip_derived_cl4036]) ).
thf(zip_derived_cl3524_069,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ X0 )
= ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1605,zip_derived_cl2882,zip_derived_cl2822,zip_derived_cl2822]) ).
thf(zip_derived_cl1434_070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X2 @ X1 ) ) )
= ( mult @ ( ld @ X0 @ ( mult @ X0 @ X2 ) ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1397,zip_derived_cl0]) ).
thf(zip_derived_cl2822_071,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl2822_072,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl2830,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( mult @ X2 @ X1 ) )
= ( mult @ ( ld @ ( ld @ X0 @ X0 ) @ X2 ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1434,zip_derived_cl2822,zip_derived_cl2822]) ).
thf(zip_derived_cl2831_073,plain,
! [X0: $i,X1: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ X0 )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1556,zip_derived_cl2822]) ).
thf(zip_derived_cl5699,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ld @ ( ld @ X1 @ X1 ) @ X2 )
= ( ld @ ( ld @ X1 @ X1 ) @ ( ld @ ( ld @ X0 @ X0 ) @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5589,zip_derived_cl5586,zip_derived_cl3524,zip_derived_cl5586,zip_derived_cl3524,zip_derived_cl2830,zip_derived_cl2831]) ).
thf(zip_derived_cl2882_074,plain,
! [X0: $i,X1: $i] :
( ( mult @ X1 @ ( ld @ ( ld @ X1 @ X1 ) @ X0 ) )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2876,zip_derived_cl2149]) ).
thf(zip_derived_cl9063,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X1 @ ( ld @ ( ld @ X1 @ X1 ) @ X0 ) )
= ( mult @ X1 @ ( ld @ ( ld @ X2 @ X2 ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl5699,zip_derived_cl2882]) ).
thf(zip_derived_cl2882_075,plain,
! [X0: $i,X1: $i] :
( ( mult @ X1 @ ( ld @ ( ld @ X1 @ X1 ) @ X0 ) )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2876,zip_derived_cl2149]) ).
thf(zip_derived_cl9228,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X1 @ X0 )
= ( mult @ X1 @ ( ld @ ( ld @ X2 @ X2 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9063,zip_derived_cl2882]) ).
thf(zip_derived_cl9473,plain,
( ( ( mult @ ( mult @ sk_ @ ( ld @ sk__1 @ sk__1 ) ) @ sk__2 )
!= ( mult @ sk_ @ sk__2 ) )
| ( ( mult @ sk_ @ sk__2 )
!= ( mult @ sk_ @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2835,zip_derived_cl9228]) ).
thf(zip_derived_cl9474,plain,
( ( mult @ ( mult @ sk_ @ ( ld @ sk__1 @ sk__1 ) ) @ sk__2 )
!= ( mult @ sk_ @ sk__2 ) ),
inference(simplify,[status(thm)],[zip_derived_cl9473]) ).
thf(zip_derived_cl1633_076,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl603,zip_derived_cl1496]) ).
thf(zip_derived_cl100_077,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 )
= ( mult @ X2 @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl1,zip_derived_cl3]) ).
thf(zip_derived_cl603_078,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl581,zip_derived_cl20,zip_derived_cl2]) ).
thf(zip_derived_cl693,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 )
= ( mult @ X2 @ ( ld @ X1 @ ( mult @ X1 @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl100,zip_derived_cl603]) ).
thf(zip_derived_cl1496_079,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl1635,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 )
= ( mult @ X2 @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl693,zip_derived_cl1496]) ).
thf(zip_derived_cl1885,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) @ X2 ) @ X2 )
= ( mult @ ( rd @ X1 @ X0 ) @ ( mult @ X0 @ ( ld @ X2 @ X2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1633,zip_derived_cl1635]) ).
thf(zip_derived_cl1635_080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 )
= ( mult @ X2 @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl693,zip_derived_cl1496]) ).
thf(zip_derived_cl1556_081,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( mult @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1492,zip_derived_cl21]) ).
thf(zip_derived_cl1905,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X1 @ ( ld @ X0 @ ( mult @ X0 @ ( ld @ X2 @ X2 ) ) ) )
= ( mult @ ( rd @ X1 @ X0 ) @ ( mult @ X0 @ ( ld @ X2 @ X2 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1885,zip_derived_cl1635,zip_derived_cl1556]) ).
thf(zip_derived_cl2822_082,plain,
! [X0: $i,X1: $i] :
( ( ld @ X1 @ ( mult @ X1 @ X0 ) )
= ( ld @ ( ld @ X1 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2802,zip_derived_cl1596,zip_derived_cl1596]) ).
thf(zip_derived_cl3649,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X1 @ ( ld @ ( ld @ X0 @ X0 ) @ ( ld @ X2 @ X2 ) ) )
= ( mult @ ( rd @ X1 @ X0 ) @ ( mult @ X0 @ ( ld @ X2 @ X2 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1905,zip_derived_cl2822]) ).
thf(zip_derived_cl9228_083,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X1 @ X0 )
= ( mult @ X1 @ ( ld @ ( ld @ X2 @ X2 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9063,zip_derived_cl2882]) ).
thf(zip_derived_cl9475,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X1 @ ( ld @ X2 @ X2 ) )
= ( mult @ ( rd @ X1 @ X0 ) @ ( mult @ X0 @ ( ld @ X2 @ X2 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3649,zip_derived_cl9228]) ).
thf(zip_derived_cl1635_084,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 )
= ( mult @ X2 @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl693,zip_derived_cl1496]) ).
thf(zip_derived_cl1636_085,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) @ X0 )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl697,zip_derived_cl1496]) ).
thf(zip_derived_cl1866,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( mult @ X2 @ ( mult @ X1 @ ( ld @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ X0 ) ) ) ) @ X0 )
= ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ ( ld @ X0 @ X0 ) ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1635,zip_derived_cl1636]) ).
thf(zip_derived_cl728_086,plain,
! [X0: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ X0 ) )
= ( ld @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl723,zip_derived_cl0]) ).
thf(zip_derived_cl728_087,plain,
! [X0: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ X0 ) )
= ( ld @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl723,zip_derived_cl0]) ).
thf(zip_derived_cl21_088,plain,
! [X0: $i] :
( ( mult @ ( ld @ X0 @ X0 ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl19]) ).
thf(zip_derived_cl100_089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 )
= ( mult @ X2 @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl1,zip_derived_cl3]) ).
thf(zip_derived_cl121,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( mult @ ( ld @ X0 @ X0 ) @ ( mult @ ( rd @ X0 @ X1 ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl21,zip_derived_cl100]) ).
thf(zip_derived_cl100_090,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 )
= ( mult @ X2 @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl1,zip_derived_cl3]) ).
thf(zip_derived_cl3_091,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(cnf,[status(esa)],[f04]) ).
thf(zip_derived_cl111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( rd @ ( rd @ ( mult @ X2 @ X1 ) @ X0 ) @ X0 ) @ X0 )
= ( rd @ ( mult @ X2 @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl100,zip_derived_cl3]) ).
thf(zip_derived_cl21_092,plain,
! [X0: $i] :
( ( mult @ ( ld @ X0 @ X0 ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl19]) ).
thf(zip_derived_cl76_093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( rd @ ( mult @ ( mult @ X0 @ X1 ) @ ( rd @ X3 @ X2 ) ) @ ( rd @ X3 @ X2 ) )
= ( mult @ X0 @ ( mult @ ( rd @ X1 @ X2 ) @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5,zip_derived_cl3]) ).
thf(zip_derived_cl91,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( rd @ ( mult @ X0 @ ( rd @ X2 @ X1 ) ) @ ( rd @ X2 @ X1 ) )
= ( mult @ ( ld @ X0 @ X0 ) @ ( mult @ ( rd @ X0 @ X1 ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl21,zip_derived_cl76]) ).
thf(zip_derived_cl121_094,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( mult @ ( ld @ X0 @ X0 ) @ ( mult @ ( rd @ X0 @ X1 ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl21,zip_derived_cl100]) ).
thf(zip_derived_cl367,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( rd @ ( mult @ X0 @ ( rd @ X2 @ X1 ) ) @ ( rd @ X2 @ X1 ) )
= ( mult @ ( rd @ X0 @ X1 ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl91,zip_derived_cl121]) ).
thf(zip_derived_cl1_095,plain,
! [X0: $i] :
( ( rd @ ( mult @ X0 @ X0 ) @ X0 )
= X0 ),
inference(cnf,[status(esa)],[f02]) ).
thf(zip_derived_cl375,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ ( rd @ X1 @ X0 ) @ X0 ) @ X0 )
= ( rd @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl367,zip_derived_cl1]) ).
thf(zip_derived_cl459,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( rd @ ( mult @ X2 @ X1 ) @ X0 )
= ( rd @ ( mult @ X2 @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl111,zip_derived_cl375]) ).
thf(zip_derived_cl474,plain,
! [X0: $i,X1: $i] :
( ( rd @ ( mult @ ( ld @ X1 @ X1 ) @ X1 ) @ X0 )
= ( rd @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl121,zip_derived_cl459]) ).
thf(zip_derived_cl21_096,plain,
! [X0: $i] :
( ( mult @ ( ld @ X0 @ X0 ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl19]) ).
thf(zip_derived_cl497,plain,
! [X0: $i,X1: $i] :
( ( rd @ X1 @ X0 )
= ( rd @ ( mult @ ( rd @ X1 @ X0 ) @ X0 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl474,zip_derived_cl21]) ).
thf(zip_derived_cl603_097,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl581,zip_derived_cl20,zip_derived_cl2]) ).
thf(zip_derived_cl702,plain,
! [X0: $i,X1: $i] :
( ( rd @ X1 @ X0 )
= ( rd @ ( ld @ X1 @ ( mult @ X1 @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl497,zip_derived_cl603]) ).
thf(zip_derived_cl1496_098,plain,
! [X0: $i,X1: $i] :
( ( ld @ X0 @ ( mult @ X0 @ ( mult @ X0 @ X1 ) ) )
= ( mult @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1434]) ).
thf(zip_derived_cl1639,plain,
! [X0: $i,X1: $i] :
( ( rd @ X1 @ X0 )
= ( rd @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl702,zip_derived_cl1496]) ).
thf(zip_derived_cl1773,plain,
! [X0: $i,X1: $i] :
( ( rd @ X1 @ ( ld @ X0 @ X0 ) )
= ( rd @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) @ ( ld @ X0 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl728,zip_derived_cl1639]) ).
thf(zip_derived_cl1634_099,plain,
! [X0: $i,X1: $i] :
( ( mult @ X0 @ ( ld @ X1 @ X1 ) )
= ( rd @ ( mult @ X0 @ X1 ) @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl689,zip_derived_cl1496]) ).
thf(zip_derived_cl728_100,plain,
! [X0: $i] :
( ( ld @ ( ld @ X0 @ X0 ) @ ( ld @ X0 @ X0 ) )
= ( ld @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl723,zip_derived_cl0]) ).
thf(zip_derived_cl1781,plain,
! [X0: $i,X1: $i] :
( ( rd @ X1 @ ( ld @ X0 @ X0 ) )
= ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1773,zip_derived_cl1634,zip_derived_cl728]) ).
thf(zip_derived_cl1636_101,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) @ X0 )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl697,zip_derived_cl1496]) ).
thf(zip_derived_cl1916,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( mult @ X2 @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) ) @ X0 )
= ( mult @ ( mult @ X2 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1866,zip_derived_cl728,zip_derived_cl1781,zip_derived_cl1636]) ).
thf(zip_derived_cl14153,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) @ X0 )
= ( mult @ ( mult @ ( rd @ X1 @ X2 ) @ X2 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl9475,zip_derived_cl1916]) ).
thf(zip_derived_cl1636_102,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( mult @ X1 @ ( ld @ X0 @ X0 ) ) @ X0 )
= ( mult @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl697,zip_derived_cl1496]) ).
thf(zip_derived_cl1633_103,plain,
! [X0: $i,X1: $i] :
( ( mult @ ( rd @ X0 @ X1 ) @ X1 )
= ( mult @ X0 @ ( ld @ X1 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl603,zip_derived_cl1496]) ).
thf(zip_derived_cl14292,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( mult @ X1 @ X0 )
= ( mult @ ( mult @ X1 @ ( ld @ X2 @ X2 ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl14153,zip_derived_cl1636,zip_derived_cl1633]) ).
thf(zip_derived_cl14434,plain,
( ( mult @ sk_ @ sk__2 )
!= ( mult @ sk_ @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl9474,zip_derived_cl14292]) ).
thf(zip_derived_cl14435,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl14434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP683+1 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Bviyjw8VxC true
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 14:14:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35 % Number of cores: 8
% 0.12/0.35 % Python version: Python 3.6.8
% 0.12/0.35 % Running in FO mode
% 0.51/0.63 % Total configuration time : 435
% 0.51/0.63 % Estimated wc time : 1092
% 0.51/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 24.35/4.11 % Solved by fo/fo7.sh.
% 24.35/4.11 % done 494 iterations in 3.339s
% 24.35/4.11 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 24.35/4.11 % SZS output start Refutation
% See solution above
% 24.35/4.11
% 24.35/4.11
% 24.35/4.11 % Terminating...
% 24.86/4.17 % Runner terminated.
% 24.86/4.18 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------