TSTP Solution File: SEU364+1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU364+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.XT8GjLabGL 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 19:12:25 EDT 2023
% Result : Theorem 12.12s 2.38s
% Output : Refutation 12.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 55
% Syntax : Number of formulae : 351 ( 29 unt; 42 typ; 0 def)
% Number of atoms : 897 ( 137 equ; 0 cnn)
% Maximal formula atoms : 24 ( 2 avg)
% Number of connectives : 7777 ( 238 ~; 510 |; 56 &;6951 @)
% ( 7 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 123 ( 123 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 4 con; 0-5 aty)
% Number of variables : 448 ( 0 ^; 426 !; 22 ?; 448 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk__21_type,type,
sk__21: $i > $i > $i > $i > $i ).
thf(sk__5_type,type,
sk__5: $i > $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(zip_tseitin_1_type,type,
zip_tseitin_1: $i > $i > $i > $i > $o ).
thf(sk__19_type,type,
sk__19: $i > $i > $i > $i ).
thf(zip_tseitin_4_type,type,
zip_tseitin_4: $i > $i > $i > $i > $i > $o ).
thf(transitive_relstr_type,type,
transitive_relstr: $i > $o ).
thf(empty_carrier_type,type,
empty_carrier: $i > $o ).
thf(sk__3_type,type,
sk__3: $i > $i ).
thf(sk__4_type,type,
sk__4: $i > $i ).
thf(sk__1_type,type,
sk__1: $i ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(element_type,type,
element: $i > $i > $o ).
thf(zip_tseitin_6_type,type,
zip_tseitin_6: $i > $i > $i > $i > $o ).
thf(zip_tseitin_8_type,type,
zip_tseitin_8: $i > $i > $i > $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(sk__type,type,
sk_: $i ).
thf(sk__20_type,type,
sk__20: $i > $i > $i > $i ).
thf(zip_tseitin_7_type,type,
zip_tseitin_7: $i > $i > $i > $i > $o ).
thf(sk__25_type,type,
sk__25: $i > $i > $i > $i ).
thf(zip_tseitin_3_type,type,
zip_tseitin_3: $i > $i > $i > $i > $o ).
thf(zip_tseitin_9_type,type,
zip_tseitin_9: $i > $i > $i > $i > $i > $o ).
thf(sk__24_type,type,
sk__24: $i > $i > $i ).
thf(relstr_set_smaller_type,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(sk__23_type,type,
sk__23: $i > $i > $i ).
thf(finite_type,type,
finite: $i > $o ).
thf(zip_tseitin_5_type,type,
zip_tseitin_5: $i > $i > $i > $i > $i > $o ).
thf(zip_tseitin_0_type,type,
zip_tseitin_0: $i > $i > $i > $i > $o ).
thf(sk__22_type,type,
sk__22: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(rel_str_type,type,
rel_str: $i > $o ).
thf(zip_tseitin_2_type,type,
zip_tseitin_2: $i > $i > $i > $i > $o ).
thf(s1_xboole_0__e11_2_1__waybel_0__1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( powerset @ C ) )
& ? [F: $i] :
( ? [G: $i] :
( ( relstr_set_smaller @ A @ F @ G )
& ( in @ G @ B )
& ( element @ G @ ( the_carrier @ A ) ) )
& ( F = E ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( powerset @ C ) )
& ? [F: $i] :
( ? [G: $i] :
( ( relstr_set_smaller @ A @ F @ G )
& ( in @ G @ B )
& ( element @ G @ ( the_carrier @ A ) ) )
& ( F = E ) ) ) ) ),
inference('cnf.neg',[status(esa)],[s1_xboole_0__e11_2_1__waybel_0__1]) ).
thf(zip_derived_cl1,plain,
! [X0: $i] :
( ( ( sk__4 @ X0 )
= ( sk__3 @ X0 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl11,plain,
element @ sk__1 @ ( powerset @ ( the_carrier @ sk_ ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6,plain,
element @ sk__2 @ ( powerset @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(s1_tarski__e11_2_1__waybel_0__1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ C @ ( powerset @ B ) )
& ( finite @ C )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( rel_str @ A )
& ( transitive_relstr @ A )
& ~ ( empty_carrier @ A ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ? [I: $i] :
( ( I = F )
& ? [J: $i] :
( ( element @ J @ ( the_carrier @ A ) )
& ( in @ J @ B )
& ( relstr_set_smaller @ A @ I @ J ) ) )
& ( D = F )
& ? [G: $i] :
( ( G = E )
& ? [H: $i] :
( ( element @ H @ ( the_carrier @ A ) )
& ( in @ H @ B )
& ( relstr_set_smaller @ A @ G @ H ) ) )
& ( D = E ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( powerset @ C ) )
& ( F = E )
& ? [K: $i] :
( ( K = E )
& ? [L: $i] :
( ( element @ L @ ( the_carrier @ A ) )
& ( in @ L @ B )
& ( relstr_set_smaller @ A @ K @ L ) ) ) ) ) ) ) ).
thf(zf_stmt_1,type,
zip_tseitin_9: $i > $i > $i > $i > $i > $o ).
thf(zf_stmt_2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( zip_tseitin_9 @ E @ D @ C @ B @ A )
=> ( ( in @ E @ D )
<=> ? [F: $i] : ( zip_tseitin_8 @ F @ E @ C @ B @ A ) ) ) ).
thf(zf_stmt_3,type,
zip_tseitin_8: $i > $i > $i > $i > $i > $o ).
thf(zf_stmt_4,axiom,
! [F: $i,E: $i,C: $i,B: $i,A: $i] :
( ( zip_tseitin_8 @ F @ E @ C @ B @ A )
<=> ( ? [K: $i] : ( zip_tseitin_7 @ K @ E @ B @ A )
& ( F = E )
& ( in @ F @ ( powerset @ C ) ) ) ) ).
thf(zf_stmt_5,type,
zip_tseitin_7: $i > $i > $i > $i > $o ).
thf(zf_stmt_6,axiom,
! [K: $i,E: $i,B: $i,A: $i] :
( ( zip_tseitin_7 @ K @ E @ B @ A )
<=> ( ? [L: $i] : ( zip_tseitin_6 @ L @ K @ B @ A )
& ( K = E ) ) ) ).
thf(zf_stmt_7,type,
zip_tseitin_6: $i > $i > $i > $i > $o ).
thf(zf_stmt_8,axiom,
! [L: $i,K: $i,B: $i,A: $i] :
( ( zip_tseitin_6 @ L @ K @ B @ A )
<=> ( ( relstr_set_smaller @ A @ K @ L )
& ( in @ L @ B )
& ( element @ L @ ( the_carrier @ A ) ) ) ) ).
thf(zf_stmt_9,type,
zip_tseitin_5: $i > $i > $i > $i > $i > $o ).
thf(zf_stmt_10,axiom,
! [F: $i,E: $i,D: $i,B: $i,A: $i] :
( ( ( zip_tseitin_4 @ F @ E @ D @ B @ A )
=> ( E = F ) )
=> ( zip_tseitin_5 @ F @ E @ D @ B @ A ) ) ).
thf(zf_stmt_11,type,
zip_tseitin_4: $i > $i > $i > $i > $i > $o ).
thf(zf_stmt_12,axiom,
! [F: $i,E: $i,D: $i,B: $i,A: $i] :
( ( zip_tseitin_4 @ F @ E @ D @ B @ A )
=> ( ( D = E )
& ? [G: $i] : ( zip_tseitin_3 @ G @ E @ B @ A )
& ( D = F )
& ? [I: $i] : ( zip_tseitin_1 @ I @ F @ B @ A ) ) ) ).
thf(zf_stmt_13,type,
zip_tseitin_3: $i > $i > $i > $i > $o ).
thf(zf_stmt_14,axiom,
! [G: $i,E: $i,B: $i,A: $i] :
( ( zip_tseitin_3 @ G @ E @ B @ A )
=> ( ? [H: $i] : ( zip_tseitin_2 @ H @ G @ B @ A )
& ( G = E ) ) ) ).
thf(zf_stmt_15,type,
zip_tseitin_2: $i > $i > $i > $i > $o ).
thf(zf_stmt_16,axiom,
! [H: $i,G: $i,B: $i,A: $i] :
( ( zip_tseitin_2 @ H @ G @ B @ A )
=> ( ( relstr_set_smaller @ A @ G @ H )
& ( in @ H @ B )
& ( element @ H @ ( the_carrier @ A ) ) ) ) ).
thf(zf_stmt_17,type,
zip_tseitin_1: $i > $i > $i > $i > $o ).
thf(zf_stmt_18,axiom,
! [I: $i,F: $i,B: $i,A: $i] :
( ( zip_tseitin_1 @ I @ F @ B @ A )
=> ( ? [J: $i] : ( zip_tseitin_0 @ J @ I @ B @ A )
& ( I = F ) ) ) ).
thf(zf_stmt_19,type,
zip_tseitin_0: $i > $i > $i > $i > $o ).
thf(zf_stmt_20,axiom,
! [J: $i,I: $i,B: $i,A: $i] :
( ( zip_tseitin_0 @ J @ I @ B @ A )
=> ( ( relstr_set_smaller @ A @ I @ J )
& ( in @ J @ B )
& ( element @ J @ ( the_carrier @ A ) ) ) ) ).
thf(zf_stmt_21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( finite @ C )
& ( element @ C @ ( powerset @ B ) ) )
=> ( ! [D: $i,E: $i,F: $i] : ( zip_tseitin_5 @ F @ E @ D @ B @ A )
=> ? [D: $i] :
! [E: $i] : ( zip_tseitin_9 @ E @ D @ C @ B @ A ) ) ) ).
thf(zip_derived_cl69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( zip_tseitin_5 @ ( sk__24 @ X0 @ X1 ) @ ( sk__23 @ X0 @ X1 ) @ ( sk__22 @ X0 @ X1 ) @ X0 @ X1 )
| ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) )
| ~ ( rel_str @ X1 )
| ~ ( transitive_relstr @ X1 )
| ( empty_carrier @ X1 )
| ~ ( finite @ X2 )
| ~ ( element @ X2 @ ( powerset @ X0 ) )
| ( zip_tseitin_9 @ X3 @ ( sk__25 @ X2 @ X0 @ X1 ) @ X2 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_21]) ).
thf(zip_derived_cl166,plain,
! [X0: $i,X1: $i] :
( ( zip_tseitin_9 @ X1 @ ( sk__25 @ sk__2 @ sk__1 @ X0 ) @ sk__2 @ sk__1 @ X0 )
| ~ ( finite @ sk__2 )
| ( empty_carrier @ X0 )
| ~ ( transitive_relstr @ X0 )
| ~ ( rel_str @ X0 )
| ~ ( element @ sk__1 @ ( powerset @ ( the_carrier @ X0 ) ) )
| ~ ( zip_tseitin_5 @ ( sk__24 @ sk__1 @ X0 ) @ ( sk__23 @ sk__1 @ X0 ) @ ( sk__22 @ sk__1 @ X0 ) @ sk__1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl69]) ).
thf(zip_derived_cl7,plain,
finite @ sk__2,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl172,plain,
! [X0: $i,X1: $i] :
( ( zip_tseitin_9 @ X1 @ ( sk__25 @ sk__2 @ sk__1 @ X0 ) @ sk__2 @ sk__1 @ X0 )
| ( empty_carrier @ X0 )
| ~ ( transitive_relstr @ X0 )
| ~ ( rel_str @ X0 )
| ~ ( element @ sk__1 @ ( powerset @ ( the_carrier @ X0 ) ) )
| ~ ( zip_tseitin_5 @ ( sk__24 @ sk__1 @ X0 ) @ ( sk__23 @ sk__1 @ X0 ) @ ( sk__22 @ sk__1 @ X0 ) @ sk__1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl166,zip_derived_cl7]) ).
thf(zip_derived_cl173,plain,
! [X0: $i] :
( ~ ( zip_tseitin_5 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( rel_str @ sk_ )
| ~ ( transitive_relstr @ sk_ )
| ( empty_carrier @ sk_ )
| ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl172]) ).
thf(zip_derived_cl10,plain,
rel_str @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9,plain,
transitive_relstr @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8,plain,
~ ( empty_carrier @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl174,plain,
! [X0: $i] :
( ~ ( zip_tseitin_5 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl173,zip_derived_cl10,zip_derived_cl9,zip_derived_cl8]) ).
thf(zip_derived_cl1_001,plain,
! [X0: $i] :
( ( ( sk__4 @ X0 )
= ( sk__3 @ X0 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( zip_tseitin_5 @ X0 @ X1 @ X2 @ X3 @ X4 )
| ( zip_tseitin_4 @ X0 @ X1 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_10]) ).
thf(zip_derived_cl174_002,plain,
! [X0: $i] :
( ~ ( zip_tseitin_5 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl173,zip_derived_cl10,zip_derived_cl9,zip_derived_cl8]) ).
thf(zip_derived_cl175,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl55,zip_derived_cl174]) ).
thf(zip_derived_cl68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( in @ X0 @ X1 )
| ( zip_tseitin_8 @ ( sk__21 @ X2 @ X3 @ X4 @ X0 ) @ X0 @ X4 @ X3 @ X2 )
| ~ ( zip_tseitin_9 @ X0 @ X1 @ X4 @ X3 @ X2 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl219,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl175,zip_derived_cl68]) ).
thf(zip_derived_cl223,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl219]) ).
thf(zip_derived_cl63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( zip_tseitin_7 @ ( sk__20 @ X0 @ X1 @ X2 ) @ X2 @ X1 @ X0 )
| ~ ( zip_tseitin_8 @ X3 @ X2 @ X4 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl235,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_7 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl223,zip_derived_cl63]) ).
thf(zip_derived_cl61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_7 @ X1 @ X0 @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl277,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl235,zip_derived_cl61]) ).
thf(zip_derived_cl235_003,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_7 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl223,zip_derived_cl63]) ).
thf(zip_derived_cl60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( zip_tseitin_6 @ ( sk__19 @ X0 @ X1 @ X2 ) @ X2 @ X1 @ X0 )
| ~ ( zip_tseitin_7 @ X2 @ X3 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl276,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl235,zip_derived_cl60]) ).
thf(zip_derived_cl62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( zip_tseitin_7 @ X0 @ X1 @ X2 @ X3 )
| ( X0 != X1 )
| ~ ( zip_tseitin_6 @ X4 @ X0 @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( zip_tseitin_6 @ X3 @ X2 @ X1 @ X0 )
| ( zip_tseitin_7 @ X2 @ X2 @ X1 @ X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl379,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_7 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl276,zip_derived_cl91]) ).
thf(zip_derived_cl399,plain,
( ( zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl277,zip_derived_cl379]) ).
thf(zip_derived_cl401,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl399]) ).
thf(zip_derived_cl60_004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( zip_tseitin_6 @ ( sk__19 @ X0 @ X1 @ X2 ) @ X2 @ X1 @ X0 )
| ~ ( zip_tseitin_7 @ X2 @ X3 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl402,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl401,zip_derived_cl60]) ).
thf(zip_derived_cl56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relstr_set_smaller @ X0 @ X1 @ X2 )
| ~ ( zip_tseitin_6 @ X2 @ X1 @ X3 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl457,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl402,zip_derived_cl56]) ).
thf(zip_derived_cl223_005,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl219]) ).
thf(zip_derived_cl64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_8 @ X1 @ X0 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl236,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl223,zip_derived_cl64]) ).
thf(zip_derived_cl223_006,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl219]) ).
thf(zip_derived_cl65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( zip_tseitin_8 @ X0 @ X2 @ X1 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl237,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( in @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( powerset @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl223,zip_derived_cl65]) ).
thf(zip_derived_cl263,plain,
( ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl236,zip_derived_cl237]) ).
thf(zip_derived_cl264,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl263]) ).
thf(zip_derived_cl1_007,plain,
! [X0: $i] :
( ( ( sk__4 @ X0 )
= ( sk__3 @ X0 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl277_008,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl235,zip_derived_cl61]) ).
thf(zip_derived_cl276_009,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl235,zip_derived_cl60]) ).
thf(zip_derived_cl57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ X0 @ X1 )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X1 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl377,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( in @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ sk__1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl276,zip_derived_cl57]) ).
thf(zip_derived_cl386,plain,
( ( in @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl277,zip_derived_cl377]) ).
thf(zip_derived_cl387,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( in @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl386]) ).
thf(zip_derived_cl5,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1
!= ( sk__3 @ X0 ) )
| ~ ( relstr_set_smaller @ sk_ @ X1 @ X2 )
| ~ ( in @ X2 @ sk__1 )
| ~ ( element @ X2 @ ( the_carrier @ sk_ ) )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl73,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( element @ X1 @ ( the_carrier @ sk_ ) )
| ~ ( in @ X1 @ sk__1 )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl389,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ~ ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ) )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl387,zip_derived_cl73]) ).
thf(zip_derived_cl277_010,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl235,zip_derived_cl61]) ).
thf(zip_derived_cl276_011,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl235,zip_derived_cl60]) ).
thf(zip_derived_cl58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X3 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl378,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( the_carrier @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl276,zip_derived_cl58]) ).
thf(zip_derived_cl391,plain,
( ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl277,zip_derived_cl378]) ).
thf(zip_derived_cl392,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl391]) ).
thf(zip_derived_cl408,plain,
! [X0: $i] :
( ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl389,zip_derived_cl392]) ).
thf(zip_derived_cl410,plain,
! [X0: $i] :
( ( ( sk__4 @ X0 )
= ( sk__3 @ X0 ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl408]) ).
thf(zip_derived_cl429,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl264,zip_derived_cl410]) ).
thf(zip_derived_cl433,plain,
( ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl429]) ).
thf(zip_derived_cl461,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl457,zip_derived_cl433]) ).
thf(zip_derived_cl2,plain,
! [X0: $i] :
( ( relstr_set_smaller @ sk_ @ ( sk__4 @ X0 ) @ ( sk__5 @ X0 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3,plain,
! [X0: $i] :
( ( in @ ( sk__5 @ X0 ) @ sk__1 )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4,plain,
! [X0: $i] :
( ( element @ ( sk__5 @ X0 ) @ ( the_carrier @ sk_ ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl219_012,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl175,zip_derived_cl68]) ).
thf(zip_derived_cl224,plain,
( ( element @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( the_carrier @ sk_ ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl219]) ).
thf(zip_derived_cl59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( zip_tseitin_6 @ X0 @ X1 @ X2 @ X3 )
| ~ ( element @ X0 @ ( the_carrier @ X3 ) )
| ~ ( in @ X0 @ X2 )
| ~ ( relstr_set_smaller @ X3 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl232,plain,
! [X0: $i,X1: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ X0 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( in @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X1 )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ X1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl224,zip_derived_cl59]) ).
thf(zip_derived_cl1173,plain,
! [X0: $i] :
( ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ X0 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl232]) ).
thf(zip_derived_cl219_013,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl175,zip_derived_cl68]) ).
thf(zip_derived_cl1509,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ X0 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl1173,zip_derived_cl219]) ).
thf(zip_derived_cl1511,plain,
( ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2,zip_derived_cl1509]) ).
thf(zip_derived_cl219_014,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl175,zip_derived_cl68]) ).
thf(zip_derived_cl1513,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl1511,zip_derived_cl219]) ).
thf(zip_derived_cl64_015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_8 @ X1 @ X0 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl1515,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1513,zip_derived_cl64]) ).
thf(zip_derived_cl1513_016,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl1511,zip_derived_cl219]) ).
thf(zip_derived_cl1518,plain,
( ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl1515,zip_derived_cl1513]) ).
thf(zip_derived_cl1519,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl1518]) ).
thf(zip_derived_cl91_017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( zip_tseitin_6 @ X3 @ X2 @ X1 @ X0 )
| ( zip_tseitin_7 @ X2 @ X2 @ X1 @ X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl1656,plain,
( ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1519,zip_derived_cl91]) ).
thf(zip_derived_cl1672,plain,
( ( zip_tseitin_7 @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl461,zip_derived_cl1656]) ).
thf(zip_derived_cl1674,plain,
( ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl1672]) ).
thf(zip_derived_cl0,plain,
! [X0: $i] :
( ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( zip_tseitin_8 @ X0 @ X1 @ X2 @ X3 @ X4 )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ( X0 != X1 )
| ~ ( zip_tseitin_7 @ X5 @ X1 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( zip_tseitin_7 @ X3 @ X2 @ X1 @ X0 )
| ~ ( in @ X2 @ ( powerset @ X4 ) )
| ( zip_tseitin_8 @ X2 @ X2 @ X4 @ X1 @ X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ ( sk__3 @ X0 ) @ X0 )
| ( zip_tseitin_8 @ ( sk__3 @ X0 ) @ ( sk__3 @ X0 ) @ sk__2 @ X2 @ X1 )
| ~ ( zip_tseitin_7 @ X3 @ ( sk__3 @ X0 ) @ X2 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl103]) ).
thf(zip_derived_cl1778,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1674,zip_derived_cl108]) ).
thf(zip_derived_cl1781,plain,
( ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl1778]) ).
thf(zip_derived_cl219_018,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl175,zip_derived_cl68]) ).
thf(zip_derived_cl1784,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1781,zip_derived_cl219]) ).
thf(zip_derived_cl1793,plain,
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl1784]) ).
thf(zip_derived_cl64_019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_8 @ X1 @ X0 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl2453,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1793,zip_derived_cl64]) ).
thf(zip_derived_cl1793_020,plain,
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl1784]) ).
thf(zip_derived_cl2456,plain,
( ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl2453,zip_derived_cl1793]) ).
thf(zip_derived_cl2457,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl2456]) ).
thf(zip_derived_cl67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( zip_tseitin_8 @ X0 @ X1 @ X2 @ X3 @ X4 )
| ( in @ X1 @ X5 )
| ~ ( zip_tseitin_9 @ X1 @ X5 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl2476,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2457,zip_derived_cl67]) ).
thf(zip_derived_cl461_021,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl457,zip_derived_cl433]) ).
thf(zip_derived_cl2_022,plain,
! [X0: $i] :
( ( relstr_set_smaller @ sk_ @ ( sk__4 @ X0 ) @ ( sk__5 @ X0 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl462,plain,
( ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl461,zip_derived_cl2]) ).
thf(zip_derived_cl1515_023,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1513,zip_derived_cl64]) ).
thf(zip_derived_cl1513_024,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl1511,zip_derived_cl219]) ).
thf(zip_derived_cl65_025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( zip_tseitin_8 @ X0 @ X2 @ X1 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl1516,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( in @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( powerset @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1513,zip_derived_cl65]) ).
thf(zip_derived_cl1619,plain,
( ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl1515,zip_derived_cl1516]) ).
thf(zip_derived_cl1620,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1619]) ).
thf(zip_derived_cl1513_026,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl1511,zip_derived_cl219]) ).
thf(zip_derived_cl67_027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( zip_tseitin_8 @ X0 @ X1 @ X2 @ X3 @ X4 )
| ( in @ X1 @ X5 )
| ~ ( zip_tseitin_9 @ X1 @ X5 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl1517,plain,
! [X0: $i] :
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1513,zip_derived_cl67]) ).
thf(zip_derived_cl3_028,plain,
! [X0: $i] :
( ( in @ ( sk__5 @ X0 ) @ sk__1 )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl73_029,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( element @ X1 @ ( the_carrier @ sk_ ) )
| ~ ( in @ X1 @ sk__1 )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl86,plain,
! [X0: $i,X1: $i] :
( ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X1 ) @ ( sk__5 @ X0 ) )
| ~ ( element @ ( sk__5 @ X0 ) @ ( the_carrier @ sk_ ) )
| ~ ( in @ ( sk__3 @ X1 ) @ ( powerset @ sk__2 ) )
| ~ ( in @ ( sk__3 @ X1 ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl73]) ).
thf(zip_derived_cl4_030,plain,
! [X0: $i] :
( ( element @ ( sk__5 @ X0 ) @ ( the_carrier @ sk_ ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl116,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( sk__3 @ X1 ) @ X1 )
| ~ ( in @ ( sk__3 @ X1 ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X1 ) @ ( sk__5 @ X0 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl86,zip_derived_cl4]) ).
thf(zip_derived_cl1561,plain,
! [X0: $i] :
( ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ X0 ) )
| ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1517,zip_derived_cl116]) ).
thf(zip_derived_cl175_031,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl55,zip_derived_cl174]) ).
thf(zip_derived_cl1612,plain,
! [X0: $i] :
( ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ X0 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl1561,zip_derived_cl175]) ).
thf(zip_derived_cl1639,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1620,zip_derived_cl1612]) ).
thf(zip_derived_cl1652,plain,
! [X0: $i] :
( ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ X0 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl1639]) ).
thf(zip_derived_cl1680,plain,
( ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl462,zip_derived_cl1652]) ).
thf(zip_derived_cl1682,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1680]) ).
thf(zip_derived_cl461_032,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl457,zip_derived_cl433]) ).
thf(zip_derived_cl1513_033,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl1511,zip_derived_cl219]) ).
thf(zip_derived_cl63_034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( zip_tseitin_7 @ ( sk__20 @ X0 @ X1 @ X2 ) @ X2 @ X1 @ X0 )
| ~ ( zip_tseitin_8 @ X3 @ X2 @ X4 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl1514,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1513,zip_derived_cl63]) ).
thf(zip_derived_cl61_035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_7 @ X1 @ X0 @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl1946,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1514,zip_derived_cl61]) ).
thf(zip_derived_cl1514_036,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1513,zip_derived_cl63]) ).
thf(zip_derived_cl1948,plain,
( ( zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl1946,zip_derived_cl1514]) ).
thf(zip_derived_cl1949,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl1948]) ).
thf(zip_derived_cl1954,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl461,zip_derived_cl1949]) ).
thf(zip_derived_cl1955,plain,
( ( zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl1954]) ).
thf(zip_derived_cl91_037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( zip_tseitin_6 @ X3 @ X2 @ X1 @ X0 )
| ( zip_tseitin_7 @ X2 @ X2 @ X1 @ X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl2048,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl1955,zip_derived_cl91]) ).
thf(zip_derived_cl60_038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( zip_tseitin_6 @ ( sk__19 @ X0 @ X1 @ X2 ) @ X2 @ X1 @ X0 )
| ~ ( zip_tseitin_7 @ X2 @ X3 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl2049,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2048,zip_derived_cl60]) ).
thf(zip_derived_cl57_039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ X0 @ X1 )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X1 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl2053,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( in @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2049,zip_derived_cl57]) ).
thf(zip_derived_cl73_040,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( element @ X1 @ ( the_carrier @ sk_ ) )
| ~ ( in @ X1 @ sk__1 )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl2057,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ~ ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ) )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2053,zip_derived_cl73]) ).
thf(zip_derived_cl2049_041,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2048,zip_derived_cl60]) ).
thf(zip_derived_cl58_042,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X3 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl2054,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2049,zip_derived_cl58]) ).
thf(zip_derived_cl2061,plain,
! [X0: $i] :
( ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl2057,zip_derived_cl2054]) ).
thf(zip_derived_cl2073,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1682,zip_derived_cl2061]) ).
thf(zip_derived_cl2082,plain,
( ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl2073]) ).
thf(zip_derived_cl1620_043,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1619]) ).
thf(zip_derived_cl2175,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl2082,zip_derived_cl1620]) ).
thf(zip_derived_cl2049_044,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2048,zip_derived_cl60]) ).
thf(zip_derived_cl56_045,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relstr_set_smaller @ X0 @ X1 @ X2 )
| ~ ( zip_tseitin_6 @ X2 @ X1 @ X3 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl2052,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2049,zip_derived_cl56]) ).
thf(zip_derived_cl2176,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl2175,zip_derived_cl2052]) ).
thf(zip_derived_cl58_046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X3 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl2179,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( element @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( the_carrier @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2176,zip_derived_cl58]) ).
thf(zip_derived_cl2176_047,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl2175,zip_derived_cl2052]) ).
thf(zip_derived_cl57_048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ X0 @ X1 )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X1 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl2178,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( in @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2176,zip_derived_cl57]) ).
thf(zip_derived_cl73_049,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( element @ X1 @ ( the_carrier @ sk_ ) )
| ~ ( in @ X1 @ sk__1 )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl2184,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( element @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( the_carrier @ sk_ ) )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2178,zip_derived_cl73]) ).
thf(zip_derived_cl2192,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2179,zip_derived_cl2184]) ).
thf(zip_derived_cl2193,plain,
! [X0: $i] :
( ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl2192]) ).
thf(zip_derived_cl2559,plain,
( ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2476,zip_derived_cl2193]) ).
thf(zip_derived_cl2596,plain,
( ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl2559]) ).
thf(zip_derived_cl461_050,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl457,zip_derived_cl433]) ).
thf(zip_derived_cl2176_051,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl2175,zip_derived_cl2052]) ).
thf(zip_derived_cl56_052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relstr_set_smaller @ X0 @ X1 @ X2 )
| ~ ( zip_tseitin_6 @ X2 @ X1 @ X3 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl2177,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( relstr_set_smaller @ sk_ @ ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2176,zip_derived_cl56]) ).
thf(zip_derived_cl2232,plain,
( ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl461,zip_derived_cl2177]) ).
thf(zip_derived_cl2233,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl2232]) ).
thf(zip_derived_cl2645,plain,
( ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl2596,zip_derived_cl2233]) ).
thf(zip_derived_cl175_053,plain,
! [X0: $i] :
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl55,zip_derived_cl174]) ).
thf(zip_derived_cl2646,plain,
( ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl2645,zip_derived_cl175]) ).
thf(zip_derived_cl2457_054,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl2456]) ).
thf(zip_derived_cl65_055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( zip_tseitin_8 @ X0 @ X2 @ X1 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl2475,plain,
( ( zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2457,zip_derived_cl65]) ).
thf(zip_derived_cl2647,plain,
zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_,
inference(clc,[status(thm)],[zip_derived_cl2646,zip_derived_cl2475]) ).
thf(zip_derived_cl50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_4 @ X2 @ X0 @ X1 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_12]) ).
thf(zip_derived_cl2648,plain,
( ( sk__22 @ sk__1 @ sk_ )
= ( sk__23 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2647,zip_derived_cl50]) ).
thf(zip_derived_cl2652,plain,
! [X0: $i] :
( ~ ( zip_tseitin_5 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_ )
| ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl174,zip_derived_cl2648]) ).
thf(zip_derived_cl2647_056,plain,
zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__23 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_,
inference(clc,[status(thm)],[zip_derived_cl2646,zip_derived_cl2475]) ).
thf(zip_derived_cl2648_057,plain,
( ( sk__22 @ sk__1 @ sk_ )
= ( sk__23 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2647,zip_derived_cl50]) ).
thf(zip_derived_cl2657,plain,
zip_tseitin_4 @ ( sk__24 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ ( sk__22 @ sk__1 @ sk_ ) @ sk__1 @ sk_,
inference(demod,[status(thm)],[zip_derived_cl2647,zip_derived_cl2648]) ).
thf(zip_derived_cl52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_4 @ X0 @ X2 @ X1 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_12]) ).
thf(zip_derived_cl2661,plain,
( ( sk__22 @ sk__1 @ sk_ )
= ( sk__24 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2657,zip_derived_cl52]) ).
thf(zip_derived_cl54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( zip_tseitin_5 @ X0 @ X1 @ X2 @ X3 @ X4 )
| ( X1 != X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_10]) ).
thf(zip_derived_cl90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ( zip_tseitin_5 @ X3 @ X3 @ X2 @ X1 @ X0 ),
inference(eq_res,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl2663,plain,
! [X0: $i] : ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ),
inference(demod,[status(thm)],[zip_derived_cl2652,zip_derived_cl2661,zip_derived_cl90]) ).
thf(zip_derived_cl68_058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( in @ X0 @ X1 )
| ( zip_tseitin_8 @ ( sk__21 @ X2 @ X3 @ X4 @ X0 ) @ X0 @ X4 @ X3 @ X2 )
| ~ ( zip_tseitin_9 @ X0 @ X1 @ X4 @ X3 @ X2 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl2665,plain,
! [X0: $i] :
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2663,zip_derived_cl68]) ).
thf(zip_derived_cl2685,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl2665]) ).
thf(zip_derived_cl63_059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( zip_tseitin_7 @ ( sk__20 @ X0 @ X1 @ X2 ) @ X2 @ X1 @ X0 )
| ~ ( zip_tseitin_8 @ X3 @ X2 @ X4 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl2860,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_7 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2685,zip_derived_cl63]) ).
thf(zip_derived_cl61_060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_7 @ X1 @ X0 @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl2907,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2860,zip_derived_cl61]) ).
thf(zip_derived_cl2907_061,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2860,zip_derived_cl61]) ).
thf(zip_derived_cl2860_062,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_7 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2685,zip_derived_cl63]) ).
thf(zip_derived_cl60_063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( zip_tseitin_6 @ ( sk__19 @ X0 @ X1 @ X2 ) @ X2 @ X1 @ X0 )
| ~ ( zip_tseitin_7 @ X2 @ X3 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl2906,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2860,zip_derived_cl60]) ).
thf(zip_derived_cl3001,plain,
( ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2907,zip_derived_cl2906]) ).
thf(zip_derived_cl3003,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl3001]) ).
thf(zip_derived_cl3078,plain,
( ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2907,zip_derived_cl3003]) ).
thf(zip_derived_cl3079,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl3078]) ).
thf(zip_derived_cl56_064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relstr_set_smaller @ X0 @ X1 @ X2 )
| ~ ( zip_tseitin_6 @ X2 @ X1 @ X3 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl3080,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3079,zip_derived_cl56]) ).
thf(zip_derived_cl2685_065,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl2665]) ).
thf(zip_derived_cl67_066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( zip_tseitin_8 @ X0 @ X1 @ X2 @ X3 @ X4 )
| ( in @ X1 @ X5 )
| ~ ( zip_tseitin_9 @ X1 @ X5 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl2863,plain,
! [X0: $i] :
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2685,zip_derived_cl67]) ).
thf(zip_derived_cl2907_067,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2860,zip_derived_cl61]) ).
thf(zip_derived_cl2906_068,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2860,zip_derived_cl60]) ).
thf(zip_derived_cl57_069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ X0 @ X1 )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X1 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl2998,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( in @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ sk__1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2906,zip_derived_cl57]) ).
thf(zip_derived_cl3007,plain,
( ( in @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2907,zip_derived_cl2998]) ).
thf(zip_derived_cl3008,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( in @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3007]) ).
thf(zip_derived_cl73_070,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( element @ X1 @ ( the_carrier @ sk_ ) )
| ~ ( in @ X1 @ sk__1 )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl3010,plain,
! [X0: $i] :
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ~ ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ) )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl3008,zip_derived_cl73]) ).
thf(zip_derived_cl2907_071,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2860,zip_derived_cl61]) ).
thf(zip_derived_cl2906_072,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2860,zip_derived_cl60]) ).
thf(zip_derived_cl58_073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X3 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl2999,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) @ ( the_carrier @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2906,zip_derived_cl58]) ).
thf(zip_derived_cl3012,plain,
( ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2907,zip_derived_cl2999]) ).
thf(zip_derived_cl3013,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3012]) ).
thf(zip_derived_cl3018,plain,
! [X0: $i] :
( ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3010,zip_derived_cl3013]) ).
thf(zip_derived_cl3023,plain,
( ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2863,zip_derived_cl3018]) ).
thf(zip_derived_cl2663_074,plain,
! [X0: $i] : ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ),
inference(demod,[status(thm)],[zip_derived_cl2652,zip_derived_cl2661,zip_derived_cl90]) ).
thf(zip_derived_cl3027,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3023,zip_derived_cl2663]) ).
thf(zip_derived_cl3028,plain,
( ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl3027]) ).
thf(zip_derived_cl2685_075,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl2665]) ).
thf(zip_derived_cl64_076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_8 @ X1 @ X0 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl2861,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2685,zip_derived_cl64]) ).
thf(zip_derived_cl2685_077,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl2665]) ).
thf(zip_derived_cl65_078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( zip_tseitin_8 @ X0 @ X2 @ X1 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl2862,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( in @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( powerset @ sk__2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2685,zip_derived_cl65]) ).
thf(zip_derived_cl2886,plain,
( ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2861,zip_derived_cl2862]) ).
thf(zip_derived_cl2889,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl2886]) ).
thf(zip_derived_cl3032,plain,
( ( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3028,zip_derived_cl2889]) ).
thf(zip_derived_cl3127,plain,
( ( sk__4 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference(clc,[status(thm)],[zip_derived_cl3080,zip_derived_cl3032]) ).
thf(zip_derived_cl2_079,plain,
! [X0: $i] :
( ( relstr_set_smaller @ sk_ @ ( sk__4 @ X0 ) @ ( sk__5 @ X0 ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3128,plain,
( ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3127,zip_derived_cl2]) ).
thf(zip_derived_cl3_080,plain,
! [X0: $i] :
( ( in @ ( sk__5 @ X0 ) @ sk__1 )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_081,plain,
! [X0: $i] :
( ( element @ ( sk__5 @ X0 ) @ ( the_carrier @ sk_ ) )
| ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2665_082,plain,
! [X0: $i] :
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2663,zip_derived_cl68]) ).
thf(zip_derived_cl2686,plain,
( ( element @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( the_carrier @ sk_ ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl2665]) ).
thf(zip_derived_cl59_083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( zip_tseitin_6 @ X0 @ X1 @ X2 @ X3 )
| ~ ( element @ X0 @ ( the_carrier @ X3 ) )
| ~ ( in @ X0 @ X2 )
| ~ ( relstr_set_smaller @ X3 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl2857,plain,
! [X0: $i,X1: $i] :
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ X0 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ~ ( in @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X1 )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ X1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl2686,zip_derived_cl59]) ).
thf(zip_derived_cl4105,plain,
! [X0: $i] :
( ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ X0 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl2857]) ).
thf(zip_derived_cl2665_084,plain,
! [X0: $i] :
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2663,zip_derived_cl68]) ).
thf(zip_derived_cl4106,plain,
! [X0: $i] :
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ~ ( relstr_set_smaller @ sk_ @ X0 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl4105,zip_derived_cl2665]) ).
thf(zip_derived_cl4107,plain,
( ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl3128,zip_derived_cl4106]) ).
thf(zip_derived_cl2665_085,plain,
! [X0: $i] :
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2663,zip_derived_cl68]) ).
thf(zip_derived_cl4110,plain,
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(clc,[status(thm)],[zip_derived_cl4107,zip_derived_cl2665]) ).
thf(zip_derived_cl63_086,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( zip_tseitin_7 @ ( sk__20 @ X0 @ X1 @ X2 ) @ X2 @ X1 @ X0 )
| ~ ( zip_tseitin_8 @ X3 @ X2 @ X4 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl4111,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl4110,zip_derived_cl63]) ).
thf(zip_derived_cl61_087,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_7 @ X1 @ X0 @ X2 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl4344,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4111,zip_derived_cl61]) ).
thf(zip_derived_cl4111_088,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__20 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl4110,zip_derived_cl63]) ).
thf(zip_derived_cl4346,plain,
( ( zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl4344,zip_derived_cl4111]) ).
thf(zip_derived_cl4347,plain,
( ( zip_tseitin_6 @ ( sk__5 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ )
| ( zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_ ) ),
inference(simplify,[status(thm)],[zip_derived_cl4346]) ).
thf(zip_derived_cl91_089,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( zip_tseitin_6 @ X3 @ X2 @ X1 @ X0 )
| ( zip_tseitin_7 @ X2 @ X2 @ X1 @ X0 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl4348,plain,
zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_,
inference(clc,[status(thm)],[zip_derived_cl4347,zip_derived_cl91]) ).
thf(zip_derived_cl108_090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ ( sk__3 @ X0 ) @ X0 )
| ( zip_tseitin_8 @ ( sk__3 @ X0 ) @ ( sk__3 @ X0 ) @ sk__2 @ X2 @ X1 )
| ~ ( zip_tseitin_7 @ X3 @ ( sk__3 @ X0 ) @ X2 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl103]) ).
thf(zip_derived_cl4351,plain,
( ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4348,zip_derived_cl108]) ).
thf(zip_derived_cl2665_091,plain,
! [X0: $i] :
( ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ X0 ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2663,zip_derived_cl68]) ).
thf(zip_derived_cl4426,plain,
( ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl4351,zip_derived_cl2665]) ).
thf(zip_derived_cl64_092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X0 )
| ~ ( zip_tseitin_8 @ X1 @ X0 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl4541,plain,
( ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) )
= ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4426,zip_derived_cl64]) ).
thf(zip_derived_cl4426_093,plain,
( ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__21 @ sk_ @ sk__1 @ sk__2 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup-',[status(thm)],[zip_derived_cl4351,zip_derived_cl2665]) ).
thf(zip_derived_cl4546,plain,
( ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ )
| ( zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_ ) ),
inference('sup+',[status(thm)],[zip_derived_cl4541,zip_derived_cl4426]) ).
thf(zip_derived_cl4549,plain,
zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_,
inference(simplify,[status(thm)],[zip_derived_cl4546]) ).
thf(zip_derived_cl67_094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( zip_tseitin_8 @ X0 @ X1 @ X2 @ X3 @ X4 )
| ( in @ X1 @ X5 )
| ~ ( zip_tseitin_9 @ X1 @ X5 @ X2 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl4555,plain,
! [X0: $i] :
( ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 @ sk__2 @ sk__1 @ sk_ )
| ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl4549,zip_derived_cl67]) ).
thf(zip_derived_cl4348_095,plain,
zip_tseitin_7 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_,
inference(clc,[status(thm)],[zip_derived_cl4347,zip_derived_cl91]) ).
thf(zip_derived_cl60_096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( zip_tseitin_6 @ ( sk__19 @ X0 @ X1 @ X2 ) @ X2 @ X1 @ X0 )
| ~ ( zip_tseitin_7 @ X2 @ X3 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl4349,plain,
zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_,
inference('sup-',[status(thm)],[zip_derived_cl4348,zip_derived_cl60]) ).
thf(zip_derived_cl57_097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ X0 @ X1 )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X1 @ X3 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl4353,plain,
in @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ sk__1,
inference('sup-',[status(thm)],[zip_derived_cl4349,zip_derived_cl57]) ).
thf(zip_derived_cl73_098,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( sk__3 @ X0 ) @ X0 )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( element @ X1 @ ( the_carrier @ sk_ ) )
| ~ ( in @ X1 @ sk__1 )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ X1 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl4357,plain,
! [X0: $i] :
( ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ~ ( element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ) )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl4353,zip_derived_cl73]) ).
thf(zip_derived_cl4349_099,plain,
zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_,
inference('sup-',[status(thm)],[zip_derived_cl4348,zip_derived_cl60]) ).
thf(zip_derived_cl58_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( element @ X0 @ ( the_carrier @ X1 ) )
| ~ ( zip_tseitin_6 @ X0 @ X2 @ X3 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl4354,plain,
element @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( the_carrier @ sk_ ),
inference('sup-',[status(thm)],[zip_derived_cl4349,zip_derived_cl58]) ).
thf(zip_derived_cl4358,plain,
! [X0: $i] :
( ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ X0 ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) )
| ~ ( in @ ( sk__3 @ X0 ) @ ( powerset @ sk__2 ) )
| ~ ( in @ ( sk__3 @ X0 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl4357,zip_derived_cl4354]) ).
thf(zip_derived_cl4645,plain,
( ~ ( zip_tseitin_9 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ )
| ~ ( in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ) )
| ~ ( relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4555,zip_derived_cl4358]) ).
thf(zip_derived_cl2663_101,plain,
! [X0: $i] : ( zip_tseitin_9 @ X0 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) @ sk__2 @ sk__1 @ sk_ ),
inference(demod,[status(thm)],[zip_derived_cl2652,zip_derived_cl2661,zip_derived_cl90]) ).
thf(zip_derived_cl4549_102,plain,
zip_tseitin_8 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__2 @ sk__1 @ sk_,
inference(simplify,[status(thm)],[zip_derived_cl4546]) ).
thf(zip_derived_cl65_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( zip_tseitin_8 @ X0 @ X2 @ X1 @ X3 @ X4 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl4554,plain,
in @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( powerset @ sk__2 ),
inference('sup-',[status(thm)],[zip_derived_cl4549,zip_derived_cl65]) ).
thf(zip_derived_cl4349_104,plain,
zip_tseitin_6 @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ) @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ sk__1 @ sk_,
inference('sup-',[status(thm)],[zip_derived_cl4348,zip_derived_cl60]) ).
thf(zip_derived_cl56_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( relstr_set_smaller @ X0 @ X1 @ X2 )
| ~ ( zip_tseitin_6 @ X2 @ X1 @ X3 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl4352,plain,
relstr_set_smaller @ sk_ @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) @ ( sk__19 @ sk_ @ sk__1 @ ( sk__3 @ ( sk__25 @ sk__2 @ sk__1 @ sk_ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4349,zip_derived_cl56]) ).
thf(zip_derived_cl4682,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl4645,zip_derived_cl2663,zip_derived_cl4554,zip_derived_cl4352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU364+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.XT8GjLabGL true
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 13:59:55 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in FO mode
% 0.22/0.69 % Total configuration time : 435
% 0.22/0.69 % Estimated wc time : 1092
% 0.22/0.69 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.58/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 12.12/2.38 % Solved by fo/fo7.sh.
% 12.12/2.38 % done 1637 iterations in 1.595s
% 12.12/2.38 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 12.12/2.38 % SZS output start Refutation
% See solution above
% 12.51/2.39
% 12.51/2.39
% 12.51/2.39 % Terminating...
% 13.01/2.50 % Runner terminated.
% 13.01/2.51 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------