TSTP Solution File: ALG222+1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG222+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YjQsDomXj3 true
% Computer : n020.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 : Wed Aug 30 17:12:17 EDT 2023
% Result : Theorem 2.33s 1.25s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 47
% Syntax : Number of formulae : 314 ( 197 unt; 33 typ; 0 def)
% Number of atoms : 855 ( 21 equ; 0 cnn)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 3273 ( 476 ~; 411 |; 97 &;2223 @)
% ( 0 <=>; 25 =>; 41 <=; 0 <~>)
% Maximal formula depth : 31 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 6 con; 0-4 aty)
% Number of variables : 137 ( 0 ^; 136 !; 1 ?; 137 :)
% Comments :
%------------------------------------------------------------------------------
thf(v5_rlvect_1_type,type,
v5_rlvect_1: $i > $o ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(sk__2_type,type,
sk__2: $i ).
thf(v6_rlvect_1_type,type,
v6_rlvect_1: $i > $o ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(sk__21_type,type,
sk__21: $i > $i ).
thf(v5_vectsp_2_type,type,
v5_vectsp_2: $i > $i > $o ).
thf(sk__3_type,type,
sk__3: $i ).
thf(v4_group_1_type,type,
v4_group_1: $i > $o ).
thf(v3_rlvect_1_type,type,
v3_rlvect_1: $i > $o ).
thf(l1_vectsp_2_type,type,
l1_vectsp_2: $i > $i > $o ).
thf(v7_vectsp_1_type,type,
v7_vectsp_1: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k2_rmod_3_type,type,
k2_rmod_3: $i > $i > $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(v3_vectsp_2_type,type,
v3_vectsp_2: $i > $i > $o ).
thf(v7_group_1_type,type,
v7_group_1: $i > $o ).
thf(sk__type,type,
sk_: $i ).
thf(l3_vectsp_1_type,type,
l3_vectsp_1: $i > $o ).
thf(m1_rmod_2_type,type,
m1_rmod_2: $i > $i > $i > $o ).
thf(v4_rlvect_1_type,type,
v4_rlvect_1: $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(v2_vectsp_2_type,type,
v2_vectsp_2: $i > $o ).
thf(v10_vectsp_1_type,type,
v10_vectsp_1: $i > $o ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(v6_vectsp_1_type,type,
v6_vectsp_1: $i > $o ).
thf(k1_rmod_5_type,type,
k1_rmod_5: $i > $i > $i > $i ).
thf(sk__1_type,type,
sk__1: $i ).
thf(v8_vectsp_1_type,type,
v8_vectsp_1: $i > $o ).
thf(redefinition_k5_subset_1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ) ).
thf(zip_derived_cl139,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( m1_subset_1 @ X0 @ ( k1_zfmisc_1 @ X1 ) )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ X1 ) )
| ( ( k5_subset_1 @ X1 @ X0 @ X2 )
= ( k3_xboole_0 @ X0 @ X2 ) ) ),
inference(cnf,[status(esa)],[redefinition_k5_subset_1]) ).
thf(t15_rmod_5,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_rlvect_1 @ A )
& ( v4_rlvect_1 @ A )
& ( v5_rlvect_1 @ A )
& ( v6_rlvect_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( v6_vectsp_1 @ A )
& ( v7_vectsp_1 @ A )
& ( v8_vectsp_1 @ A )
& ~ ( v10_vectsp_1 @ A )
& ( v2_vectsp_2 @ A )
& ( l3_vectsp_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_rlvect_1 @ B )
& ( v4_rlvect_1 @ B )
& ( v5_rlvect_1 @ B )
& ( v6_rlvect_1 @ B )
& ( v5_vectsp_2 @ B @ A )
& ( l1_vectsp_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( m1_rmod_2 @ ( k1_rmod_5 @ A @ B @ C ) @ A @ ( k1_rmod_5 @ A @ B @ D ) ) ) ) ) ) ) ).
thf(zip_derived_cl143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( v3_struct_0 @ X0 )
| ~ ( v3_rlvect_1 @ X0 )
| ~ ( v4_rlvect_1 @ X0 )
| ~ ( v5_rlvect_1 @ X0 )
| ~ ( v6_rlvect_1 @ X0 )
| ~ ( v5_vectsp_2 @ X0 @ X1 )
| ~ ( l1_vectsp_2 @ X0 @ X1 )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ X0 ) ) )
| ( m1_rmod_2 @ ( k1_rmod_5 @ X1 @ X0 @ X3 ) @ X1 @ ( k1_rmod_5 @ X1 @ X0 @ X2 ) )
| ~ ( r1_tarski @ X3 @ X2 )
| ~ ( m1_subset_1 @ X3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ X0 ) ) )
| ~ ( l3_vectsp_1 @ X1 )
| ~ ( v2_vectsp_2 @ X1 )
| ( v10_vectsp_1 @ X1 )
| ~ ( v8_vectsp_1 @ X1 )
| ~ ( v7_vectsp_1 @ X1 )
| ~ ( v6_vectsp_1 @ X1 )
| ~ ( v7_group_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v6_rlvect_1 @ X1 )
| ~ ( v5_rlvect_1 @ X1 )
| ~ ( v4_rlvect_1 @ X1 )
| ~ ( v3_rlvect_1 @ X1 )
| ( v3_struct_0 @ X1 ) ),
inference(cnf,[status(esa)],[t15_rmod_5]) ).
thf(t24_rmod_3,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_rlvect_1 @ A )
& ( v4_rlvect_1 @ A )
& ( v5_rlvect_1 @ A )
& ( v6_rlvect_1 @ A )
& ( v4_group_1 @ A )
& ( v6_vectsp_1 @ A )
& ( v7_vectsp_1 @ A )
& ( v8_vectsp_1 @ A )
& ( l3_vectsp_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_rlvect_1 @ B )
& ( v4_rlvect_1 @ B )
& ( v5_rlvect_1 @ B )
& ( v6_rlvect_1 @ B )
& ( v5_vectsp_2 @ B @ A )
& ( l1_vectsp_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_rmod_2 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_rmod_2 @ D @ A @ B )
=> ! [E: $i] :
( ( m1_rmod_2 @ E @ A @ B )
=> ( ( ( m1_rmod_2 @ C @ A @ D )
& ( m1_rmod_2 @ C @ A @ E ) )
=> ( m1_rmod_2 @ C @ A @ ( k2_rmod_3 @ A @ B @ D @ E ) ) ) ) ) ) ) ) ).
thf(zip_derived_cl146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( v3_struct_0 @ X0 )
| ~ ( v3_rlvect_1 @ X0 )
| ~ ( v4_rlvect_1 @ X0 )
| ~ ( v5_rlvect_1 @ X0 )
| ~ ( v6_rlvect_1 @ X0 )
| ~ ( v5_vectsp_2 @ X0 @ X1 )
| ~ ( l1_vectsp_2 @ X0 @ X1 )
| ~ ( m1_rmod_2 @ X2 @ X1 @ X0 )
| ~ ( m1_rmod_2 @ X3 @ X1 @ X2 )
| ~ ( m1_rmod_2 @ X3 @ X1 @ X4 )
| ( m1_rmod_2 @ X3 @ X1 @ ( k2_rmod_3 @ X1 @ X0 @ X2 @ X4 ) )
| ~ ( m1_rmod_2 @ X4 @ X1 @ X0 )
| ~ ( m1_rmod_2 @ X3 @ X1 @ X0 )
| ~ ( l3_vectsp_1 @ X1 )
| ~ ( v8_vectsp_1 @ X1 )
| ~ ( v7_vectsp_1 @ X1 )
| ~ ( v6_vectsp_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v6_rlvect_1 @ X1 )
| ~ ( v5_rlvect_1 @ X1 )
| ~ ( v4_rlvect_1 @ X1 )
| ~ ( v3_rlvect_1 @ X1 )
| ( v3_struct_0 @ X1 ) ),
inference(cnf,[status(esa)],[t24_rmod_3]) ).
thf(t18_rmod_5,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_rlvect_1 @ A )
& ( v4_rlvect_1 @ A )
& ( v5_rlvect_1 @ A )
& ( v6_rlvect_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( v6_vectsp_1 @ A )
& ( v7_vectsp_1 @ A )
& ( v8_vectsp_1 @ A )
& ~ ( v10_vectsp_1 @ A )
& ( v2_vectsp_2 @ A )
& ( l3_vectsp_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_rlvect_1 @ B )
& ( v4_rlvect_1 @ B )
& ( v5_rlvect_1 @ B )
& ( v6_rlvect_1 @ B )
& ( v5_vectsp_2 @ B @ A )
& ( l1_vectsp_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_rmod_2 @ ( k1_rmod_5 @ A @ B @ ( k5_subset_1 @ ( u1_struct_0 @ B ) @ C @ D ) ) @ A @ ( k2_rmod_3 @ A @ B @ ( k1_rmod_5 @ A @ B @ C ) @ ( k1_rmod_5 @ A @ B @ D ) ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_rlvect_1 @ A )
& ( v4_rlvect_1 @ A )
& ( v5_rlvect_1 @ A )
& ( v6_rlvect_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( v6_vectsp_1 @ A )
& ( v7_vectsp_1 @ A )
& ( v8_vectsp_1 @ A )
& ~ ( v10_vectsp_1 @ A )
& ( v2_vectsp_2 @ A )
& ( l3_vectsp_1 @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v3_rlvect_1 @ B )
& ( v4_rlvect_1 @ B )
& ( v5_rlvect_1 @ B )
& ( v6_rlvect_1 @ B )
& ( v5_vectsp_2 @ B @ A )
& ( l1_vectsp_2 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_rmod_2 @ ( k1_rmod_5 @ A @ B @ ( k5_subset_1 @ ( u1_struct_0 @ B ) @ C @ D ) ) @ A @ ( k2_rmod_3 @ A @ B @ ( k1_rmod_5 @ A @ B @ C ) @ ( k1_rmod_5 @ A @ B @ D ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[t18_rmod_5]) ).
thf(zip_derived_cl14,plain,
~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1234,plain,
( ( v3_struct_0 @ sk_ )
| ~ ( v3_rlvect_1 @ sk_ )
| ~ ( v4_rlvect_1 @ sk_ )
| ~ ( v5_rlvect_1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk_ )
| ~ ( v4_group_1 @ sk_ )
| ~ ( v6_vectsp_1 @ sk_ )
| ~ ( v7_vectsp_1 @ sk_ )
| ~ ( v8_vectsp_1 @ sk_ )
| ~ ( l3_vectsp_1 @ sk_ )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1 )
| ~ ( l1_vectsp_2 @ sk__1 @ sk_ )
| ~ ( v5_vectsp_2 @ sk__1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk__1 )
| ~ ( v5_rlvect_1 @ sk__1 )
| ~ ( v4_rlvect_1 @ sk__1 )
| ~ ( v3_rlvect_1 @ sk__1 )
| ( v3_struct_0 @ sk__1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl146,zip_derived_cl14]) ).
thf(zip_derived_cl0,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
v3_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2,plain,
v4_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3,plain,
v5_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4,plain,
v6_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7,plain,
v6_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8,plain,
v7_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9,plain,
v8_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12,plain,
l3_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16,plain,
l1_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl17,plain,
v5_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl18,plain,
v6_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl19,plain,
v5_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl20,plain,
v4_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21,plain,
v3_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl22,plain,
~ ( v3_struct_0 @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1273,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1234,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl3,zip_derived_cl4,zip_derived_cl5,zip_derived_cl7,zip_derived_cl8,zip_derived_cl9,zip_derived_cl12,zip_derived_cl16,zip_derived_cl17,zip_derived_cl18,zip_derived_cl19,zip_derived_cl20,zip_derived_cl21,zip_derived_cl22]) ).
thf(zip_derived_cl1572,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) ) ),
inference(split,[status(esa)],[zip_derived_cl1273]) ).
thf(dt_k5_subset_1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ).
thf(zip_derived_cl46,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( m1_subset_1 @ X0 @ ( k1_zfmisc_1 @ X1 ) )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ X1 ) )
| ( m1_subset_1 @ ( k5_subset_1 @ X1 @ X0 @ X2 ) @ ( k1_zfmisc_1 @ X1 ) ) ),
inference(cnf,[status(esa)],[dt_k5_subset_1]) ).
thf(dt_k1_rmod_5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_rlvect_1 @ A )
& ( v4_rlvect_1 @ A )
& ( v5_rlvect_1 @ A )
& ( v6_rlvect_1 @ A )
& ( v4_group_1 @ A )
& ( v7_group_1 @ A )
& ( v6_vectsp_1 @ A )
& ( v7_vectsp_1 @ A )
& ( v8_vectsp_1 @ A )
& ~ ( v10_vectsp_1 @ A )
& ( v2_vectsp_2 @ A )
& ( l3_vectsp_1 @ A )
& ~ ( v3_struct_0 @ B )
& ( v3_rlvect_1 @ B )
& ( v4_rlvect_1 @ B )
& ( v5_rlvect_1 @ B )
& ( v6_rlvect_1 @ B )
& ( v5_vectsp_2 @ B @ A )
& ( l1_vectsp_2 @ B @ A )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( v3_vectsp_2 @ ( k1_rmod_5 @ A @ B @ C ) @ A )
& ( m1_rmod_2 @ ( k1_rmod_5 @ A @ B @ C ) @ A @ B ) ) ) ).
thf(zip_derived_cl39,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( l1_vectsp_2 @ X0 @ X1 )
| ~ ( v5_vectsp_2 @ X0 @ X1 )
| ~ ( v6_rlvect_1 @ X0 )
| ~ ( v5_rlvect_1 @ X0 )
| ~ ( v4_rlvect_1 @ X0 )
| ~ ( v3_rlvect_1 @ X0 )
| ( v3_struct_0 @ X0 )
| ~ ( l3_vectsp_1 @ X1 )
| ~ ( v2_vectsp_2 @ X1 )
| ( v10_vectsp_1 @ X1 )
| ~ ( v8_vectsp_1 @ X1 )
| ~ ( v7_vectsp_1 @ X1 )
| ~ ( v6_vectsp_1 @ X1 )
| ~ ( v7_group_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v6_rlvect_1 @ X1 )
| ~ ( v5_rlvect_1 @ X1 )
| ~ ( v4_rlvect_1 @ X1 )
| ~ ( v3_rlvect_1 @ X1 )
| ( v3_struct_0 @ X1 )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ X0 ) ) )
| ( m1_rmod_2 @ ( k1_rmod_5 @ X1 @ X0 @ X2 ) @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_rmod_5]) ).
thf(zip_derived_cl1569,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ sk__1 )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ sk__1 ) ),
inference(split,[status(esa)],[zip_derived_cl1273]) ).
thf(zip_derived_cl1575,plain,
( ( ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ( v3_struct_0 @ sk_ )
| ~ ( v3_rlvect_1 @ sk_ )
| ~ ( v4_rlvect_1 @ sk_ )
| ~ ( v5_rlvect_1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk_ )
| ~ ( v4_group_1 @ sk_ )
| ~ ( v7_group_1 @ sk_ )
| ~ ( v6_vectsp_1 @ sk_ )
| ~ ( v7_vectsp_1 @ sk_ )
| ~ ( v8_vectsp_1 @ sk_ )
| ( v10_vectsp_1 @ sk_ )
| ~ ( v2_vectsp_2 @ sk_ )
| ~ ( l3_vectsp_1 @ sk_ )
| ( v3_struct_0 @ sk__1 )
| ~ ( v3_rlvect_1 @ sk__1 )
| ~ ( v4_rlvect_1 @ sk__1 )
| ~ ( v5_rlvect_1 @ sk__1 )
| ~ ( v6_rlvect_1 @ sk__1 )
| ~ ( v5_vectsp_2 @ sk__1 @ sk_ )
| ~ ( l1_vectsp_2 @ sk__1 @ sk_ ) )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ sk__1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl1569]) ).
thf(zip_derived_cl0_001,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_002,plain,
v3_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_003,plain,
v4_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3_004,plain,
v5_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_005,plain,
v6_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5_006,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6,plain,
v7_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7_007,plain,
v6_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8_008,plain,
v7_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9_009,plain,
v8_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10,plain,
~ ( v10_vectsp_1 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl11,plain,
v2_vectsp_2 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12_010,plain,
l3_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl22_011,plain,
~ ( v3_struct_0 @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21_012,plain,
v3_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl20_013,plain,
v4_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl19_014,plain,
v5_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl18_015,plain,
v6_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl17_016,plain,
v5_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_017,plain,
l1_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1577,plain,
( ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ sk__1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1575,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl3,zip_derived_cl4,zip_derived_cl5,zip_derived_cl6,zip_derived_cl7,zip_derived_cl8,zip_derived_cl9,zip_derived_cl10,zip_derived_cl11,zip_derived_cl12,zip_derived_cl22,zip_derived_cl21,zip_derived_cl20,zip_derived_cl19,zip_derived_cl18,zip_derived_cl17,zip_derived_cl16]) ).
thf(zip_derived_cl1583,plain,
( ( ~ ( m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) ) )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ sk__1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl1577]) ).
thf(zip_derived_cl15,plain,
m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl13,plain,
m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('0',plain,
m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ sk__1,
inference(demod,[status(thm)],[zip_derived_cl1583,zip_derived_cl15,zip_derived_cl13]) ).
thf(zip_derived_cl139_018,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( m1_subset_1 @ X0 @ ( k1_zfmisc_1 @ X1 ) )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ X1 ) )
| ( ( k5_subset_1 @ X1 @ X0 @ X2 )
= ( k3_xboole_0 @ X0 @ X2 ) ) ),
inference(cnf,[status(esa)],[redefinition_k5_subset_1]) ).
thf(zip_derived_cl143_019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( v3_struct_0 @ X0 )
| ~ ( v3_rlvect_1 @ X0 )
| ~ ( v4_rlvect_1 @ X0 )
| ~ ( v5_rlvect_1 @ X0 )
| ~ ( v6_rlvect_1 @ X0 )
| ~ ( v5_vectsp_2 @ X0 @ X1 )
| ~ ( l1_vectsp_2 @ X0 @ X1 )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ X0 ) ) )
| ( m1_rmod_2 @ ( k1_rmod_5 @ X1 @ X0 @ X3 ) @ X1 @ ( k1_rmod_5 @ X1 @ X0 @ X2 ) )
| ~ ( r1_tarski @ X3 @ X2 )
| ~ ( m1_subset_1 @ X3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ X0 ) ) )
| ~ ( l3_vectsp_1 @ X1 )
| ~ ( v2_vectsp_2 @ X1 )
| ( v10_vectsp_1 @ X1 )
| ~ ( v8_vectsp_1 @ X1 )
| ~ ( v7_vectsp_1 @ X1 )
| ~ ( v6_vectsp_1 @ X1 )
| ~ ( v7_group_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v6_rlvect_1 @ X1 )
| ~ ( v5_rlvect_1 @ X1 )
| ~ ( v4_rlvect_1 @ X1 )
| ~ ( v3_rlvect_1 @ X1 )
| ( v3_struct_0 @ X1 ) ),
inference(cnf,[status(esa)],[t15_rmod_5]) ).
thf(zip_derived_cl1571,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) ) ),
inference(split,[status(esa)],[zip_derived_cl1273]) ).
thf(zip_derived_cl1598,plain,
( ( ( v3_struct_0 @ sk_ )
| ~ ( v3_rlvect_1 @ sk_ )
| ~ ( v4_rlvect_1 @ sk_ )
| ~ ( v5_rlvect_1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk_ )
| ~ ( v4_group_1 @ sk_ )
| ~ ( v7_group_1 @ sk_ )
| ~ ( v6_vectsp_1 @ sk_ )
| ~ ( v7_vectsp_1 @ sk_ )
| ~ ( v8_vectsp_1 @ sk_ )
| ( v10_vectsp_1 @ sk_ )
| ~ ( v2_vectsp_2 @ sk_ )
| ~ ( l3_vectsp_1 @ sk_ )
| ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__3 )
| ~ ( m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( l1_vectsp_2 @ sk__1 @ sk_ )
| ~ ( v5_vectsp_2 @ sk__1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk__1 )
| ~ ( v5_rlvect_1 @ sk__1 )
| ~ ( v4_rlvect_1 @ sk__1 )
| ~ ( v3_rlvect_1 @ sk__1 )
| ( v3_struct_0 @ sk__1 ) )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl1571]) ).
thf(zip_derived_cl0_020,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_021,plain,
v3_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_022,plain,
v4_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3_023,plain,
v5_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_024,plain,
v6_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5_025,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6_026,plain,
v7_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7_027,plain,
v6_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8_028,plain,
v7_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9_029,plain,
v8_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10_030,plain,
~ ( v10_vectsp_1 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl11_031,plain,
v2_vectsp_2 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12_032,plain,
l3_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl15_033,plain,
m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_034,plain,
l1_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl17_035,plain,
v5_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl18_036,plain,
v6_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl19_037,plain,
v5_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl20_038,plain,
v4_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21_039,plain,
v3_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl22_040,plain,
~ ( v3_struct_0 @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1600,plain,
( ( ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__3 ) )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1598,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl3,zip_derived_cl4,zip_derived_cl5,zip_derived_cl6,zip_derived_cl7,zip_derived_cl8,zip_derived_cl9,zip_derived_cl10,zip_derived_cl11,zip_derived_cl12,zip_derived_cl15,zip_derived_cl16,zip_derived_cl17,zip_derived_cl18,zip_derived_cl19,zip_derived_cl20,zip_derived_cl21,zip_derived_cl22]) ).
thf(zip_derived_cl1629,plain,
( ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__3 )
<= ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__3 ) ),
inference(split,[status(esa)],[zip_derived_cl1600]) ).
thf(zip_derived_cl1635,plain,
( ( ~ ( m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( r1_tarski @ ( k3_xboole_0 @ sk__2 @ sk__3 ) @ sk__3 ) )
<= ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__3 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl139,zip_derived_cl1629]) ).
thf(zip_derived_cl15_041,plain,
m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl13_042,plain,
m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(commutativity_k3_xboole_0,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ) ).
thf(zip_derived_cl34,plain,
! [X0: $i,X1: $i] :
( ( k3_xboole_0 @ X1 @ X0 )
= ( k3_xboole_0 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[commutativity_k3_xboole_0]) ).
thf(t17_xboole_1,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ) ).
thf(zip_derived_cl144,plain,
! [X0: $i,X1: $i] : ( r1_tarski @ ( k3_xboole_0 @ X0 @ X1 ) @ X0 ),
inference(cnf,[status(esa)],[t17_xboole_1]) ).
thf(zip_derived_cl233,plain,
! [X0: $i,X1: $i] : ( r1_tarski @ ( k3_xboole_0 @ X1 @ X0 ) @ X0 ),
inference('s_sup+',[status(thm)],[zip_derived_cl34,zip_derived_cl144]) ).
thf('1',plain,
r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__3,
inference(demod,[status(thm)],[zip_derived_cl1635,zip_derived_cl15,zip_derived_cl13,zip_derived_cl233]) ).
thf(zip_derived_cl46_043,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( m1_subset_1 @ X0 @ ( k1_zfmisc_1 @ X1 ) )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ X1 ) )
| ( m1_subset_1 @ ( k5_subset_1 @ X1 @ X0 @ X2 ) @ ( k1_zfmisc_1 @ X1 ) ) ),
inference(cnf,[status(esa)],[dt_k5_subset_1]) ).
thf(zip_derived_cl1630,plain,
( ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
<= ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl1600]) ).
thf(zip_derived_cl1641,plain,
( ( ~ ( m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) ) )
<= ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl1630]) ).
thf(zip_derived_cl15_044,plain,
m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl13_045,plain,
m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('2',plain,
m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1641,zip_derived_cl15,zip_derived_cl13]) ).
thf('3',plain,
( ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) )
| ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__3 ) ),
inference(split,[status(esa)],[zip_derived_cl1600]) ).
thf(zip_derived_cl39_046,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( l1_vectsp_2 @ X0 @ X1 )
| ~ ( v5_vectsp_2 @ X0 @ X1 )
| ~ ( v6_rlvect_1 @ X0 )
| ~ ( v5_rlvect_1 @ X0 )
| ~ ( v4_rlvect_1 @ X0 )
| ~ ( v3_rlvect_1 @ X0 )
| ( v3_struct_0 @ X0 )
| ~ ( l3_vectsp_1 @ X1 )
| ~ ( v2_vectsp_2 @ X1 )
| ( v10_vectsp_1 @ X1 )
| ~ ( v8_vectsp_1 @ X1 )
| ~ ( v7_vectsp_1 @ X1 )
| ~ ( v6_vectsp_1 @ X1 )
| ~ ( v7_group_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v6_rlvect_1 @ X1 )
| ~ ( v5_rlvect_1 @ X1 )
| ~ ( v4_rlvect_1 @ X1 )
| ~ ( v3_rlvect_1 @ X1 )
| ( v3_struct_0 @ X1 )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ X0 ) ) )
| ( m1_rmod_2 @ ( k1_rmod_5 @ X1 @ X0 @ X2 ) @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_rmod_5]) ).
thf(zip_derived_cl139_047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( m1_subset_1 @ X0 @ ( k1_zfmisc_1 @ X1 ) )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ X1 ) )
| ( ( k5_subset_1 @ X1 @ X0 @ X2 )
= ( k3_xboole_0 @ X0 @ X2 ) ) ),
inference(cnf,[status(esa)],[redefinition_k5_subset_1]) ).
thf(t2_subset,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ) ).
thf(zip_derived_cl148,plain,
! [X0: $i,X1: $i] :
( ( r2_hidden @ X0 @ X1 )
| ( v1_xboole_0 @ X1 )
| ~ ( m1_subset_1 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[t2_subset]) ).
thf(zip_derived_cl13_048,plain,
m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(t5_subset,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ) ).
thf(zip_derived_cl152,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( r2_hidden @ X0 @ X1 )
| ~ ( v1_xboole_0 @ X2 )
| ~ ( m1_subset_1 @ X1 @ ( k1_zfmisc_1 @ X2 ) ) ),
inference(cnf,[status(esa)],[t5_subset]) ).
thf(zip_derived_cl157,plain,
! [X0: $i] :
( ~ ( r2_hidden @ X0 @ sk__2 )
| ~ ( v1_xboole_0 @ ( u1_struct_0 @ sk__1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl152]) ).
thf(zip_derived_cl162,plain,
( ! [X0: $i] :
~ ( r2_hidden @ X0 @ sk__2 )
<= ! [X0: $i] :
~ ( r2_hidden @ X0 @ sk__2 ) ),
inference(split,[status(esa)],[zip_derived_cl157]) ).
thf(zip_derived_cl346,plain,
( ! [X0: $i] :
( ~ ( m1_subset_1 @ X0 @ sk__2 )
| ( v1_xboole_0 @ sk__2 ) )
<= ! [X0: $i] :
~ ( r2_hidden @ X0 @ sk__2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl148,zip_derived_cl162]) ).
thf(zip_derived_cl365,plain,
( ( v1_xboole_0 @ sk__2 )
<= ( v1_xboole_0 @ sk__2 ) ),
inference(split,[status(esa)],[zip_derived_cl346]) ).
thf(t6_boole,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ) ).
thf(zip_derived_cl153,plain,
! [X0: $i] :
( ( X0 = k1_xboole_0 )
| ~ ( v1_xboole_0 @ X0 ) ),
inference(cnf,[status(esa)],[t6_boole]) ).
thf(zip_derived_cl368,plain,
( ( sk__2 = k1_xboole_0 )
<= ( v1_xboole_0 @ sk__2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl365,zip_derived_cl153]) ).
thf(zip_derived_cl14_049,plain,
~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl372,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ k1_xboole_0 @ sk__3 ) ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) ) )
<= ( v1_xboole_0 @ sk__2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl368,zip_derived_cl14]) ).
thf(zip_derived_cl687,plain,
( ( ~ ( m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k3_xboole_0 @ k1_xboole_0 @ sk__3 ) ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) ) ) )
<= ( v1_xboole_0 @ sk__2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl139,zip_derived_cl372]) ).
thf(zip_derived_cl15_050,plain,
m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(rc2_subset_1,axiom,
! [A: $i] :
? [B: $i] :
( ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ) ).
thf(zip_derived_cl126,plain,
! [X0: $i] : ( m1_subset_1 @ ( sk__21 @ X0 ) @ ( k1_zfmisc_1 @ X0 ) ),
inference(cnf,[status(esa)],[rc2_subset_1]) ).
thf(zip_derived_cl127,plain,
! [X0: $i] : ( v1_xboole_0 @ ( sk__21 @ X0 ) ),
inference(cnf,[status(esa)],[rc2_subset_1]) ).
thf(zip_derived_cl153_051,plain,
! [X0: $i] :
( ( X0 = k1_xboole_0 )
| ~ ( v1_xboole_0 @ X0 ) ),
inference(cnf,[status(esa)],[t6_boole]) ).
thf(zip_derived_cl183,plain,
! [X0: $i] :
( ( sk__21 @ X0 )
= k1_xboole_0 ),
inference('s_sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl153]) ).
thf(zip_derived_cl215,plain,
! [X0: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl126,zip_derived_cl183]) ).
thf(t2_boole,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ).
thf(zip_derived_cl147,plain,
! [X0: $i] :
( ( k3_xboole_0 @ X0 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[t2_boole]) ).
thf(zip_derived_cl34_052,plain,
! [X0: $i,X1: $i] :
( ( k3_xboole_0 @ X1 @ X0 )
= ( k3_xboole_0 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[commutativity_k3_xboole_0]) ).
thf(zip_derived_cl194,plain,
! [X0: $i] :
( k1_xboole_0
= ( k3_xboole_0 @ k1_xboole_0 @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl147,zip_derived_cl34]) ).
thf(zip_derived_cl698,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) ) )
<= ( v1_xboole_0 @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl687,zip_derived_cl15,zip_derived_cl215,zip_derived_cl194]) ).
thf(zip_derived_cl146_053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( v3_struct_0 @ X0 )
| ~ ( v3_rlvect_1 @ X0 )
| ~ ( v4_rlvect_1 @ X0 )
| ~ ( v5_rlvect_1 @ X0 )
| ~ ( v6_rlvect_1 @ X0 )
| ~ ( v5_vectsp_2 @ X0 @ X1 )
| ~ ( l1_vectsp_2 @ X0 @ X1 )
| ~ ( m1_rmod_2 @ X2 @ X1 @ X0 )
| ~ ( m1_rmod_2 @ X3 @ X1 @ X2 )
| ~ ( m1_rmod_2 @ X3 @ X1 @ X4 )
| ( m1_rmod_2 @ X3 @ X1 @ ( k2_rmod_3 @ X1 @ X0 @ X2 @ X4 ) )
| ~ ( m1_rmod_2 @ X4 @ X1 @ X0 )
| ~ ( m1_rmod_2 @ X3 @ X1 @ X0 )
| ~ ( l3_vectsp_1 @ X1 )
| ~ ( v8_vectsp_1 @ X1 )
| ~ ( v7_vectsp_1 @ X1 )
| ~ ( v6_vectsp_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v6_rlvect_1 @ X1 )
| ~ ( v5_rlvect_1 @ X1 )
| ~ ( v4_rlvect_1 @ X1 )
| ~ ( v3_rlvect_1 @ X1 )
| ( v3_struct_0 @ X1 ) ),
inference(cnf,[status(esa)],[t24_rmod_3]) ).
thf(zip_derived_cl1251,plain,
( ( ( v3_struct_0 @ sk__1 )
| ~ ( v3_rlvect_1 @ sk__1 )
| ~ ( v4_rlvect_1 @ sk__1 )
| ~ ( v5_rlvect_1 @ sk__1 )
| ~ ( v6_rlvect_1 @ sk__1 )
| ~ ( v5_vectsp_2 @ sk__1 @ sk_ )
| ~ ( l1_vectsp_2 @ sk__1 @ sk_ )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 )
| ~ ( l3_vectsp_1 @ sk_ )
| ~ ( v8_vectsp_1 @ sk_ )
| ~ ( v7_vectsp_1 @ sk_ )
| ~ ( v6_vectsp_1 @ sk_ )
| ~ ( v4_group_1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk_ )
| ~ ( v5_rlvect_1 @ sk_ )
| ~ ( v4_rlvect_1 @ sk_ )
| ~ ( v3_rlvect_1 @ sk_ )
| ( v3_struct_0 @ sk_ ) )
<= ( v1_xboole_0 @ sk__2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl698,zip_derived_cl146]) ).
thf(zip_derived_cl22_054,plain,
~ ( v3_struct_0 @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21_055,plain,
v3_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl20_056,plain,
v4_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl19_057,plain,
v5_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl18_058,plain,
v6_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl17_059,plain,
v5_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_060,plain,
l1_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12_061,plain,
l3_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9_062,plain,
v8_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8_063,plain,
v7_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7_064,plain,
v6_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5_065,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_066,plain,
v6_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3_067,plain,
v5_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_068,plain,
v4_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_069,plain,
v3_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_070,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1263,plain,
( ( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 ) )
<= ( v1_xboole_0 @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1251,zip_derived_cl22,zip_derived_cl21,zip_derived_cl20,zip_derived_cl19,zip_derived_cl18,zip_derived_cl17,zip_derived_cl16,zip_derived_cl12,zip_derived_cl9,zip_derived_cl8,zip_derived_cl7,zip_derived_cl5,zip_derived_cl4,zip_derived_cl3,zip_derived_cl2,zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl1264,plain,
( ( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 ) )
<= ( v1_xboole_0 @ sk__2 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1263]) ).
thf(zip_derived_cl1381,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1 )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1 ) ),
inference(split,[status(esa)],[zip_derived_cl1264]) ).
thf(zip_derived_cl1387,plain,
( ( ~ ( m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ( v3_struct_0 @ sk_ )
| ~ ( v3_rlvect_1 @ sk_ )
| ~ ( v4_rlvect_1 @ sk_ )
| ~ ( v5_rlvect_1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk_ )
| ~ ( v4_group_1 @ sk_ )
| ~ ( v7_group_1 @ sk_ )
| ~ ( v6_vectsp_1 @ sk_ )
| ~ ( v7_vectsp_1 @ sk_ )
| ~ ( v8_vectsp_1 @ sk_ )
| ( v10_vectsp_1 @ sk_ )
| ~ ( v2_vectsp_2 @ sk_ )
| ~ ( l3_vectsp_1 @ sk_ )
| ( v3_struct_0 @ sk__1 )
| ~ ( v3_rlvect_1 @ sk__1 )
| ~ ( v4_rlvect_1 @ sk__1 )
| ~ ( v5_rlvect_1 @ sk__1 )
| ~ ( v6_rlvect_1 @ sk__1 )
| ~ ( v5_vectsp_2 @ sk__1 @ sk_ )
| ~ ( l1_vectsp_2 @ sk__1 @ sk_ ) )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl1381]) ).
thf(zip_derived_cl15_071,plain,
m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_072,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_073,plain,
v3_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_074,plain,
v4_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3_075,plain,
v5_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_076,plain,
v6_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5_077,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6_078,plain,
v7_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7_079,plain,
v6_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8_080,plain,
v7_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9_081,plain,
v8_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10_082,plain,
~ ( v10_vectsp_1 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl11_083,plain,
v2_vectsp_2 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12_084,plain,
l3_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl22_085,plain,
~ ( v3_struct_0 @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21_086,plain,
v3_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl20_087,plain,
v4_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl19_088,plain,
v5_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl18_089,plain,
v6_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl17_090,plain,
v5_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_091,plain,
l1_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('4',plain,
m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1,
inference(demod,[status(thm)],[zip_derived_cl1387,zip_derived_cl15,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl3,zip_derived_cl4,zip_derived_cl5,zip_derived_cl6,zip_derived_cl7,zip_derived_cl8,zip_derived_cl9,zip_derived_cl10,zip_derived_cl11,zip_derived_cl12,zip_derived_cl22,zip_derived_cl21,zip_derived_cl20,zip_derived_cl19,zip_derived_cl18,zip_derived_cl17,zip_derived_cl16]) ).
thf(zip_derived_cl39_092,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( l1_vectsp_2 @ X0 @ X1 )
| ~ ( v5_vectsp_2 @ X0 @ X1 )
| ~ ( v6_rlvect_1 @ X0 )
| ~ ( v5_rlvect_1 @ X0 )
| ~ ( v4_rlvect_1 @ X0 )
| ~ ( v3_rlvect_1 @ X0 )
| ( v3_struct_0 @ X0 )
| ~ ( l3_vectsp_1 @ X1 )
| ~ ( v2_vectsp_2 @ X1 )
| ( v10_vectsp_1 @ X1 )
| ~ ( v8_vectsp_1 @ X1 )
| ~ ( v7_vectsp_1 @ X1 )
| ~ ( v6_vectsp_1 @ X1 )
| ~ ( v7_group_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v6_rlvect_1 @ X1 )
| ~ ( v5_rlvect_1 @ X1 )
| ~ ( v4_rlvect_1 @ X1 )
| ~ ( v3_rlvect_1 @ X1 )
| ( v3_struct_0 @ X1 )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ X0 ) ) )
| ( m1_rmod_2 @ ( k1_rmod_5 @ X1 @ X0 @ X2 ) @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_rmod_5]) ).
thf(zip_derived_cl139_093,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( m1_subset_1 @ X0 @ ( k1_zfmisc_1 @ X1 ) )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ X1 ) )
| ( ( k5_subset_1 @ X1 @ X0 @ X2 )
= ( k3_xboole_0 @ X0 @ X2 ) ) ),
inference(cnf,[status(esa)],[redefinition_k5_subset_1]) ).
thf(commutativity_k5_subset_1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ C @ B ) ) ) ).
thf(zip_derived_cl35,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( m1_subset_1 @ X0 @ ( k1_zfmisc_1 @ X1 ) )
| ~ ( m1_subset_1 @ X2 @ ( k1_zfmisc_1 @ X1 ) )
| ( ( k5_subset_1 @ X1 @ X0 @ X2 )
= ( k5_subset_1 @ X1 @ X2 @ X0 ) ) ),
inference(cnf,[status(esa)],[commutativity_k5_subset_1]) ).
thf(zip_derived_cl148_094,plain,
! [X0: $i,X1: $i] :
( ( r2_hidden @ X0 @ X1 )
| ( v1_xboole_0 @ X1 )
| ~ ( m1_subset_1 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[t2_subset]) ).
thf(zip_derived_cl15_095,plain,
m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl152_096,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( r2_hidden @ X0 @ X1 )
| ~ ( v1_xboole_0 @ X2 )
| ~ ( m1_subset_1 @ X1 @ ( k1_zfmisc_1 @ X2 ) ) ),
inference(cnf,[status(esa)],[t5_subset]) ).
thf(zip_derived_cl170,plain,
! [X0: $i] :
( ~ ( r2_hidden @ X0 @ sk__3 )
| ~ ( v1_xboole_0 @ ( u1_struct_0 @ sk__1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl152]) ).
thf(zip_derived_cl171,plain,
( ! [X0: $i] :
~ ( r2_hidden @ X0 @ sk__3 )
<= ! [X0: $i] :
~ ( r2_hidden @ X0 @ sk__3 ) ),
inference(split,[status(esa)],[zip_derived_cl170]) ).
thf(zip_derived_cl348,plain,
( ! [X0: $i] :
( ~ ( m1_subset_1 @ X0 @ sk__3 )
| ( v1_xboole_0 @ sk__3 ) )
<= ! [X0: $i] :
~ ( r2_hidden @ X0 @ sk__3 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl148,zip_derived_cl171]) ).
thf(zip_derived_cl377,plain,
( ( v1_xboole_0 @ sk__3 )
<= ( v1_xboole_0 @ sk__3 ) ),
inference(split,[status(esa)],[zip_derived_cl348]) ).
thf(zip_derived_cl153_097,plain,
! [X0: $i] :
( ( X0 = k1_xboole_0 )
| ~ ( v1_xboole_0 @ X0 ) ),
inference(cnf,[status(esa)],[t6_boole]) ).
thf(zip_derived_cl380,plain,
( ( sk__3 = k1_xboole_0 )
<= ( v1_xboole_0 @ sk__3 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl377,zip_derived_cl153]) ).
thf(zip_derived_cl14_098,plain,
~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl383,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ k1_xboole_0 ) ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) ) )
<= ( v1_xboole_0 @ sk__3 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl380,zip_derived_cl14]) ).
thf(zip_derived_cl419,plain,
( ( ~ ( m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ k1_xboole_0 @ sk__2 ) ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) ) ) )
<= ( v1_xboole_0 @ sk__3 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl383]) ).
thf(zip_derived_cl13_099,plain,
m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl215_100,plain,
! [X0: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl126,zip_derived_cl183]) ).
thf(zip_derived_cl422,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ k1_xboole_0 @ sk__2 ) ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) ) )
<= ( v1_xboole_0 @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl419,zip_derived_cl13,zip_derived_cl215]) ).
thf(zip_derived_cl686,plain,
( ( ~ ( m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k3_xboole_0 @ k1_xboole_0 @ sk__2 ) ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) ) ) )
<= ( v1_xboole_0 @ sk__3 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl139,zip_derived_cl422]) ).
thf(zip_derived_cl13_101,plain,
m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl215_102,plain,
! [X0: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl126,zip_derived_cl183]) ).
thf(zip_derived_cl194_103,plain,
! [X0: $i] :
( k1_xboole_0
= ( k3_xboole_0 @ k1_xboole_0 @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl147,zip_derived_cl34]) ).
thf(zip_derived_cl697,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k2_rmod_3 @ sk_ @ sk__1 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) ) )
<= ( v1_xboole_0 @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl686,zip_derived_cl13,zip_derived_cl215,zip_derived_cl194]) ).
thf(zip_derived_cl146_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( v3_struct_0 @ X0 )
| ~ ( v3_rlvect_1 @ X0 )
| ~ ( v4_rlvect_1 @ X0 )
| ~ ( v5_rlvect_1 @ X0 )
| ~ ( v6_rlvect_1 @ X0 )
| ~ ( v5_vectsp_2 @ X0 @ X1 )
| ~ ( l1_vectsp_2 @ X0 @ X1 )
| ~ ( m1_rmod_2 @ X2 @ X1 @ X0 )
| ~ ( m1_rmod_2 @ X3 @ X1 @ X2 )
| ~ ( m1_rmod_2 @ X3 @ X1 @ X4 )
| ( m1_rmod_2 @ X3 @ X1 @ ( k2_rmod_3 @ X1 @ X0 @ X2 @ X4 ) )
| ~ ( m1_rmod_2 @ X4 @ X1 @ X0 )
| ~ ( m1_rmod_2 @ X3 @ X1 @ X0 )
| ~ ( l3_vectsp_1 @ X1 )
| ~ ( v8_vectsp_1 @ X1 )
| ~ ( v7_vectsp_1 @ X1 )
| ~ ( v6_vectsp_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v6_rlvect_1 @ X1 )
| ~ ( v5_rlvect_1 @ X1 )
| ~ ( v4_rlvect_1 @ X1 )
| ~ ( v3_rlvect_1 @ X1 )
| ( v3_struct_0 @ X1 ) ),
inference(cnf,[status(esa)],[t24_rmod_3]) ).
thf(zip_derived_cl1250,plain,
( ( ( v3_struct_0 @ sk__1 )
| ~ ( v3_rlvect_1 @ sk__1 )
| ~ ( v4_rlvect_1 @ sk__1 )
| ~ ( v5_rlvect_1 @ sk__1 )
| ~ ( v6_rlvect_1 @ sk__1 )
| ~ ( v5_vectsp_2 @ sk__1 @ sk_ )
| ~ ( l1_vectsp_2 @ sk__1 @ sk_ )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 )
| ~ ( l3_vectsp_1 @ sk_ )
| ~ ( v8_vectsp_1 @ sk_ )
| ~ ( v7_vectsp_1 @ sk_ )
| ~ ( v6_vectsp_1 @ sk_ )
| ~ ( v4_group_1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk_ )
| ~ ( v5_rlvect_1 @ sk_ )
| ~ ( v4_rlvect_1 @ sk_ )
| ~ ( v3_rlvect_1 @ sk_ )
| ( v3_struct_0 @ sk_ ) )
<= ( v1_xboole_0 @ sk__3 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl697,zip_derived_cl146]) ).
thf(zip_derived_cl22_105,plain,
~ ( v3_struct_0 @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21_106,plain,
v3_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl20_107,plain,
v4_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl19_108,plain,
v5_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl18_109,plain,
v6_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl17_110,plain,
v5_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_111,plain,
l1_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12_112,plain,
l3_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9_113,plain,
v8_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8_114,plain,
v7_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7_115,plain,
v6_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5_116,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_117,plain,
v6_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3_118,plain,
v5_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_119,plain,
v4_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_120,plain,
v3_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_121,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1261,plain,
( ( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 ) )
<= ( v1_xboole_0 @ sk__3 ) ),
inference(demod,[status(thm)],[zip_derived_cl1250,zip_derived_cl22,zip_derived_cl21,zip_derived_cl20,zip_derived_cl19,zip_derived_cl18,zip_derived_cl17,zip_derived_cl16,zip_derived_cl12,zip_derived_cl9,zip_derived_cl8,zip_derived_cl7,zip_derived_cl5,zip_derived_cl4,zip_derived_cl3,zip_derived_cl2,zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl1262,plain,
( ( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ k1_xboole_0 ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1 ) )
<= ( v1_xboole_0 @ sk__3 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1261]) ).
thf(zip_derived_cl1346,plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1 )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1 ) ),
inference(split,[status(esa)],[zip_derived_cl1262]) ).
thf(zip_derived_cl1353,plain,
( ( ~ ( m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ( v3_struct_0 @ sk_ )
| ~ ( v3_rlvect_1 @ sk_ )
| ~ ( v4_rlvect_1 @ sk_ )
| ~ ( v5_rlvect_1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk_ )
| ~ ( v4_group_1 @ sk_ )
| ~ ( v7_group_1 @ sk_ )
| ~ ( v6_vectsp_1 @ sk_ )
| ~ ( v7_vectsp_1 @ sk_ )
| ~ ( v8_vectsp_1 @ sk_ )
| ( v10_vectsp_1 @ sk_ )
| ~ ( v2_vectsp_2 @ sk_ )
| ~ ( l3_vectsp_1 @ sk_ )
| ( v3_struct_0 @ sk__1 )
| ~ ( v3_rlvect_1 @ sk__1 )
| ~ ( v4_rlvect_1 @ sk__1 )
| ~ ( v5_rlvect_1 @ sk__1 )
| ~ ( v6_rlvect_1 @ sk__1 )
| ~ ( v5_vectsp_2 @ sk__1 @ sk_ )
| ~ ( l1_vectsp_2 @ sk__1 @ sk_ ) )
<= ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl1346]) ).
thf(zip_derived_cl13_122,plain,
m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_123,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_124,plain,
v3_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_125,plain,
v4_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3_126,plain,
v5_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_127,plain,
v6_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5_128,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6_129,plain,
v7_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7_130,plain,
v6_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8_131,plain,
v7_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9_132,plain,
v8_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10_133,plain,
~ ( v10_vectsp_1 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl11_134,plain,
v2_vectsp_2 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12_135,plain,
l3_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl22_136,plain,
~ ( v3_struct_0 @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21_137,plain,
v3_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl20_138,plain,
v4_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl19_139,plain,
v5_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl18_140,plain,
v6_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl17_141,plain,
v5_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_142,plain,
l1_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('5',plain,
m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1,
inference(demod,[status(thm)],[zip_derived_cl1353,zip_derived_cl13,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl3,zip_derived_cl4,zip_derived_cl5,zip_derived_cl6,zip_derived_cl7,zip_derived_cl8,zip_derived_cl9,zip_derived_cl10,zip_derived_cl11,zip_derived_cl12,zip_derived_cl22,zip_derived_cl21,zip_derived_cl20,zip_derived_cl19,zip_derived_cl18,zip_derived_cl17,zip_derived_cl16]) ).
thf('6',plain,
( ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ sk__1 )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__3 ) )
| ~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) ) ),
inference(split,[status(esa)],[zip_derived_cl1273]) ).
thf('7',plain,
~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) ),
inference('sat_resolution*',[status(thm)],['0','1','2','3','4','5','6']) ).
thf(zip_derived_cl1646,plain,
~ ( m1_rmod_2 @ ( k1_rmod_5 @ sk_ @ sk__1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) ) @ sk_ @ ( k1_rmod_5 @ sk_ @ sk__1 @ sk__2 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl1572,'7']) ).
thf(zip_derived_cl1648,plain,
( ( v3_struct_0 @ sk_ )
| ~ ( v3_rlvect_1 @ sk_ )
| ~ ( v4_rlvect_1 @ sk_ )
| ~ ( v5_rlvect_1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk_ )
| ~ ( v4_group_1 @ sk_ )
| ~ ( v7_group_1 @ sk_ )
| ~ ( v6_vectsp_1 @ sk_ )
| ~ ( v7_vectsp_1 @ sk_ )
| ~ ( v8_vectsp_1 @ sk_ )
| ( v10_vectsp_1 @ sk_ )
| ~ ( v2_vectsp_2 @ sk_ )
| ~ ( l3_vectsp_1 @ sk_ )
| ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__2 )
| ~ ( m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( l1_vectsp_2 @ sk__1 @ sk_ )
| ~ ( v5_vectsp_2 @ sk__1 @ sk_ )
| ~ ( v6_rlvect_1 @ sk__1 )
| ~ ( v5_rlvect_1 @ sk__1 )
| ~ ( v4_rlvect_1 @ sk__1 )
| ~ ( v3_rlvect_1 @ sk__1 )
| ( v3_struct_0 @ sk__1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl1646]) ).
thf(zip_derived_cl0_143,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_144,plain,
v3_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_145,plain,
v4_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3_146,plain,
v5_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_147,plain,
v6_rlvect_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5_148,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6_149,plain,
v7_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7_150,plain,
v6_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl8_151,plain,
v7_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl9_152,plain,
v8_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10_153,plain,
~ ( v10_vectsp_1 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl11_154,plain,
v2_vectsp_2 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12_155,plain,
l3_vectsp_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl13_156,plain,
m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl16_157,plain,
l1_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl17_158,plain,
v5_vectsp_2 @ sk__1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl18_159,plain,
v6_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl19_160,plain,
v5_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl20_161,plain,
v4_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21_162,plain,
v3_rlvect_1 @ sk__1,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl22_163,plain,
~ ( v3_struct_0 @ sk__1 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1650,plain,
( ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1648,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl3,zip_derived_cl4,zip_derived_cl5,zip_derived_cl6,zip_derived_cl7,zip_derived_cl8,zip_derived_cl9,zip_derived_cl10,zip_derived_cl11,zip_derived_cl12,zip_derived_cl13,zip_derived_cl16,zip_derived_cl17,zip_derived_cl18,zip_derived_cl19,zip_derived_cl20,zip_derived_cl21,zip_derived_cl22]) ).
thf(zip_derived_cl1710,plain,
( ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__2 )
<= ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference(split,[status(esa)],[zip_derived_cl1650]) ).
thf(zip_derived_cl1716,plain,
( ( ~ ( m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( r1_tarski @ ( k3_xboole_0 @ sk__2 @ sk__3 ) @ sk__2 ) )
<= ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl139,zip_derived_cl1710]) ).
thf(zip_derived_cl15_164,plain,
m1_subset_1 @ sk__3 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl13_165,plain,
m1_subset_1 @ sk__2 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl144_166,plain,
! [X0: $i,X1: $i] : ( r1_tarski @ ( k3_xboole_0 @ X0 @ X1 ) @ X0 ),
inference(cnf,[status(esa)],[t17_xboole_1]) ).
thf(zip_derived_cl1719,plain,
( $false
<= ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference(demod,[status(thm)],[zip_derived_cl1716,zip_derived_cl15,zip_derived_cl13,zip_derived_cl144]) ).
thf('8',plain,
( ~ ( m1_subset_1 @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ sk__1 ) ) )
| ~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__2 ) ),
inference(split,[status(esa)],[zip_derived_cl1650]) ).
thf('9',plain,
~ ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ sk__1 ) @ sk__2 @ sk__3 ) @ sk__2 ),
inference('sat_resolution*',[status(thm)],['2','8']) ).
thf(zip_derived_cl1720,plain,
$false,
inference(simpl_trail,[status(thm)],[zip_derived_cl1719,'9']) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG222+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YjQsDomXj3 true
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 02:36:59 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35 % Number of cores: 8
% 0.20/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.21/0.64 % Total configuration time : 435
% 0.21/0.64 % Estimated wc time : 1092
% 0.21/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 2.33/1.25 % Solved by fo/fo1_av.sh.
% 2.33/1.25 % done 776 iterations in 0.470s
% 2.33/1.25 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.33/1.25 % SZS output start Refutation
% See solution above
% 2.33/1.26
% 2.33/1.26
% 2.33/1.26 % Terminating...
% 2.93/1.36 % Runner terminated.
% 2.93/1.37 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------