%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP624+1 : TPTP v9.2.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ij2kTc5QWL true
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:49 PM UTC 2025
% Result : Theorem 4.22s 1.26s
% Output : Refutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 114 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 381 ( 27 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1745 ( 210 ~; 208 |; 37 &;1268 @)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 4 con; 0-6 aty)
% Number of variables : 111 ( 0 ^; 111 !; 0 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
thf(v4_group_1_type,type,
v4_group_1: $i > $o ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(l1_group_1_type,type,
l1_group_1: $i > $o ).
thf(m2_fraenkel_type,type,
m2_fraenkel: $i > $i > $i > $i > $o ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(m1_fraenkel_type,type,
m1_fraenkel: $i > $i > $i > $o ).
thf(v1_group_1_type,type,
v1_group_1: $i > $o ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k4_autgroup_type,type,
k4_autgroup: $i > $i ).
thf(sk__type,type,
sk_: $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k2_autgroup_type,type,
k2_autgroup: $i > $i ).
thf(v1_fraenkel_type,type,
v1_fraenkel: $i > $o ).
thf(v3_group_1_type,type,
v3_group_1: $i > $o ).
thf(sk__1_type,type,
sk__1: $i ).
thf(k1_autgroup_type,type,
k1_autgroup: $i > $i ).
thf(k1_binop_1_type,type,
k1_binop_1: $i > $i > $i > $i ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(t15_autgroup,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_fraenkel @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k4_autgroup @ A ) )
=> ! [C: $i] :
( ( m2_fraenkel @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k4_autgroup @ A ) )
=> ( ( k1_binop_1 @ ( k2_autgroup @ A ) @ B @ C )
= ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_fraenkel @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k4_autgroup @ A ) )
=> ! [C: $i] :
( ( m2_fraenkel @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k4_autgroup @ A ) )
=> ( ( k1_binop_1 @ ( k2_autgroup @ A ) @ B @ C )
= ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ),
inference('cnf.neg',[status(esa)],[t15_autgroup]) ).
thf(zip_derived_cl3,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(redefinition_m2_relset_1,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ) ).
thf(zip_derived_cl127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( m2_relset_1 @ X0 @ X1 @ X2 )
| ~ ( m1_relset_1 @ X0 @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[redefinition_m2_relset_1]) ).
thf(d2_autgroup,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_autgroup @ A ) @ ( k1_autgroup @ A ) ) @ ( k1_autgroup @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_autgroup @ A ) @ ( k1_autgroup @ A ) ) @ ( k1_autgroup @ A ) ) )
=> ( ( B
= ( k2_autgroup @ A ) )
<=> ! [C: $i] :
( ( m2_fraenkel @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k1_autgroup @ A ) )
=> ! [D: $i] :
( ( m2_fraenkel @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k1_autgroup @ A ) )
=> ( ( k2_binop_1 @ ( k1_autgroup @ A ) @ ( k1_autgroup @ A ) @ ( k1_autgroup @ A ) @ B @ C @ D )
= ( k7_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ C ) ) ) ) ) ) ) ).
thf(zip_derived_cl30,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( v1_funct_1 @ X0 )
| ~ ( v1_funct_2 @ X0 @ ( k2_zfmisc_1 @ ( k1_autgroup @ X1 ) @ ( k1_autgroup @ X1 ) ) @ ( k1_autgroup @ X1 ) )
| ~ ( m2_relset_1 @ X0 @ ( k2_zfmisc_1 @ ( k1_autgroup @ X1 ) @ ( k1_autgroup @ X1 ) ) @ ( k1_autgroup @ X1 ) )
| ( X0
!= ( k2_autgroup @ X1 ) )
| ~ ( m2_fraenkel @ X2 @ ( u1_struct_0 @ X1 ) @ ( u1_struct_0 @ X1 ) @ ( k1_autgroup @ X1 ) )
| ( ( k2_binop_1 @ ( k1_autgroup @ X1 ) @ ( k1_autgroup @ X1 ) @ ( k1_autgroup @ X1 ) @ X0 @ X3 @ X2 )
= ( k7_funct_2 @ ( u1_struct_0 @ X1 ) @ ( u1_struct_0 @ X1 ) @ ( u1_struct_0 @ X1 ) @ X2 @ X3 ) )
| ~ ( m2_fraenkel @ X3 @ ( u1_struct_0 @ X1 ) @ ( u1_struct_0 @ X1 ) @ ( k1_autgroup @ X1 ) )
| ~ ( l1_group_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v3_group_1 @ X1 )
| ~ ( v1_group_1 @ X1 )
| ( v3_struct_0 @ X1 ) ),
inference(cnf,[status(esa)],[d2_autgroup]) ).
thf(zip_derived_cl900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( m1_relset_1 @ X1 @ ( k2_zfmisc_1 @ ( k1_autgroup @ X0 ) @ ( k1_autgroup @ X0 ) ) @ ( k1_autgroup @ X0 ) )
| ( v3_struct_0 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( l1_group_1 @ X0 )
| ~ ( m2_fraenkel @ X3 @ ( u1_struct_0 @ X0 ) @ ( u1_struct_0 @ X0 ) @ ( k1_autgroup @ X0 ) )
| ( ( k2_binop_1 @ ( k1_autgroup @ X0 ) @ ( k1_autgroup @ X0 ) @ ( k1_autgroup @ X0 ) @ X1 @ X3 @ X2 )
= ( k7_funct_2 @ ( u1_struct_0 @ X0 ) @ ( u1_struct_0 @ X0 ) @ ( u1_struct_0 @ X0 ) @ X2 @ X3 ) )
| ~ ( m2_fraenkel @ X2 @ ( u1_struct_0 @ X0 ) @ ( u1_struct_0 @ X0 ) @ ( k1_autgroup @ X0 ) )
| ( X1
!= ( k2_autgroup @ X0 ) )
| ~ ( v1_funct_2 @ X1 @ ( k2_zfmisc_1 @ ( k1_autgroup @ X0 ) @ ( k1_autgroup @ X0 ) ) @ ( k1_autgroup @ X0 ) )
| ~ ( v1_funct_1 @ X1 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl127,zip_derived_cl30]) ).
thf(zip_derived_cl925,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( v1_funct_1 @ X0 )
| ~ ( v1_funct_2 @ X0 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ( X0
!= ( k2_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ( ( k2_binop_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) @ X0 @ X1 @ X2 )
= ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ X2 @ X1 ) )
| ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( l1_group_1 @ sk_ )
| ~ ( v3_group_1 @ sk_ )
| ~ ( v1_group_1 @ sk_ )
| ( v3_struct_0 @ sk_ )
| ~ ( m1_relset_1 @ X0 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl900]) ).
thf(zip_derived_cl4,plain,
l1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2,plain,
v3_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
v1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( v1_funct_1 @ X0 )
| ~ ( v1_funct_2 @ X0 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ( X0
!= ( k2_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ( ( k2_binop_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) @ X0 @ X1 @ X2 )
= ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ X2 @ X1 ) )
| ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_relset_1 @ X0 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl925,zip_derived_cl4,zip_derived_cl2,zip_derived_cl1,zip_derived_cl0]) ).
thf(redefinition_k2_binop_1,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m1_subset_1 @ E @ A )
& ( m1_subset_1 @ F @ B ) )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
= ( k1_binop_1 @ D @ E @ F ) ) ) ).
thf(zip_derived_cl122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( m1_subset_1 @ X0 @ X1 )
| ~ ( m1_relset_1 @ X2 @ ( k2_zfmisc_1 @ X1 @ X3 ) @ X4 )
| ~ ( v1_funct_2 @ X2 @ ( k2_zfmisc_1 @ X1 @ X3 ) @ X4 )
| ~ ( v1_funct_1 @ X2 )
| ( v1_xboole_0 @ X3 )
| ( v1_xboole_0 @ X1 )
| ~ ( m1_subset_1 @ X5 @ X3 )
| ( ( k2_binop_1 @ X1 @ X3 @ X4 @ X2 @ X0 @ X5 )
= ( k1_binop_1 @ X2 @ X0 @ X5 ) ) ),
inference(cnf,[status(esa)],[redefinition_k2_binop_1]) ).
thf(zip_derived_cl4076,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( m1_relset_1 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ( X2
!= ( k2_autgroup @ sk_ ) )
| ~ ( v1_funct_2 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( v1_funct_1 @ X2 )
| ~ ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_relset_1 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( v1_funct_2 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( v1_funct_1 @ X2 )
| ( v1_xboole_0 @ ( k1_autgroup @ sk_ ) )
| ( v1_xboole_0 @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X1 @ ( k1_autgroup @ sk_ ) )
| ( ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ X1 @ X0 )
= ( k1_binop_1 @ X2 @ X0 @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4074,zip_derived_cl122]) ).
thf(zip_derived_cl3_001,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(dt_k1_autgroup,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( m1_fraenkel @ ( k1_autgroup @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ).
thf(zip_derived_cl37,plain,
! [X0: $i] :
( ( m1_fraenkel @ ( k1_autgroup @ X0 ) @ ( u1_struct_0 @ X0 ) @ ( u1_struct_0 @ X0 ) )
| ~ ( l1_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ( v3_struct_0 @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_autgroup]) ).
thf(dt_m1_fraenkel,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_fraenkel @ C @ A @ B )
=> ( ~ ( v1_xboole_0 @ C )
& ( v1_fraenkel @ C ) ) ) ).
thf(zip_derived_cl57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( v1_xboole_0 @ X0 )
| ~ ( m1_fraenkel @ X0 @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[dt_m1_fraenkel]) ).
thf(zip_derived_cl861,plain,
! [X0: $i] :
( ( v3_struct_0 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( l1_group_1 @ X0 )
| ~ ( v1_xboole_0 @ ( k1_autgroup @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl37,zip_derived_cl57]) ).
thf(zip_derived_cl908,plain,
( ~ ( v1_xboole_0 @ ( k1_autgroup @ sk_ ) )
| ~ ( l1_group_1 @ sk_ )
| ~ ( v3_group_1 @ sk_ )
| ~ ( v1_group_1 @ sk_ )
| ( v3_struct_0 @ sk_ ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl861]) ).
thf(zip_derived_cl4_002,plain,
l1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_003,plain,
v3_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_004,plain,
v1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_005,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3273,plain,
~ ( v1_xboole_0 @ ( k1_autgroup @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl4,zip_derived_cl2,zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl3273_006,plain,
~ ( v1_xboole_0 @ ( k1_autgroup @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl4,zip_derived_cl2,zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl4091,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( m1_relset_1 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ( X2
!= ( k2_autgroup @ sk_ ) )
| ~ ( v1_funct_2 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( v1_funct_1 @ X2 )
| ~ ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_relset_1 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( v1_funct_2 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( v1_funct_1 @ X2 )
| ~ ( m1_subset_1 @ X1 @ ( k1_autgroup @ sk_ ) )
| ( ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ X1 @ X0 )
= ( k1_binop_1 @ X2 @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4076,zip_derived_cl3273,zip_derived_cl3273]) ).
thf(zip_derived_cl4092,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ X1 @ X0 )
= ( k1_binop_1 @ X2 @ X0 @ X1 ) )
| ~ ( m1_subset_1 @ X1 @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( v1_funct_1 @ X2 )
| ~ ( v1_funct_2 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ( X2
!= ( k2_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_relset_1 @ X2 @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl4091]) ).
thf(zip_derived_cl5042,plain,
! [X0: $i,X1: $i] :
( ~ ( m1_relset_1 @ ( k2_autgroup @ sk_ ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( v1_funct_2 @ ( k2_autgroup @ sk_ ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( v1_funct_1 @ ( k2_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X1 @ ( k1_autgroup @ sk_ ) )
| ( ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ X1 @ X0 )
= ( k1_binop_1 @ ( k2_autgroup @ sk_ ) @ X0 @ X1 ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl4092]) ).
thf(zip_derived_cl3_007,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(dt_k2_autgroup,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ( ( v1_funct_1 @ ( k2_autgroup @ A ) )
& ( v1_funct_2 @ ( k2_autgroup @ A ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ A ) @ ( k1_autgroup @ A ) ) @ ( k1_autgroup @ A ) )
& ( m2_relset_1 @ ( k2_autgroup @ A ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ A ) @ ( k1_autgroup @ A ) ) @ ( k1_autgroup @ A ) ) ) ) ).
thf(zip_derived_cl45,plain,
! [X0: $i] :
( ( m2_relset_1 @ ( k2_autgroup @ X0 ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ X0 ) @ ( k1_autgroup @ X0 ) ) @ ( k1_autgroup @ X0 ) )
| ~ ( l1_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ( v3_struct_0 @ X0 ) ),
inference(cnf,[status(esa)],[dt_k2_autgroup]) ).
thf(zip_derived_cl126,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( m1_relset_1 @ X0 @ X1 @ X2 )
| ~ ( m2_relset_1 @ X0 @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[redefinition_m2_relset_1]) ).
thf(zip_derived_cl893,plain,
! [X0: $i] :
( ( v3_struct_0 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( l1_group_1 @ X0 )
| ( m1_relset_1 @ ( k2_autgroup @ X0 ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ X0 ) @ ( k1_autgroup @ X0 ) ) @ ( k1_autgroup @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl45,zip_derived_cl126]) ).
thf(zip_derived_cl922,plain,
( ( m1_relset_1 @ ( k2_autgroup @ sk_ ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) )
| ~ ( l1_group_1 @ sk_ )
| ~ ( v3_group_1 @ sk_ )
| ~ ( v1_group_1 @ sk_ )
| ( v3_struct_0 @ sk_ ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl893]) ).
thf(zip_derived_cl4_008,plain,
l1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_009,plain,
v3_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_010,plain,
v1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_011,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3636,plain,
m1_relset_1 @ ( k2_autgroup @ sk_ ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ),
inference(demod,[status(thm)],[zip_derived_cl922,zip_derived_cl4,zip_derived_cl2,zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl3_012,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl44,plain,
! [X0: $i] :
( ( v1_funct_2 @ ( k2_autgroup @ X0 ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ X0 ) @ ( k1_autgroup @ X0 ) ) @ ( k1_autgroup @ X0 ) )
| ~ ( l1_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ( v3_struct_0 @ X0 ) ),
inference(cnf,[status(esa)],[dt_k2_autgroup]) ).
thf(zip_derived_cl906,plain,
( ( v3_struct_0 @ sk_ )
| ~ ( v1_group_1 @ sk_ )
| ~ ( v3_group_1 @ sk_ )
| ~ ( l1_group_1 @ sk_ )
| ( v1_funct_2 @ ( k2_autgroup @ sk_ ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl44]) ).
thf(zip_derived_cl0_013,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_014,plain,
v1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_015,plain,
v3_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_016,plain,
l1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3565,plain,
v1_funct_2 @ ( k2_autgroup @ sk_ ) @ ( k2_zfmisc_1 @ ( k1_autgroup @ sk_ ) @ ( k1_autgroup @ sk_ ) ) @ ( k1_autgroup @ sk_ ),
inference(demod,[status(thm)],[zip_derived_cl906,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl4]) ).
thf(zip_derived_cl3_017,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl43,plain,
! [X0: $i] :
( ( v1_funct_1 @ ( k2_autgroup @ X0 ) )
| ~ ( l1_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ( v3_struct_0 @ X0 ) ),
inference(cnf,[status(esa)],[dt_k2_autgroup]) ).
thf(zip_derived_cl905,plain,
( ( v3_struct_0 @ sk_ )
| ~ ( v1_group_1 @ sk_ )
| ~ ( v3_group_1 @ sk_ )
| ~ ( l1_group_1 @ sk_ )
| ( v1_funct_1 @ ( k2_autgroup @ sk_ ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl43]) ).
thf(zip_derived_cl0_018,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_019,plain,
v1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_020,plain,
v3_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_021,plain,
l1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3065,plain,
v1_funct_1 @ ( k2_autgroup @ sk_ ),
inference(demod,[status(thm)],[zip_derived_cl905,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl4]) ).
thf(zip_derived_cl5043,plain,
! [X0: $i,X1: $i] :
( ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X1 @ ( k1_autgroup @ sk_ ) )
| ( ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ X1 @ X0 )
= ( k1_binop_1 @ ( k2_autgroup @ sk_ ) @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5042,zip_derived_cl3636,zip_derived_cl3565,zip_derived_cl3065]) ).
thf(zip_derived_cl3_022,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl37_023,plain,
! [X0: $i] :
( ( m1_fraenkel @ ( k1_autgroup @ X0 ) @ ( u1_struct_0 @ X0 ) @ ( u1_struct_0 @ X0 ) )
| ~ ( l1_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ( v3_struct_0 @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_autgroup]) ).
thf(redefinition_m2_fraenkel,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ! [D: $i] :
( ( m2_fraenkel @ D @ A @ B @ C )
<=> ( m1_subset_1 @ D @ C ) ) ) ).
thf(zip_derived_cl125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( v1_xboole_0 @ X0 )
| ~ ( m1_fraenkel @ X1 @ X2 @ X0 )
| ( m2_fraenkel @ X3 @ X2 @ X0 @ X1 )
| ~ ( m1_subset_1 @ X3 @ X1 ) ),
inference(cnf,[status(esa)],[redefinition_m2_fraenkel]) ).
thf(zip_derived_cl868,plain,
! [X0: $i,X1: $i] :
( ( v3_struct_0 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( l1_group_1 @ X0 )
| ~ ( m1_subset_1 @ X1 @ ( k1_autgroup @ X0 ) )
| ( m2_fraenkel @ X1 @ ( u1_struct_0 @ X0 ) @ ( u1_struct_0 @ X0 ) @ ( k1_autgroup @ X0 ) )
| ( v1_xboole_0 @ ( u1_struct_0 @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl37,zip_derived_cl125]) ).
thf(zip_derived_cl914,plain,
! [X0: $i] :
( ( v1_xboole_0 @ ( u1_struct_0 @ sk_ ) )
| ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( l1_group_1 @ sk_ )
| ~ ( v3_group_1 @ sk_ )
| ~ ( v1_group_1 @ sk_ )
| ( v3_struct_0 @ sk_ ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl868]) ).
thf(dt_l1_group_1,axiom,
! [A: $i] :
( ( l1_group_1 @ A )
=> ( l1_struct_0 @ A ) ) ).
thf(zip_derived_cl55,plain,
! [X0: $i] :
( ( l1_struct_0 @ X0 )
| ~ ( l1_group_1 @ X0 ) ),
inference(cnf,[status(esa)],[dt_l1_group_1]) ).
thf(fc1_struct_0,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ).
thf(zip_derived_cl80,plain,
! [X0: $i] :
( ~ ( v1_xboole_0 @ ( u1_struct_0 @ X0 ) )
| ~ ( l1_struct_0 @ X0 )
| ( v3_struct_0 @ X0 ) ),
inference(cnf,[status(esa)],[fc1_struct_0]) ).
thf(zip_derived_cl852,plain,
! [X0: $i] :
( ~ ( l1_group_1 @ X0 )
| ( v3_struct_0 @ X0 )
| ~ ( v1_xboole_0 @ ( u1_struct_0 @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl55,zip_derived_cl80]) ).
thf(zip_derived_cl0_024,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3067,plain,
( ~ ( v1_xboole_0 @ ( u1_struct_0 @ sk_ ) )
| ~ ( l1_group_1 @ sk_ ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl852,zip_derived_cl0]) ).
thf(zip_derived_cl4_025,plain,
l1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3071,plain,
~ ( v1_xboole_0 @ ( u1_struct_0 @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl3067,zip_derived_cl4]) ).
thf(zip_derived_cl4_026,plain,
l1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_027,plain,
v3_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_028,plain,
v1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_029,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3850,plain,
! [X0: $i] :
( ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl914,zip_derived_cl3071,zip_derived_cl4,zip_derived_cl2,zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl5074,plain,
! [X0: $i,X1: $i] :
( ( ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ X1 @ X0 )
= ( k1_binop_1 @ ( k2_autgroup @ sk_ ) @ X0 @ X1 ) )
| ~ ( m1_subset_1 @ X1 @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) ) ),
inference(clc,[status(thm)],[zip_derived_cl5043,zip_derived_cl3850]) ).
thf(zip_derived_cl3_030,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl37_031,plain,
! [X0: $i] :
( ( m1_fraenkel @ ( k1_autgroup @ X0 ) @ ( u1_struct_0 @ X0 ) @ ( u1_struct_0 @ X0 ) )
| ~ ( l1_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ( v3_struct_0 @ X0 ) ),
inference(cnf,[status(esa)],[dt_k1_autgroup]) ).
thf(zip_derived_cl124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( v1_xboole_0 @ X0 )
| ~ ( m1_fraenkel @ X1 @ X2 @ X0 )
| ( m1_subset_1 @ X3 @ X1 )
| ~ ( m2_fraenkel @ X3 @ X2 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[redefinition_m2_fraenkel]) ).
thf(zip_derived_cl867,plain,
! [X0: $i,X1: $i] :
( ( v3_struct_0 @ X0 )
| ~ ( v1_group_1 @ X0 )
| ~ ( v3_group_1 @ X0 )
| ~ ( v4_group_1 @ X0 )
| ~ ( l1_group_1 @ X0 )
| ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ X0 ) @ ( u1_struct_0 @ X0 ) @ ( k1_autgroup @ X0 ) )
| ( m1_subset_1 @ X1 @ ( k1_autgroup @ X0 ) )
| ( v1_xboole_0 @ ( u1_struct_0 @ X0 ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl37,zip_derived_cl124]) ).
thf(zip_derived_cl913,plain,
! [X0: $i] :
( ( v1_xboole_0 @ ( u1_struct_0 @ sk_ ) )
| ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( l1_group_1 @ sk_ )
| ~ ( v3_group_1 @ sk_ )
| ~ ( v1_group_1 @ sk_ )
| ( v3_struct_0 @ sk_ ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl867]) ).
thf(zip_derived_cl3071_032,plain,
~ ( v1_xboole_0 @ ( u1_struct_0 @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl3067,zip_derived_cl4]) ).
thf(zip_derived_cl4_033,plain,
l1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_034,plain,
v3_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_035,plain,
v1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_036,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3809,plain,
! [X0: $i] :
( ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl913,zip_derived_cl3071,zip_derived_cl4,zip_derived_cl2,zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl5075,plain,
! [X0: $i,X1: $i] :
( ~ ( m2_fraenkel @ X1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ( ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ X1 @ X0 )
= ( k1_binop_1 @ ( k2_autgroup @ sk_ ) @ X0 @ X1 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl5074,zip_derived_cl3809]) ).
thf(zip_derived_cl6,plain,
( ( k1_binop_1 @ ( k2_autgroup @ sk_ ) @ sk__1 @ sk__2 )
!= ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ sk__2 @ sk__1 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5076,plain,
( ~ ( m1_subset_1 @ sk__1 @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ sk__2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ( ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ sk__2 @ sk__1 )
!= ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ sk__2 @ sk__1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5075,zip_derived_cl6]) ).
thf(zip_derived_cl7,plain,
m2_fraenkel @ sk__1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k4_autgroup @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3_037,plain,
v4_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(t13_autgroup,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v1_group_1 @ A )
& ( v3_group_1 @ A )
& ( v4_group_1 @ A )
& ( l1_group_1 @ A ) )
=> ! [B: $i] :
( ( m2_fraenkel @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k4_autgroup @ A ) )
=> ( m2_fraenkel @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ ( k1_autgroup @ A ) ) ) ) ).
thf(zip_derived_cl129,plain,
! [X0: $i,X1: $i] :
( ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ X1 ) @ ( u1_struct_0 @ X1 ) @ ( k4_autgroup @ X1 ) )
| ( m2_fraenkel @ X0 @ ( u1_struct_0 @ X1 ) @ ( u1_struct_0 @ X1 ) @ ( k1_autgroup @ X1 ) )
| ~ ( l1_group_1 @ X1 )
| ~ ( v4_group_1 @ X1 )
| ~ ( v3_group_1 @ X1 )
| ~ ( v1_group_1 @ X1 )
| ( v3_struct_0 @ X1 ) ),
inference(cnf,[status(esa)],[t13_autgroup]) ).
thf(zip_derived_cl907,plain,
! [X0: $i] :
( ( v3_struct_0 @ sk_ )
| ~ ( v1_group_1 @ sk_ )
| ~ ( v3_group_1 @ sk_ )
| ~ ( l1_group_1 @ sk_ )
| ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k4_autgroup @ sk_ ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl129]) ).
thf(zip_derived_cl0_038,plain,
~ ( v3_struct_0 @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_039,plain,
v1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2_040,plain,
v3_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4_041,plain,
l1_group_1 @ sk_,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3550,plain,
! [X0: $i] :
( ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k4_autgroup @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl907,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl4]) ).
thf(zip_derived_cl3551,plain,
m2_fraenkel @ sk__1 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ),
inference('s_sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl3550]) ).
thf(zip_derived_cl3809_042,plain,
! [X0: $i] :
( ( m1_subset_1 @ X0 @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl913,zip_derived_cl3071,zip_derived_cl4,zip_derived_cl2,zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl3810,plain,
m1_subset_1 @ sk__1 @ ( k1_autgroup @ sk_ ),
inference('s_sup-',[status(thm)],[zip_derived_cl3551,zip_derived_cl3809]) ).
thf(zip_derived_cl5,plain,
m2_fraenkel @ sk__2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k4_autgroup @ sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3550_043,plain,
! [X0: $i] :
( ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ) )
| ~ ( m2_fraenkel @ X0 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k4_autgroup @ sk_ ) ) ),
inference(demod,[status(thm)],[zip_derived_cl907,zip_derived_cl0,zip_derived_cl1,zip_derived_cl2,zip_derived_cl4]) ).
thf(zip_derived_cl3552,plain,
m2_fraenkel @ sk__2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( k1_autgroup @ sk_ ),
inference('s_sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl3550]) ).
thf(zip_derived_cl5080,plain,
( ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ sk__2 @ sk__1 )
!= ( k7_funct_2 @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ ( u1_struct_0 @ sk_ ) @ sk__2 @ sk__1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5076,zip_derived_cl3810,zip_derived_cl3552]) ).
thf(zip_derived_cl5081,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl5080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP624+1 : TPTP v9.2.0. Released v3.4.0.
% 0.11/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ij2kTc5QWL true
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 14:24:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.57/0.66 % Total configuration time : 435
% 0.57/0.66 % Estimated wc time : 1092
% 0.57/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.57/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.57/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.57/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.57/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.57/0.94 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 4.22/1.26 % Solved by fo/fo6_bce.sh.
% 4.22/1.26 % BCE start: 139
% 4.22/1.26 % BCE eliminated: 5
% 4.22/1.26 % PE start: 134
% 4.22/1.26 logic: eq
% 4.22/1.26 % PE eliminated: -30
% 4.22/1.26 % done 468 iterations in 0.484s
% 4.22/1.26 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 4.22/1.26 % SZS output start Refutation
% See solution above
% 4.22/1.26
% 4.22/1.26
% 4.22/1.26 % Terminating...
% 4.61/1.45 % Runner terminated.
% 4.64/1.47 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------