TSTP Solution File: LAT292+2 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT292+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 : Fri May 19 11:27:25 EDT 2023
% Result : Theorem 48.42s 12.09s
% Output : Refutation 49.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1588
% Syntax : Number of formulae : 2961 ( 185 unt; 217 typ; 0 def)
% Number of atoms : 15965 (1923 equ; 0 cnn)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 56098 (2176 ~; 111 |;6658 &;40701 @)
% ( 227 <=>;6225 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 446 ( 446 >; 0 *; 0 +; 0 <<)
% Number of symbols : 219 ( 217 usr; 5 con; 0-6 aty)
% Number of variables : 7668 ( 0 ^;7353 !; 315 ?;7668 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
thf(v10_lattices_type,type,
v10_lattices: $i > $o ).
thf(v17_lattices_type,type,
v17_lattices: $i > $o ).
thf(v3_realset2_type,type,
v3_realset2: $i > $o ).
thf(l3_lattices_type,type,
l3_lattices: $i > $o ).
thf(v2_pre_topc_type,type,
v2_pre_topc: $i > $o ).
thf(l1_pre_topc_type,type,
l1_pre_topc: $i > $o ).
thf(r1_filter_1_type,type,
r1_filter_1: $i > $i > $o ).
thf(k6_lopclset_type,type,
k6_lopclset: $i > $i ).
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
thf(k5_finsub_1_type,type,
k5_finsub_1: $i > $i ).
thf(k2_lattice2_type,type,
k2_lattice2: $i > $i > $i > $i > $i ).
thf(k5_setwiseo_type,type,
k5_setwiseo: $i > $i > $i > $i ).
thf(k2_setwiseo_type,type,
k2_setwiseo: $i > $i > $i ).
thf(k5_lattice4_type,type,
k5_lattice4: $i > $i ).
thf(k3_lattices_type,type,
k3_lattices: $i > $i > $i > $i ).
thf(k7_lattices_type,type,
k7_lattices: $i > $i > $i ).
thf(v1_xboole_0_type,type,
v1_xboole_0: $i > $o ).
thf(k3_lattice2_type,type,
k3_lattice2: $i > $i > $i > $i > $i ).
thf(k4_lattices_type,type,
k4_lattices: $i > $i > $i > $i ).
thf(k2_lattice4_type,type,
k2_lattice4: $i > $i > $i ).
thf(v1_funct_1_type,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_type,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k10_setwiseo_type,type,
k10_setwiseo: $i > $i > $i > $i > $i ).
thf(k8_funct_2_type,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(v13_lattices_type,type,
v13_lattices: $i > $o ).
thf(k1_lattice4_type,type,
k1_lattice4: $i > $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(v14_lattices_type,type,
v14_lattices: $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(r1_xboole_0_type,type,
r1_xboole_0: $i > $i > $o ).
thf(k4_xboole_0_type,type,
k4_xboole_0: $i > $i > $i ).
thf(k2_xboole_0_type,type,
k2_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(k4_subset_1_type,type,
k4_subset_1: $i > $i > $i > $i ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(v3_pre_topc_type,type,
v3_pre_topc: $i > $i > $o ).
thf(v4_pre_topc_type,type,
v4_pre_topc: $i > $i > $o ).
thf(m2_connsp_2_type,type,
m2_connsp_2: $i > $i > $i > $o ).
thf(m1_connsp_2_type,type,
m1_connsp_2: $i > $i > $i > $o ).
thf(k10_borsuk_1_type,type,
k10_borsuk_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k6_borsuk_1_type,type,
k6_borsuk_1: $i > $i > $i ).
thf(k7_borsuk_1_type,type,
k7_borsuk_1: $i > $i > $i > $i > $i ).
thf(k1_struct_0_type,type,
k1_struct_0: $i > $i > $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(k2_binop_1_type,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k6_subset_1_type,type,
k6_subset_1: $i > $i > $i > $i ).
thf(l2_lattices_type,type,
l2_lattices: $i > $o ).
thf(r1_lattices_type,type,
r1_lattices: $i > $i > $i > $o ).
thf(k1_lattices_type,type,
k1_lattices: $i > $i > $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $i > $i ).
thf(k1_relat_1_type,type,
k1_relat_1: $i > $i ).
thf(m2_subset_1_type,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k1_lopclset_type,type,
k1_lopclset: $i > $i ).
thf(k2_partfun1_type,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(k1_funct_4_type,type,
k1_funct_4: $i > $i > $i ).
thf(l1_struct_0_type,type,
l1_struct_0: $i > $o ).
thf(k2_pre_topc_type,type,
k2_pre_topc: $i > $i ).
thf(k3_relat_1_type,type,
k3_relat_1: $i > $i ).
thf(k6_setfam_1_type,type,
k6_setfam_1: $i > $i > $i ).
thf(k7_subset_1_type,type,
k7_subset_1: $i > $i > $i > $i ).
thf(v3_tops_1_type,type,
v3_tops_1: $i > $i > $o ).
thf(v1_tops_1_type,type,
v1_tops_1: $i > $i > $o ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(k3_funct_3_type,type,
k3_funct_3: $i > $i ).
thf(k5_relat_1_type,type,
k5_relat_1: $i > $i > $i ).
thf(k10_relat_1_type,type,
k10_relat_1: $i > $i > $i ).
thf(k9_relat_1_type,type,
k9_relat_1: $i > $i > $i ).
thf(k2_funct_1_type,type,
k2_funct_1: $i > $i ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(m1_realset1_type,type,
m1_realset1: $i > $i > $i > $o ).
thf(v3_lattices_type,type,
v3_lattices: $i > $o ).
thf(k8_setfam_1_type,type,
k8_setfam_1: $i > $i > $i ).
thf(m1_filter_1_type,type,
m1_filter_1: $i > $i > $i > $o ).
thf(v1_borsuk_1_type,type,
v1_borsuk_1: $i > $i > $o ).
thf(m1_pre_topc_type,type,
m1_pre_topc: $i > $i > $o ).
thf(v2_borsuk_1_type,type,
v2_borsuk_1: $i > $i > $o ).
thf(m1_borsuk_1_type,type,
m1_borsuk_1: $i > $i > $o ).
thf(v1_pre_topc_type,type,
v1_pre_topc: $i > $o ).
thf(k21_borsuk_1_type,type,
k21_borsuk_1: $i > $i > $i > $i ).
thf(k16_borsuk_1_type,type,
k16_borsuk_1: $i > $i > $i ).
thf(k20_borsuk_1_type,type,
k20_borsuk_1: $i > $i > $i > $i ).
thf(m2_realset1_type,type,
m2_realset1: $i > $i > $i > $o ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(k1_tops_1_type,type,
k1_tops_1: $i > $i > $i ).
thf(k2_lopclset_type,type,
k2_lopclset: $i > $i > $i > $i ).
thf(k1_lattice2_type,type,
k1_lattice2: $i > $i ).
thf(v2_tops_1_type,type,
v2_tops_1: $i > $i > $o ).
thf(k2_tops_1_type,type,
k2_tops_1: $i > $i > $i ).
thf(v5_tops_1_type,type,
v5_tops_1: $i > $i > $o ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(k17_borsuk_1_type,type,
k17_borsuk_1: $i > $i > $i ).
thf(v5_pre_topc_type,type,
v5_pre_topc: $i > $i > $i > $o ).
thf(k1_funct_3_type,type,
k1_funct_3: $i > $i ).
thf(k6_pre_topc_type,type,
k6_pre_topc: $i > $i > $i ).
thf(k2_borsuk_1_type,type,
k2_borsuk_1: $i > $i > $i ).
thf(k3_borsuk_1_type,type,
k3_borsuk_1: $i > $i > $i > $i ).
thf(v4_tops_1_type,type,
v4_tops_1: $i > $i > $o ).
thf(r2_borsuk_1_type,type,
r2_borsuk_1: $i > $i > $o ).
thf(k1_pre_topc_type,type,
k1_pre_topc: $i > $i ).
thf(k1_subset_1_type,type,
k1_subset_1: $i > $i ).
thf(v3_filter_0_type,type,
v3_filter_0: $i > $o ).
thf(k2_lattices_type,type,
k2_lattices: $i > $i > $i > $i ).
thf(k5_setfam_1_type,type,
k5_setfam_1: $i > $i > $i ).
thf(k12_mcart_1_type,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(r3_lattices_type,type,
r3_lattices: $i > $i > $i > $o ).
thf(k2_filter_0_type,type,
k2_filter_0: $i > $i > $i ).
thf(k1_setwiseo_type,type,
k1_setwiseo: $i > $i ).
thf(l1_lattices_type,type,
l1_lattices: $i > $o ).
thf(k18_borsuk_1_type,type,
k18_borsuk_1: $i > $i > $i > $i ).
thf(r1_realset1_type,type,
r1_realset1: $i > $i > $i > $o ).
thf(k4_filter_0_type,type,
k4_filter_0: $i > $i > $i > $i ).
thf(v1_lattice2_type,type,
v1_lattice2: $i > $o ).
thf(r2_tarski_type,type,
r2_tarski: $i > $i > $o ).
thf(v6_group_1_type,type,
v6_group_1: $i > $o ).
thf(m1_filter_0_type,type,
m1_filter_0: $i > $i > $o ).
thf(k5_filter_1_type,type,
k5_filter_1: $i > $i > $i ).
thf(k6_filter_1_type,type,
k6_filter_1: $i > $i > $i > $i ).
thf(k2_funct_4_type,type,
k2_funct_4: $i > $i ).
thf(k4_lopclset_type,type,
k4_lopclset: $i > $i ).
thf(k9_filter_0_type,type,
k9_filter_0: $i > $i > $i > $i ).
thf(m1_lattice4_type,type,
m1_lattice4: $i > $i > $i > $o ).
thf(r1_lattice4_type,type,
r1_lattice4: $i > $i > $i > $o ).
thf(m2_lattice4_type,type,
m2_lattice4: $i > $i > $o ).
thf(k5_lattices_type,type,
k5_lattices: $i > $i ).
thf(k6_lattices_type,type,
k6_lattices: $i > $i ).
thf(k4_lattice4_type,type,
k4_lattice4: $i > $i > $i ).
thf(k11_borsuk_1_type,type,
k11_borsuk_1: $i > $i > $i > $i ).
thf(v11_lattices_type,type,
v11_lattices: $i > $o ).
thf(v2_lattice4_type,type,
v2_lattice4: $i > $i > $i > $o ).
thf(v15_lattices_type,type,
v15_lattices: $i > $o ).
thf(v16_lattices_type,type,
v16_lattices: $i > $o ).
thf(v1_lattice4_type,type,
v1_lattice4: $i > $i > $i > $o ).
thf(k1_domain_1_type,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(r2_lattices_type,type,
r2_lattices: $i > $i > $i > $o ).
thf(k8_filter_1_type,type,
k8_filter_1: $i > $i > $i ).
thf(k10_filter_1_type,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(k15_borsuk_1_type,type,
k15_borsuk_1: $i > $i ).
thf(r1_pre_topc_type,type,
r1_pre_topc: $i > $i > $o ).
thf(k9_filter_1_type,type,
k9_filter_1: $i > $i ).
thf(k8_lopclset_type,type,
k8_lopclset: $i > $i ).
thf(g1_pre_topc_type,type,
g1_pre_topc: $i > $i > $i ).
thf(v12_lattices_type,type,
v12_lattices: $i > $o ).
thf(v6_compts_1_type,type,
v6_compts_1: $i > $i > $o ).
thf(k3_filter_0_type,type,
k3_filter_0: $i > $i > $i ).
thf(k1_finsub_1_type,type,
k1_finsub_1: $i > $i > $i > $i ).
thf(k8_borsuk_1_type,type,
k8_borsuk_1: $i > $i > $i > $i > $i ).
thf(k5_lopclset_type,type,
k5_lopclset: $i > $i ).
thf(k3_lopclset_type,type,
k3_lopclset: $i > $i > $i > $i ).
thf(k19_borsuk_1_type,type,
k19_borsuk_1: $i > $i > $i > $i ).
thf(k2_filter_1_type,type,
k2_filter_1: $i > $i > $i > $i ).
thf(k11_filter_0_type,type,
k11_filter_0: $i > $i > $i ).
thf(a_2_3_borsuk_1_type,type,
a_2_3_borsuk_1: $i > $i > $i ).
thf(u1_pre_topc_type,type,
u1_pre_topc: $i > $i ).
thf(a_2_2_borsuk_1_type,type,
a_2_2_borsuk_1: $i > $i > $i ).
thf(a_2_1_lattice4_type,type,
a_2_1_lattice4: $i > $i > $i ).
thf(l2_struct_0_type,type,
l2_struct_0: $i > $o ).
thf(a_2_0_borsuk_1_type,type,
a_2_0_borsuk_1: $i > $i > $i ).
thf(a_2_0_filter_0_type,type,
a_2_0_filter_0: $i > $i > $i ).
thf(k22_borsuk_1_type,type,
k22_borsuk_1: $i ).
thf(k23_borsuk_1_type,type,
k23_borsuk_1: $i ).
thf(k24_borsuk_1_type,type,
k24_borsuk_1: $i ).
thf(k12_filter_0_type,type,
k12_filter_0: $i > $i > $i ).
thf(v3_borsuk_1_type,type,
v3_borsuk_1: $i > $i > $i > $o ).
thf(a_3_1_filter_0_type,type,
a_3_1_filter_0: $i > $i > $i > $i ).
thf(a_3_1_borsuk_1_type,type,
a_3_1_borsuk_1: $i > $i > $i > $i ).
thf(r1_filter_0_type,type,
r1_filter_0: $i > $i > $i > $i > $o ).
thf(k10_filter_0_type,type,
k10_filter_0: $i > $i > $i ).
thf(k5_filter_0_type,type,
k5_filter_0: $i > $i > $i > $i ).
thf(v1_filter_0_type,type,
v1_filter_0: $i > $i > $o ).
thf(r2_lattice4_type,type,
r2_lattice4: $i > $i > $i > $o ).
thf(a_3_0_filter_0_type,type,
a_3_0_filter_0: $i > $i > $i > $i ).
thf(r8_relat_2_type,type,
r8_relat_2: $i > $i > $o ).
thf(k6_domain_1_type,type,
k6_domain_1: $i > $i > $i ).
thf(k3_lattice4_type,type,
k3_lattice4: $i > $i > $i ).
thf(a_2_0_lopclset_type,type,
a_2_0_lopclset: $i > $i > $i ).
thf(k8_filter_0_type,type,
k8_filter_0: $i > $i > $i ).
thf(k3_pre_topc_type,type,
k3_pre_topc: $i > $i > $i ).
thf(k7_lopclset_type,type,
k7_lopclset: $i > $i ).
thf(k9_lopclset_type,type,
k9_lopclset: $i > $i ).
thf(m3_lattice4_type,type,
m3_lattice4: $i > $i > $o ).
thf(k10_lopclset_type,type,
k10_lopclset: $i > $i ).
thf(a_1_0_filter_1_type,type,
a_1_0_filter_1: $i > $i ).
thf(a_3_0_borsuk_1_type,type,
a_3_0_borsuk_1: $i > $i > $i > $i ).
thf(r3_lattice4_type,type,
r3_lattice4: $i > $i > $i > $o ).
thf(a_2_0_lattice4_type,type,
a_2_0_lattice4: $i > $i > $i ).
thf(k6_filter_0_type,type,
k6_filter_0: $i > $i > $i > $i ).
thf(a_1_0_lopclset_type,type,
a_1_0_lopclset: $i > $i ).
thf(r4_lattice4_type,type,
r4_lattice4: $i > $i > $i > $o ).
thf(a_2_1_borsuk_1_type,type,
a_2_1_borsuk_1: $i > $i > $i ).
thf(v3_lattice4_type,type,
v3_lattice4: $i > $i > $i > $o ).
thf(k7_filter_0_type,type,
k7_filter_0: $i > $i > $i > $i ).
thf(r1_relat_2_type,type,
r1_relat_2: $i > $i > $o ).
thf(k1_filter_0_type,type,
k1_filter_0: $i > $i ).
thf(v1_tops_2_type,type,
v1_tops_2: $i > $i > $o ).
thf(v2_filter_0_type,type,
v2_filter_0: $i > $i > $o ).
thf(r3_relat_2_type,type,
r3_relat_2: $i > $i > $o ).
thf(u2_struct_0_type,type,
u2_struct_0: $i > $i ).
thf(k11_lopclset_type,type,
k11_lopclset: $i > $i ).
thf(r1_compts_1_type,type,
r1_compts_1: $i > $i > $i > $o ).
thf(r4_wellord1_type,type,
r4_wellord1: $i > $i > $o ).
thf(k13_lopclset_type,type,
k13_lopclset: $i > $i ).
thf(k12_lopclset_type,type,
k12_lopclset: $i > $i ).
thf(k1_filter_1_type,type,
k1_filter_1: $i > $i > $i > $i ).
thf(a_1_1_lopclset_type,type,
a_1_1_lopclset: $i > $i ).
thf(a_1_2_lopclset_type,type,
a_1_2_lopclset: $i > $i ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(5810,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( D
= ( k1_funct_1 @ C @ E ) ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( k2_relat_1 @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).
thf(2630,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( D
= ( k1_funct_1 @ C @ E ) ) ) )
=> ( ( B = k1_xboole_0 )
| ( ( k2_relat_1 @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(245,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relat_1) ).
thf(2336,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(980,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_0) ).
thf(5320,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(137,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t105_zfmisc_1) ).
thf(1899,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(543,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_lattices @ A @ B @ C )
<=> ( ( ( k1_lattices @ A @ B @ C )
= ( k6_lattices @ A ) )
& ( ( k1_lattices @ A @ C @ B )
= ( k6_lattices @ A ) )
& ( ( k2_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
& ( ( k2_lattices @ A @ C @ B )
= ( k5_lattices @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_lattices) ).
thf(3581,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_lattices @ A @ B @ C )
=> ( ( ( k1_lattices @ A @ B @ C )
= ( k6_lattices @ A ) )
& ( ( k1_lattices @ A @ C @ B )
= ( k6_lattices @ A ) )
& ( ( k2_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
& ( ( k2_lattices @ A @ C @ B )
= ( k5_lattices @ A ) ) ) )
& ( ( ( ( k1_lattices @ A @ B @ C )
= ( k6_lattices @ A ) )
& ( ( k1_lattices @ A @ C @ B )
= ( k6_lattices @ A ) )
& ( ( k2_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
& ( ( k2_lattices @ A @ C @ B )
= ( k5_lattices @ A ) ) )
=> ( r2_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(2427,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(946,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_filter_0) ).
thf(5205,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k5_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(1338,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_lattice4) ).
thf(6845,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_xboole_0 @ D @ C ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_subset_1) ).
thf(1686,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_xboole_0 @ D @ C ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(788,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tops_1) ).
thf(4560,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(758,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(4447,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_partfun1) ).
thf(1718,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(3944,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
<=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_subset_1) ).
thf(1411,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ B @ C ) )
& ( ( r1_tarski @ B @ C )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(987,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(5365,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1170,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_borsuk_1) ).
thf(6167,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( r1_tarski @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ~ ( ~ ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_xboole_1) ).
thf(1469,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ~ ( ~ ( ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
& ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(792,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( v1_tops_1 @ C @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v1_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_tops_1) ).
thf(4571,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( v1_tops_1 @ C @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v1_tops_1 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1087,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(5857,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_xboole_1) ).
thf(2341,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(5136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1244,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( m1_subset_1 @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_borsuk_1) ).
thf(6530,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
=> ( m1_subset_1 @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(668,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tops_1) ).
thf(4062,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(178,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).
thf(2072,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m3_lattice4 @ ( k3_lattice4 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice4) ).
thf(5260,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m3_lattice4 @ ( k3_lattice4 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(588,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_filter_0) ).
thf(3798,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1301,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) )
& ( v10_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) )
& ( l3_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lopclset) ).
thf(6712,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) )
& ( v10_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) )
& ( l3_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(700,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) @ ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_3) ).
thf(4183,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) @ ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_subset_1) ).
thf(4290,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(565,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( k1_tops_1 @ ( k6_borsuk_1 @ A @ B ) @ C )
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_borsuk_1) ).
thf(3698,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( k1_tops_1 @ ( k6_borsuk_1 @ A @ B ) @ C )
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_relat_1) ).
thf(2787,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(315,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(2595,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(599,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( k3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) @ ( k3_lattices @ B @ E @ F ) ) )
& ( ( k4_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) @ ( k4_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_filter_1) ).
thf(3830,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( k3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) @ ( k3_lattices @ B @ E @ F ) ) )
& ( ( k4_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
= ( k10_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) @ ( k4_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(1222,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( B
= ( k1_filter_0 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_0) ).
thf(6431,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( B
= ( k1_filter_0 @ A ) )
& ( B
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(2544,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(1073,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice4 @ A @ ( k1_setwiseo @ ( u1_struct_0 @ A ) ) )
= ( k5_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattice4) ).
thf(5778,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice4 @ A @ ( k1_setwiseo @ ( u1_struct_0 @ A ) ) )
= ( k5_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1253,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( k2_filter_0 @ A @ ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_0) ).
thf(6555,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( k2_filter_0 @ A @ ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(2331,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(821,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_funct_3 @ A ) )
& ( v1_funct_1 @ ( k1_funct_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_3) ).
thf(4682,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k1_funct_3 @ A ) )
& ( v1_funct_1 @ ( k1_funct_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1064,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(5733,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(1372,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v15_lattices @ A )
& ( v15_lattices @ B ) )
<=> ( v15_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_filter_1) ).
thf(6954,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v15_lattices @ A )
& ( v15_lattices @ B ) )
=> ( v15_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v15_lattices @ A )
& ( v15_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(867,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(4877,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(1818,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1034,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
<=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_1) ).
thf(5582,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v15_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v16_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( v16_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(927,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v14_lattices @ A )
& ( r2_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lattice4) ).
thf(5131,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v14_lattices @ A )
& ( r2_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_subset_1) ).
thf(2363,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
= ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(325,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(2644,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(541,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( m1_filter_1 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k8_funct_2 @ A @ A @ C @ D ) @ ( k8_funct_2 @ A @ A @ C @ E ) ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_1) ).
thf(3549,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( ( m1_filter_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k8_funct_2 @ A @ A @ C @ D ) @ ( k8_funct_2 @ A @ A @ C @ E ) ) @ B ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k8_funct_2 @ A @ A @ C @ D ) @ ( k8_funct_2 @ A @ A @ C @ E ) ) @ B ) ) ) )
=> ( m1_filter_1 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(519,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_funct_3 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k1_funct_3 @ A ) @ ( k1_funct_3 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_3) ).
thf(3417,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_funct_3 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k1_funct_3 @ A ) @ ( k1_funct_3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(1328,axiom,
l1_pre_topc @ k22_borsuk_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k22_borsuk_1) ).
thf(6798,plain,
l1_pre_topc @ k22_borsuk_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ B ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_xboole_1) ).
thf(1728,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ B ) )
& ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1221,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(6426,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(531,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).
thf(3498,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(983,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_xboole_0 @ ( k7_lopclset @ A ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k7_lattices @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lopclset) ).
thf(5348,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_xboole_0 @ ( k7_lopclset @ A ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k7_lattices @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(1127,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v4_pre_topc @ C @ B )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_pre_topc) ).
thf(6022,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v4_pre_topc @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) )
= C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ D @ A )
& ( ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) )
= C ) )
=> ( v4_pre_topc @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1325,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] : ( m1_borsuk_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_borsuk_1) ).
thf(6791,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] : ( m1_borsuk_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(931,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ C @ E @ D @ D )
& ( r1_filter_0 @ A @ B @ F @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_filter_0) ).
thf(5141,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ C )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ C @ E @ D @ D )
& ( r1_filter_0 @ A @ B @ F @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(12,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) )
= ( k4_lattices @ A @ ( k2_lattice4 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice4) ).
thf(1406,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) )
= ( k4_lattices @ A @ ( k2_lattice4 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1369,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_lattices) ).
thf(6944,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r1_tarski @ ( k1_relat_1 @ ( k2_funct_4 @ C ) ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_4) ).
thf(3813,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( r1_tarski @ ( k1_relat_1 @ ( k2_funct_4 @ C ) ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(258,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 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(2381,plain,
! [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 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1349,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m3_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattice4) ).
thf(6883,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m3_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(294,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(2527,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(745,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_relat_1) ).
thf(4391,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(447,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(3153,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(2953,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(2590,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(973,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k1_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice4) ).
thf(5297,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k1_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1355,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_relat_1 @ ( k8_lopclset @ A ) )
& ( v1_funct_1 @ ( k8_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_lopclset) ).
thf(6900,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_relat_1 @ ( k8_lopclset @ A ) )
& ( v1_funct_1 @ ( k8_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(1569,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k6_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(827,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v4_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_1 @ ( k2_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_tops_1) ).
thf(4697,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v4_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_1 @ ( k2_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ D @ C ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice2) ).
thf(1971,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ D @ C ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(514,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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(3402,plain,
! [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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(46,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( C
= ( k1_funct_4 @ A @ B ) )
<=> ( ( ( k1_relat_1 @ C )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) )
& ( ~ ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ A @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_4) ).
thf(1533,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( C
= ( k1_funct_4 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) )
& ( ~ ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ A @ D ) ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ D ) ) )
& ( ~ ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ A @ D ) ) ) ) ) )
=> ( C
= ( k1_funct_4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1053,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattices) ).
thf(5691,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(112,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).
thf(1793,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(23,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1437,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(770,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_4) ).
thf(4487,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1233,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ E @ F ) @ B ) )
=> ( ( r2_hidden @ ( k9_filter_0 @ A @ ( k3_lattices @ A @ C @ E ) @ ( k3_lattices @ A @ D @ F ) ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ ( k4_lattices @ A @ C @ E ) @ ( k4_lattices @ A @ D @ F ) ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_1) ).
thf(6480,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ E @ F ) @ B ) )
=> ( ( r2_hidden @ ( k9_filter_0 @ A @ ( k3_lattices @ A @ C @ E ) @ ( k3_lattices @ A @ D @ F ) ) @ B )
& ( r2_hidden @ ( k9_filter_0 @ A @ ( k4_lattices @ A @ C @ E ) @ ( k4_lattices @ A @ D @ F ) ) @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ ( k4_xboole_0 @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_zfmisc_1) ).
thf(1608,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ ( k4_xboole_0 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(678,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ D ) ) @ ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_1) ).
thf(4090,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ D ) ) @ ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(1212,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_filter_0 @ ( k2_filter_0 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_filter_0) ).
thf(6401,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_filter_0 @ ( k2_filter_0 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(649,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_setwiseo @ A ) )
& ( m1_subset_1 @ ( k1_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setwiseo) ).
thf(4011,plain,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_setwiseo @ A ) )
& ( m1_subset_1 @ ( k1_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(870,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( D
= ( k4_filter_0 @ A @ B @ C ) )
<=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_0) ).
thf(4884,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( D
= ( k4_filter_0 @ A @ B @ C ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) )
& ( ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) )
=> ( D
= ( k4_filter_0 @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(653,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(4026,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1278,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_0) ).
thf(6634,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(5713,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(143,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k2_tops_1 @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_tops_1) ).
thf(1919,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k2_tops_1 @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(713,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(4247,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k2_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1331,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( k7_lopclset @ B ) )
<=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( C = A )
& ( v1_filter_0 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lopclset) ).
thf(6804,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( k7_lopclset @ B ) )
=> ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( C = A )
& ( v1_filter_0 @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_filter_0 @ C @ B )
& ( C = A )
& ( v1_filter_0 @ C @ B ) )
=> ( r2_hidden @ A @ ( k7_lopclset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(4980,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(252,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k2_xboole_0 @ A @ B )
= ( k1_funct_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_4) ).
thf(2360,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k2_xboole_0 @ A @ B )
= ( k1_funct_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
<=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(1705,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_relset_1 @ C @ A @ B )
=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
& ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( m1_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(417,axiom,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(3017,plain,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1031,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattices) ).
thf(5550,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k4_lattices @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k2_lopclset @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_lopclset) ).
thf(1788,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k2_lopclset @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_zfmisc_1) ).
thf(1426,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
=> ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funct_4) ).
thf(4234,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(76,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relat_1) ).
thf(1671,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(579,axiom,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
thf(3745,plain,
! [A: $i,B: $i] :
~ ( ~ ( ( A = k1_xboole_0 )
& ( B != k1_xboole_0 ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ~ ( ( B
= ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(837,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 @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(4739,plain,
! [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 @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ C @ ( k3_tarski @ ( k2_xboole_0 @ A @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_xboole_0 @ D @ C ) ) )
=> ( r1_tarski @ C @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_setfam_1) ).
thf(1756,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ C @ ( k3_tarski @ ( k2_xboole_0 @ A @ B ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ B )
=> ( r1_xboole_0 @ D @ C ) ) )
=> ( r1_tarski @ C @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1098,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_lopclset @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = C )
& ( v3_pre_topc @ C @ B )
& ( v4_pre_topc @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_lopclset) ).
thf(5906,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_lopclset @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = C )
& ( v3_pre_topc @ C @ B )
& ( v4_pre_topc @ C @ B ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( A = C )
& ( v3_pre_topc @ C @ B )
& ( v4_pre_topc @ C @ B ) )
=> ( r2_hidden @ A @ ( a_1_0_lopclset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(1288,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k7_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).
thf(6675,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k7_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(493,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v2_lattice4 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lattice4) ).
thf(3332,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v2_lattice4 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( D
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(2316,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funct_3) ).
thf(3446,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(394,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( v3_pre_topc @ D @ B ) )
=> ( v3_pre_topc @ ( k7_borsuk_1 @ A @ B @ C @ D ) @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_borsuk_1) ).
thf(2933,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ C @ A )
& ( v3_pre_topc @ D @ B ) )
=> ( v3_pre_topc @ ( k7_borsuk_1 @ A @ B @ C @ D ) @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1151,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice2) ).
thf(6089,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_lattice2 @ ( k1_lattice2 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
thf(3338,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
& ( C
= ( k1_funct_1 @ B @ D ) ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1281,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_relat_1 @ ( k13_lopclset @ A ) )
= ( u1_struct_0 @ ( k12_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lopclset) ).
thf(6655,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_relat_1 @ ( k13_lopclset @ A ) )
= ( u1_struct_0 @ ( k12_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(964,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(5257,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(1218,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(6416,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(344,axiom,
! [A: $i] :
( ( k1_setwiseo @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setwiseo) ).
thf(2712,plain,
! [A: $i] :
( ( k1_setwiseo @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1340,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k10_lopclset @ A )
= ( k1_lopclset @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lopclset) ).
thf(6851,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k10_lopclset @ A )
= ( k1_lopclset @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(861,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(4856,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1252,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_lopclset) ).
thf(6551,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(1290,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ B @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_1) ).
thf(6680,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ B @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(387,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_1) ).
thf(2901,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(489,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_lattices @ A @ B @ ( k3_lattice2 @ C @ A @ D @ E ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ B @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_lattice2) ).
thf(3313,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_lattices @ A @ B @ ( k3_lattice2 @ C @ A @ D @ E ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ B @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1258,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( r2_hidden @ k1_xboole_0 @ ( u1_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_pre_topc) ).
thf(6570,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( r2_hidden @ k1_xboole_0 @ ( u1_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( ( k1_funct_1 @ D @ F )
= ( k1_funct_1 @ E @ F ) ) ) )
=> ( ( k1_funct_4 @ E @ ( k2_partfun1 @ A @ B @ D @ C ) )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice2) ).
thf(4142,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( ( k1_funct_1 @ D @ F )
= ( k1_funct_1 @ E @ F ) ) ) )
=> ( ( k1_funct_4 @ E @ ( k2_partfun1 @ A @ B @ D @ C ) )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k10_setwiseo @ A @ B @ ( k2_setwiseo @ A @ D ) @ C )
= ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setwiseo) ).
thf(1391,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( k10_setwiseo @ A @ B @ ( k2_setwiseo @ A @ D ) @ C )
= ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(630,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice4) ).
thf(3947,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).
thf(5938,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v4_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
thf(2886,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v4_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1315,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ~ ( v3_struct_0 @ ( k6_borsuk_1 @ A @ B ) )
& ( v1_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k6_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_borsuk_1) ).
thf(6754,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ~ ( v3_struct_0 @ ( k6_borsuk_1 @ A @ B ) )
& ( v1_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k6_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(879,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_pre_topc) ).
thf(4948,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(546,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).
thf(3597,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) )
=> ( r2_hidden @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) )
=> ( r2_hidden @ C @ D ) ) )
=> ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(498,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(3350,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(1360,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k6_lattices @ A ) )
= ( k5_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lattice4) ).
thf(6914,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k6_lattices @ A ) )
= ( k5_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(1186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) )
<=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).
thf(6251,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) )
=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) )
& ( ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_lattices @ B @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) )
=> ( r2_hidden @ A @ ( a_3_0_filter_0 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(644,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_relat_1) ).
thf(3994,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(1017,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k2_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(5486,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k2_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t175_relat_1) ).
thf(1782,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1025,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k5_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k5_lattices @ A ) @ ( k5_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_filter_1) ).
thf(5518,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k5_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k5_lattices @ A ) @ ( k5_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_lattices @ A @ B @ C )
= ( g3_lattices @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(1441,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( g3_lattices @ A @ B @ C )
= ( g3_lattices @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(718,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ( ( k1_tops_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_tops_1) ).
thf(4266,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ( ( k1_tops_1 @ A @ B )
= k1_xboole_0 ) )
& ( ( ( k1_tops_1 @ A @ B )
= k1_xboole_0 )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).
thf(2020,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( v2_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(820,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ E ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
| ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_borsuk_1) ).
thf(4679,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ E ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
| ( D = E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(806,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
<=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(4618,plain,
! [A: $i,B: $i] :
( ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) )
& ( ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) )
=> ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(583,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v3_realset2 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_realset2) ).
thf(3777,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ( v3_realset2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(655,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_pre_topc) ).
thf(4030,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
thf(1724,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
!= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(881,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_tops_1) ).
thf(4963,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( k1_tops_1 @ A @ ( k1_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_xboole_1) ).
thf(2067,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1234,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_compts_1 @ A @ C @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_tarski @ E @ C )
& ( r1_compts_1 @ A @ E @ D )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ E )
& ( r1_xboole_0 @ F @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_borsuk_1) ).
thf(6483,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_compts_1 @ A @ C @ D )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_tarski @ E @ C )
& ( r1_compts_1 @ A @ E @ D )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ E )
& ( r1_xboole_0 @ F @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(695,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( ( k2_relat_1 @ D )
= B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ D @ E )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).
thf(4156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ~ ( ( r2_hidden @ C @ B )
& ( ( k2_relat_1 @ D )
= B )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ D @ E )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(968,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ~ ( ( ( k7_lopclset @ B )
= ( k3_tarski @ A ) )
& ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k10_lopclset @ B ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ( ( k7_lopclset @ B )
!= ( k3_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lopclset) ).
thf(5269,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ~ ( ( ( k7_lopclset @ B )
= ( k3_tarski @ A ) )
& ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ ( k10_lopclset @ B ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ( ( k7_lopclset @ B )
!= ( k3_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(714,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( C
= ( k2_borsuk_1 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( r2_hidden @ D @ ( k8_funct_2 @ A @ B @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_borsuk_1) ).
thf(4249,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( C
= ( k2_borsuk_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( r2_hidden @ D @ ( k8_funct_2 @ A @ B @ C @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( r2_hidden @ D @ ( k8_funct_2 @ A @ B @ C @ D ) ) )
=> ( C
= ( k2_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(134,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(1887,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(743,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= B ) )
& ( ( k2_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_filter_0) ).
thf(4386,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= B ) )
& ( ( k2_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(1299,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m3_lattice4 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_lattice4) ).
thf(6707,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m3_lattice4 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(838,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tops_1) ).
thf(4743,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1094,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k6_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_0) ).
thf(5883,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k6_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(332,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k3_funct_3 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
& ! [C: $i] :
( ( r1_tarski @ C @ ( k2_relat_1 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k10_relat_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_3) ).
thf(2667,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k3_funct_3 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
& ! [C: $i] :
( ( r1_tarski @ C @ ( k2_relat_1 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k10_relat_1 @ A @ C ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
& ! [C: $i] :
( ( r1_tarski @ C @ ( k2_relat_1 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k10_relat_1 @ A @ C ) ) ) )
=> ( B
= ( k3_funct_3 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(1153,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_filter_1 @ A @ ( k8_filter_1 @ ( k5_filter_1 @ A @ ( k2_filter_0 @ A @ B ) ) @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_1) ).
thf(6095,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_filter_1 @ A @ ( k8_filter_1 @ ( k5_filter_1 @ A @ ( k2_filter_0 @ A @ B ) ) @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(530,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(3495,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(969,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(5274,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) )
& ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(1826,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( k7_borsuk_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_borsuk_1) ).
thf(4023,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( k7_borsuk_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(280,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ D @ C )
= ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ E @ C ) )
=> ( ( C = k1_xboole_0 )
| ( ( k2_lattice2 @ B @ A @ C @ D )
= ( k2_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice2) ).
thf(2466,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ D @ C )
= ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ E @ C ) )
=> ( ( C = k1_xboole_0 )
| ( ( k2_lattice2 @ B @ A @ C @ D )
= ( k2_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(754,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_tops_1) ).
thf(4428,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(613,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_lopclset @ A ) @ ( k3_lattices @ A @ B @ C ) )
= ( k2_xboole_0 @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lopclset) ).
thf(3891,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_lopclset @ A ) @ ( k3_lattices @ A @ B @ C ) )
= ( k2_xboole_0 @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(1032,axiom,
! [A: $i,B: $i] :
( ( B
= ( k3_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(5553,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k3_tarski @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).
thf(4637,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).
thf(1409,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(463,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k2_tops_1 @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D ) )
=> ( ~ ( r1_xboole_0 @ B @ D )
& ~ ( r1_xboole_0 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_tops_1) ).
thf(3204,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k2_tops_1 @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D ) )
=> ( ~ ( r1_xboole_0 @ B @ D )
& ~ ( r1_xboole_0 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ D ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D ) )
=> ( ~ ( r1_xboole_0 @ B @ D )
& ~ ( r1_xboole_0 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ D ) ) ) )
=> ( r2_hidden @ C @ ( k2_tops_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1112,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( v6_compts_1 @ C @ A )
<=> ( v6_compts_1 @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_borsuk_1) ).
thf(5953,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( ( v6_compts_1 @ C @ A )
=> ( v6_compts_1 @ D @ B ) )
& ( ( v6_compts_1 @ D @ B )
=> ( v6_compts_1 @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(782,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).
thf(4539,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ ( k5_relat_1 @ B @ C ) ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k1_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_3) ).
thf(3263,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ ( k5_relat_1 @ B @ C ) ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k1_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m2_lattice4 @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_1_lattice4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k2_lattice4 @ B @ D ) )
& ( r1_tarski @ D @ ( k4_lattice4 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice4) ).
thf(4439,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m2_lattice4 @ C @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_lattice4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k2_lattice4 @ B @ D ) )
& ( r1_tarski @ D @ ( k4_lattice4 @ B @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ B ) ) )
& ( A
= ( k2_lattice4 @ B @ D ) )
& ( r1_tarski @ D @ ( k4_lattice4 @ B @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_1_lattice4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(638,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(3976,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
thf(2328,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_tarski @ A ) )
=> ( ( k2_relat_1 @ B )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_realset1 @ A @ B @ C )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_realset1) ).
thf(2735,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_realset1 @ A @ B @ C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
=> ( r1_realset1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(789,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_setwiseo) ).
thf(4563,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r1_tarski @ C @ B )
=> ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(3275,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1130,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_filter_1) ).
thf(6034,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(1132,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(6039,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_xboole_1) ).
thf(2339,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(825,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(4692,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).
thf(4224,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ D )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k1_tarski @ B ) )
<=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(1871,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) )
& ( ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) )
=> ( r1_tarski @ A @ ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1303,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k10_lopclset @ A )
= ( k2_relat_1 @ ( k9_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lopclset) ).
thf(6723,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k10_lopclset @ A )
= ( k2_relat_1 @ ( k9_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(840,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ B @ C ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(4761,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ B @ C ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(550,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relat_1) ).
thf(3617,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k3_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k3_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(129,axiom,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(1860,plain,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(548,axiom,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(3612,plain,
! [A: $i] :
( ( l2_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(445,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
<=> ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finset_1) ).
thf(3148,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ A ) )
& ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_zfmisc_1) ).
thf(1511,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
<=> ~ ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(2274,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
=> ~ ( r2_hidden @ A @ B ) )
& ( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).
thf(2185,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(482,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( m1_borsuk_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ C @ E )
& ( r1_tarski @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ F @ B )
=> ( ( r1_xboole_0 @ F @ E )
| ( r1_tarski @ F @ E ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_borsuk_1) ).
thf(3280,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m1_borsuk_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ C @ E )
& ( r1_tarski @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ F @ B )
=> ( ( r1_xboole_0 @ F @ E )
| ( r1_tarski @ F @ E ) ) ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ E @ A )
& ( r1_tarski @ C @ E )
& ( r1_tarski @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ F @ B )
=> ( ( r1_xboole_0 @ F @ E )
| ( r1_tarski @ F @ E ) ) ) ) ) ) ) )
=> ( m1_borsuk_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1284,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v17_lattices @ A )
<=> ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d20_lattices) ).
thf(6662,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v17_lattices @ A )
=> ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) ) )
& ( ( ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( v11_lattices @ A ) )
=> ( v17_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(1201,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ ( k1_funct_4 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_4) ).
thf(6332,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ ( k1_funct_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(1242,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(6519,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(159,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v5_tops_1 @ B @ A )
& ( v5_tops_1 @ C @ A ) )
=> ( v5_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_tops_1) ).
thf(1992,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v5_tops_1 @ B @ A )
& ( v5_tops_1 @ C @ A ) )
=> ( v5_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1058,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k1_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_tops_1) ).
thf(5706,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k1_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(791,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_1 @ ( k1_funct_3 @ A ) @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_3) ).
thf(4568,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_1 @ ( k1_funct_3 @ A ) @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(499,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_pre_topc) ).
thf(3353,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(351,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_tops_1) ).
thf(2745,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).
thf(2571,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( v1_finset_1 @ ( k10_relat_1 @ B @ A ) ) )
=> ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finset_1) ).
thf(3713,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( v1_finset_1 @ ( k10_relat_1 @ B @ A ) ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(144,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
thf(1922,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1137,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( m1_subset_1 @ ( k3_tarski @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_borsuk_1) ).
thf(6049,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( m1_subset_1 @ ( k3_tarski @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(646,axiom,
! [A: $i] :
( ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) )
<=> ( v1_finset_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finset_1) ).
thf(3998,plain,
! [A: $i] :
( ( ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) )
=> ( v1_finset_1 @ ( k3_tarski @ A ) ) )
& ( ( v1_finset_1 @ ( k3_tarski @ A ) )
=> ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_finset_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(601,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k1_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k2_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k3_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_filter_1) ).
thf(3840,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( k1_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k2_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) )
& ( ( k3_relat_1 @ ( k9_filter_1 @ A ) )
= ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(1275,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v6_group_1 @ A )
<=> ( v6_group_1 @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_lattice2) ).
thf(6626,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v6_group_1 @ A )
=> ( v6_group_1 @ ( k1_lattice2 @ A ) ) )
& ( ( v6_group_1 @ ( k1_lattice2 @ A ) )
=> ( v6_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_4) ).
thf(2767,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(33,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ B @ C )
<=> ( ( k1_lattices @ A @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
thf(1479,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_lattices @ A @ B @ C )
=> ( ( k1_lattices @ A @ B @ C )
= C ) )
& ( ( ( k1_lattices @ A @ B @ C )
= C )
=> ( r1_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(622,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice4) ).
thf(3919,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(466,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) )
& ( r1_tarski @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_funct_4) ).
thf(3216,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) )
& ( r1_tarski @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(1366,axiom,
? [A: $i] : ( l3_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_lattices) ).
thf(6936,plain,
? [A: $i] : ( l3_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_xboole_1) ).
thf(1931,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
= ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1068,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_lattice4) ).
thf(5746,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) ) @ ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_3) ).
thf(1778,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) ) @ ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(817,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_relat_1) ).
thf(4669,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(1144,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ( ( r1_tarski @ B @ C )
=> ( m2_connsp_2 @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_borsuk_1) ).
thf(6071,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m2_connsp_2 @ D @ A @ C )
=> ( ( r1_tarski @ B @ C )
=> ( m2_connsp_2 @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finset_1) ).
thf(2420,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1036,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lopclset) ).
thf(5605,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(863,axiom,
! [A: $i,B: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(4862,plain,
! [A: $i,B: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(553,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_borsuk_1) ).
thf(3638,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(42,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 ) )
=> ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(1514,plain,
! [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 ) )
=> ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1357,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_lattice4) ).
thf(6905,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m2_lattice4 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(1270,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_hidden @ B @ ( k15_borsuk_1 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B
!= ( k1_struct_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_borsuk_1) ).
thf(6611,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_hidden @ B @ ( k15_borsuk_1 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B
!= ( k1_struct_0 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(1210,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k6_lattices @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattices) ).
thf(6396,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k6_lattices @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(738,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_tops_1) ).
thf(4368,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1109,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r4_lattice4 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice4) ).
thf(5942,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r4_lattice4 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k7_lattices @ A @ D ) )
= ( k7_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) ) ) )
=> ( r4_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
thf(1641,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k2_relat_1 @ B )
= ( k1_tarski @ A ) )
& ( ( k2_relat_1 @ C )
= ( k1_tarski @ A ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(600,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_pre_topc @ A @ B )
<=> ( ( k2_pre_topc @ A )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_pre_topc) ).
thf(3835,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r1_pre_topc @ A @ B )
=> ( ( k2_pre_topc @ A )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) ) )
& ( ( ( k2_pre_topc @ A )
= ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( r1_pre_topc @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(742,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ B @ A )
=> ( ( k1_funct_4 @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice2) ).
thf(4383,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ B @ A )
=> ( ( k1_funct_4 @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ B @ A )
& ( m2_relset_1 @ C @ B @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( ( k2_funct_2 @ B @ A @ C @ ( k1_tarski @ D ) )
= ( k1_tarski @ ( k8_funct_2 @ B @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_setwiseo) ).
thf(1815,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ B @ A )
& ( m2_relset_1 @ C @ B @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( ( k2_funct_2 @ B @ A @ C @ ( k1_tarski @ D ) )
= ( k1_tarski @ ( k8_funct_2 @ B @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(763,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_1 @ ( k2_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_tops_1) ).
thf(4460,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v2_tops_1 @ ( k2_tops_1 @ A @ B ) @ A )
& ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(409,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) @ E ) ) )
=> ( r3_lattices @ C @ ( k2_lattice2 @ A @ C @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_lattice2) ).
thf(2989,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) @ E ) ) )
=> ( r3_lattices @ C @ ( k2_lattice2 @ A @ C @ B @ D ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(911,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( r2_hidden @ ( k8_funct_2 @ A @ B @ E @ F ) @ D ) ) )
=> ( r1_tarski @ ( k2_funct_2 @ A @ B @ E @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_setwiseo) ).
thf(5076,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( r2_hidden @ ( k8_funct_2 @ A @ B @ E @ F ) @ D ) ) )
=> ( r1_tarski @ ( k2_funct_2 @ A @ B @ E @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).
thf(1963,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1307,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_pre_topc @ ( k11_lopclset @ A ) )
& ( v2_pre_topc @ ( k11_lopclset @ A ) )
& ( l1_pre_topc @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_lopclset) ).
thf(6734,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_pre_topc @ ( k11_lopclset @ A ) )
& ( v2_pre_topc @ ( k11_lopclset @ A ) )
& ( l1_pre_topc @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(376,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2852,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ! [E: $i] :
( ( r1_tarski @ E @ C )
=> ( r2_hidden @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(3268,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(648,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_partfun1) ).
thf(4008,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
= ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
thf(3258,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
= ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(3788,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1077,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( v3_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_1) ).
thf(5792,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( v3_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_xboole_1) ).
thf(2456,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(2237,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
!= k1_xboole_0 )
& ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1123,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m3_lattice4) ).
thf(6002,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m3_lattice4 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_xboole_0 @ B @ D ) )
=> ( r1_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(2782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D )
& ( r1_xboole_0 @ B @ D ) )
=> ( r1_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(2650,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1243,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ ( k5_filter_0 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k4_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_0) ).
thf(6523,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ B @ ( k5_filter_0 @ A @ C @ D ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ A ) )
=> ~ ( ( B
= ( k4_lattices @ A @ E @ F ) )
& ( r2_hidden @ E @ C )
& ( r2_hidden @ F @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(637,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(3973,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1029,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_borsuk_1) ).
thf(5541,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(936,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_lattices) ).
thf(5156,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k5_filter_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_0) ).
thf(5457,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k5_filter_0 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(4556,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1255,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(6562,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_xboole_1) ).
thf(2017,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1050,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v14_lattices @ A )
=> ( ( k6_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_filter_0) ).
thf(5682,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( v14_lattices @ A )
=> ( ( k6_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
= ( k6_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(1076,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
<=> ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattices) ).
thf(5787,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) )
=> ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( r3_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
=> ( ( k4_lattices @ A @ B @ C )
= ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(1147,axiom,
m1_subset_1 @ k23_borsuk_1 @ ( u1_struct_0 @ k22_borsuk_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k23_borsuk_1) ).
thf(6081,plain,
m1_subset_1 @ k23_borsuk_1 @ ( u1_struct_0 @ k22_borsuk_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(751,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( k16_borsuk_1 @ A @ B ) )
<=> ( ( ( u1_struct_0 @ C )
= B )
& ( ( u1_pre_topc @ C )
= ( a_2_2_borsuk_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_borsuk_1) ).
thf(4411,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( ( C
= ( k16_borsuk_1 @ A @ B ) )
=> ( ( ( u1_struct_0 @ C )
= B )
& ( ( u1_pre_topc @ C )
= ( a_2_2_borsuk_1 @ A @ B ) ) ) )
& ( ( ( ( u1_struct_0 @ C )
= B )
& ( ( u1_pre_topc @ C )
= ( a_2_2_borsuk_1 @ A @ B ) ) )
=> ( C
= ( k16_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_zfmisc_1) ).
thf(1946,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(747,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( k18_borsuk_1 @ A @ B @ C )
= ( k2_xboole_0 @ C @ ( a_2_3_borsuk_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_borsuk_1) ).
thf(4396,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( k18_borsuk_1 @ A @ B @ C )
= ( k2_xboole_0 @ C @ ( a_2_3_borsuk_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(1049,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ~ ( ( r2_hidden @ E @ C )
<=> ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_subset_1) ).
thf(5663,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) ) )
& ( ~ ( ( ( r2_hidden @ E @ C )
=> ( r2_hidden @ E @ D ) )
& ( ( r2_hidden @ E @ D )
=> ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setwiseo) ).
thf(1664,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(366,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v2_funct_1 @ A )
& ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B )
= ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_3) ).
thf(2794,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v2_funct_1 @ A )
& ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B )
= ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(634,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(3966,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(88,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_partfun1) ).
thf(1714,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_xboole_0 @ A @ B )
= C )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ D )
= ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1182,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(6227,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( m1_subset_1 @ ( u2_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(699,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) )
=> ( ( B
= ( k5_lopclset @ A ) )
<=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( k2_binop_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ B @ C @ D )
= ( k3_lopclset @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lopclset) ).
thf(4173,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) )
=> ( ( ( B
= ( k5_lopclset @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( k2_binop_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ B @ C @ D )
= ( k3_lopclset @ A @ C @ D ) ) ) ) )
& ( ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( k2_binop_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ B @ C @ D )
= ( k3_lopclset @ A @ C @ D ) ) ) )
=> ( B
= ( k5_lopclset @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( ( r1_tarski @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(5084,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( ( r1_tarski @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(432,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(3075,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(672,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_mcart_1) ).
thf(4072,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).
thf(1450,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k2_funct_2 @ A @ A @ B @ A )
= ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1286,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_tarski @ ( k10_lopclset @ A ) )
= ( k7_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lopclset) ).
thf(6670,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_tarski @ ( k10_lopclset @ A ) )
= ( k7_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(902,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( v14_lattices @ A )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattices) ).
thf(5027,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( ( v14_lattices @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) )
=> ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1089,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattice2) ).
thf(5861,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( r3_lattices @ ( k1_lattice2 @ A ) @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( r1_filter_1 @ A @ ( k6_lopclset @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lopclset) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( r1_filter_1 @ A @ ( k6_lopclset @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1373,plain,
~ ! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( r1_filter_1 @ A @ ( k6_lopclset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(411,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_tops_1) ).
thf(2996,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( r1_tarski @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(385,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
= ( k6_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( ( k4_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
= ( k6_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_1) ).
thf(2893,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
= ( k6_filter_1 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( ( k4_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
= ( k6_filter_1 @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(65,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) @ D )
= ( k3_lattices @ A @ ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_lattice4) ).
thf(1632,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) @ D )
= ( k3_lattices @ A @ ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(281,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v3_filter_0 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_lattices @ A @ ( k2_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ ( k2_lattices @ A @ B @ E ) @ C )
=> ( r1_lattices @ A @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_filter_0) ).
thf(2469,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v3_filter_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_lattices @ A @ ( k2_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ ( k2_lattices @ A @ B @ E ) @ C )
=> ( r1_lattices @ A @ E @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r1_lattices @ A @ ( k2_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ ( k2_lattices @ A @ B @ E ) @ C )
=> ( r1_lattices @ A @ E @ D ) ) ) ) ) )
=> ( v3_filter_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(835,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_filter_0) ).
thf(4733,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ ( k4_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(223,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(2259,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1216,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( ( k3_filter_0 @ A @ C )
= ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_0) ).
thf(6410,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( C
= ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) )
=> ( ( k3_filter_0 @ A @ C )
= ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(525,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_1) ).
thf(3473,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(641,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(3983,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1311,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_lattice4) ).
thf(6745,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_lattice4 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(79,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
thf(1682,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
& ( ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(4847,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(664,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_filter_0 @ A @ D ) @ B ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ E @ B )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ E ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice4) ).
thf(4050,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k2_filter_0 @ A @ D ) @ B ) ) )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ( r2_hidden @ E @ B )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ E ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(189,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(2122,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1174,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( v1_tops_2 @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k6_borsuk_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_borsuk_1) ).
thf(6176,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( v1_tops_2 @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k6_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(832,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) )
=> ( ( k9_relat_1 @ B @ ( k3_tarski @ A ) )
= ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_3) ).
thf(4724,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) )
=> ( ( k9_relat_1 @ B @ ( k3_tarski @ A ) )
= ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(230,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_3 @ A ) )
& ( v1_funct_1 @ ( k3_funct_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_3) ).
thf(2291,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_3 @ A ) )
& ( v1_funct_1 @ ( k3_funct_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k2_setwiseo @ A @ B ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_setwiseo) ).
thf(1383,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( m1_subset_1 @ ( k2_setwiseo @ A @ B ) @ ( k5_finsub_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1337,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v13_lattices @ A )
& ( v13_lattices @ B ) )
<=> ( v13_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_1) ).
thf(6841,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v13_lattices @ A )
& ( v13_lattices @ B ) )
=> ( v13_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v13_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v13_lattices @ A )
& ( v13_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
thf(3357,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k5_setfam_1 @ A @ B )
= A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( D
= ( k3_tarski @ C ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ D ) @ ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_borsuk_1) ).
thf(2540,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k5_setfam_1 @ A @ B )
= A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( D
= ( k3_tarski @ C ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ D ) @ ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(977,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( k1_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) @ B @ C )
= ( k2_lopclset @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lopclset) ).
thf(5311,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( k1_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) @ B @ C )
= ( k2_lopclset @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1254,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_filter_0 @ A @ B @ C @ D )
<=> ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_filter_0) ).
thf(6559,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r1_filter_0 @ A @ B @ C @ D )
=> ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ B )
=> ( r1_filter_0 @ A @ B @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(624,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_tops_1) ).
thf(3923,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).
thf(2555,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(484,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_filter_0) ).
thf(3300,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ E ) )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ E ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ E @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(684,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).
thf(4115,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1223,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_0) ).
thf(6438,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(1066,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_filter_0) ).
thf(5738,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(1277,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
<=> ( r4_wellord1 @ ( k9_filter_1 @ A ) @ ( k9_filter_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_1) ).
thf(6631,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r1_filter_1 @ A @ B )
=> ( r4_wellord1 @ ( k9_filter_1 @ A ) @ ( k9_filter_1 @ B ) ) )
& ( ( r4_wellord1 @ ( k9_filter_1 @ A ) @ ( k9_filter_1 @ B ) )
=> ( r1_filter_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(993,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k10_filter_0 @ A @ B ) )
<=> ( ( r1_tarski @ ( k3_relat_1 @ C ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C )
<=> ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_filter_0) ).
thf(5384,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k10_filter_0 @ A @ B ) )
=> ( ( r1_tarski @ ( k3_relat_1 @ C ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C )
=> ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B ) )
& ( ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C ) ) ) ) ) ) )
& ( ( ( r1_tarski @ ( k3_relat_1 @ C ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C )
=> ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B ) )
& ( ( r2_hidden @ ( k9_filter_0 @ A @ D @ E ) @ B )
=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ E ) @ C ) ) ) ) ) )
=> ( C
= ( k10_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(1236,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m1_pre_topc @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pre_topc) ).
thf(6491,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] : ( m1_pre_topc @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(1344,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) )
<=> ( v1_filter_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_filter_0) ).
thf(6863,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) )
=> ( v1_filter_0 @ B @ A ) )
& ( ( v1_filter_0 @ B @ A )
=> ( ( B
!= ( k1_filter_0 @ A ) )
& ( v2_filter_0 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ D ) @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_3) ).
thf(4038,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ D ) @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ ( k2_funct_1 @ B ) @ ( k1_funct_1 @ B @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ B @ ( k2_funct_1 @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_funct_1) ).
thf(2103,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ ( k2_funct_1 @ B ) @ ( k1_funct_1 @ B @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ B @ ( k2_funct_1 @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v1_funct_1 @ ( k1_funct_3 @ C ) )
& ( v1_funct_2 @ ( k1_funct_3 @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) )
& ( m2_relset_1 @ ( k1_funct_3 @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_3) ).
thf(3226,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v1_funct_1 @ ( k1_funct_3 @ C ) )
& ( v1_funct_2 @ ( k1_funct_3 @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) )
& ( m2_relset_1 @ ( k1_funct_3 @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(1041,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( l1_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pre_topc) ).
thf(5629,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( l1_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1116,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( m1_filter_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_1) ).
thf(5970,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( m1_filter_0 @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1230,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_tops_1) ).
thf(6474,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(5045,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(908,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
=> ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
= ( k1_funct_4 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_funct_4) ).
thf(5059,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
=> ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
= ( k1_funct_4 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1264,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k2_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).
thf(6591,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ C )
=> ( r1_tarski @ ( k2_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).
thf(3986,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1104,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ( ( v2_borsuk_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v6_compts_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_borsuk_1) ).
thf(5929,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ( ( ( v2_borsuk_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v6_compts_1 @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v6_compts_1 @ C @ A ) ) )
=> ( v2_borsuk_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(173,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_tops_1) ).
thf(2058,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) @ ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(537,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) @ ( k17_borsuk_1 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_borsuk_1) ).
thf(3537,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) @ ( k17_borsuk_1 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(1928,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
| ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(431,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r1_lattice4 @ A @ B @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice4) ).
thf(3068,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r1_lattice4 @ A @ B @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_filter_0 @ A @ D @ E ) )
= ( k4_filter_0 @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) )
=> ( r1_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(1005,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(5448,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(985,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B
!= ( k1_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_pre_topc) ).
thf(5353,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( B
!= ( k1_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(375,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ( l3_lattices @ A ) )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_lattice2) ).
thf(2833,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ E ) @ C )
=> ( r3_lattices @ A @ E @ D ) ) ) ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v1_lattice2 @ A )
& ( l3_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ C )
= B ) )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_2) ).
thf(2281,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
& ( ( k2_relat_1 @ C )
= B ) )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1292,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
<=> ? [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
& ( v3_lattice4 @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lattice4) ).
thf(6685,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r1_filter_1 @ A @ B )
=> ? [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
& ( v3_lattice4 @ C @ A @ B ) ) )
& ( ? [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
& ( v3_lattice4 @ C @ A @ B ) )
=> ( r1_filter_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k9_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_0) ).
thf(5210,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k9_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1320,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_subset_1 @ ( k2_pre_topc @ A ) @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_lopclset) ).
thf(6777,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_subset_1 @ ( k2_pre_topc @ A ) @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(918,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( k11_borsuk_1 @ A @ B @ C )
= ( a_3_1_borsuk_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_borsuk_1) ).
thf(5096,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( k11_borsuk_1 @ A @ B @ C )
= ( a_3_1_borsuk_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(533,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).
thf(3505,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
| ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1370,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k1_lattice2 @ ( k8_filter_1 @ A @ B ) )
= ( k8_filter_1 @ ( k1_lattice2 @ A ) @ ( k1_lattice2 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_1) ).
thf(6947,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k1_lattice2 @ ( k8_filter_1 @ A @ B ) )
= ( k8_filter_1 @ ( k1_lattice2 @ A ) @ ( k1_lattice2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(1072,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ ( k5_lattices @ A ) @ ( k3_filter_0 @ A @ B ) )
& ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ( ( k2_lattice4 @ A @ C )
= ( k5_lattices @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lopclset) ).
thf(5772,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r2_hidden @ ( k5_lattices @ A ) @ ( k3_filter_0 @ A @ B ) )
& ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( ( r1_tarski @ C @ B )
& ( ( k2_lattice4 @ A @ C )
= ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(591,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_1) ).
thf(3808,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_3 @ B ) ) )
=> ( ( k1_funct_1 @ ( k3_funct_3 @ B ) @ A )
= ( k10_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funct_3) ).
thf(1796,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_3 @ B ) ) )
=> ( ( k1_funct_1 @ ( k3_funct_3 @ B ) @ A )
= ( k10_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ D )
& ( r1_xboole_0 @ B @ D )
& ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_xboole_1) ).
thf(2530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ D )
& ( r1_xboole_0 @ B @ D )
& ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
thf(1622,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ( B != C )
& ( B != k1_xboole_0 )
& ( C != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(2424,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k1_funct_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1205,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_filter_0 @ B @ A )
<=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_filter_0) ).
thf(6347,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m1_filter_0 @ B @ A )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) ) )
& ( ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r3_lattices @ A @ C @ D ) )
=> ( r2_hidden @ D @ B ) ) ) ) )
=> ( m1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(8,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) )
= ( k3_lattices @ A @ ( k1_lattice4 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice4) ).
thf(1394,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) )
= ( k3_lattices @ A @ ( k1_lattice4 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(893,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_finset_1) ).
thf(4996,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(449,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_tops_1) ).
thf(3157,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(963,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(5246,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).
thf(4307,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(659,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(4040,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_xboole_0 @ C @ B ) )
=> ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(4536,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_xboole_0 @ C @ B ) )
=> ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(471,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
thf(3243,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(369,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(2809,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(54,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) @ ( k5_finsub_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finsub_1) ).
thf(1600,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) @ ( k5_finsub_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1166,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_relat_1 @ ( k10_filter_0 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_filter_0) ).
thf(6156,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( k3_relat_1 @ ( k10_filter_0 @ A @ B ) )
= ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m2_relset_1 @ E @ A @ C )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( m2_relset_1 @ E @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(3211,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( m2_relset_1 @ E @ A @ C )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( m2_relset_1 @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(261,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) ) @ ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_3) ).
thf(2392,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) ) @ ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(199,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pre_topc) ).
thf(2154,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(618,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ B @ D ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ A @ B @ D ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lattices) ).
thf(3906,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ A @ B @ D ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ A @ B @ D ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1324,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v3_filter_0 @ A )
& ( v3_filter_0 @ B ) )
<=> ( v3_filter_0 @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_1) ).
thf(6787,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v3_filter_0 @ A )
& ( v3_filter_0 @ B ) )
=> ( v3_filter_0 @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v3_filter_0 @ ( k8_filter_1 @ A @ B ) )
=> ( ( v3_filter_0 @ A )
& ( v3_filter_0 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(807,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_mcart_1) ).
thf(4628,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(84,axiom,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(1696,plain,
! [A: $i,B: $i] :
~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= k1_xboole_0 )
& ( A != k1_xboole_0 )
& ( A
!= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1343,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ ( k9_filter_0 @ A @ B @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_filter_1) ).
thf(6860,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ ( k9_filter_0 @ A @ B @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(311,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(2586,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(768,axiom,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(4483,plain,
! [A: $i] :
( ( l2_struct_0 @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(669,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_tops_1) ).
thf(4065,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(3899,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(1342,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v12_lattices @ A )
& ( v12_lattices @ B ) )
<=> ( v12_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_1) ).
thf(6856,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v12_lattices @ A )
& ( v12_lattices @ B ) )
=> ( v12_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v12_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v12_lattices @ A )
& ( v12_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(485,axiom,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(3303,plain,
! [A: $i] :
( ( l1_lattices @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1306,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( k3_filter_0 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_filter_0) ).
thf(6731,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( k3_filter_0 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(924,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
<=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( D = A )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_lopclset) ).
thf(5117,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
=> ( ( ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) )
=> ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( D = A )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_filter_0 @ D @ B )
& ( D = A )
& ( v1_filter_0 @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ A @ ( k1_funct_1 @ ( k8_lopclset @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).
thf(2641,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k9_relat_1 @ C @ A )
= ( k2_relat_1 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1309,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( v2_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_pre_topc) ).
thf(6741,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( v2_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(1152,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r1_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_filter_0) ).
thf(6092,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r1_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1180,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v13_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( ( k5_lattices @ ( k5_filter_1 @ A @ B ) )
= ( k6_filter_1 @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_1) ).
thf(6200,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v13_lattices @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v13_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( ( k5_lattices @ ( k5_filter_1 @ A @ B ) )
= ( k6_filter_1 @ A @ B @ ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(828,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_funct_1) ).
thf(4700,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(72,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
=> ( ( ( k1_funct_1 @ A @ C )
= D )
<=> ( ( k1_funct_1 @ B @ D )
= C ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
thf(1651,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
=> ( ( ( ( k1_funct_1 @ A @ C )
= D )
=> ( ( k1_funct_1 @ B @ D )
= C ) )
& ( ( ( k1_funct_1 @ B @ D )
= C )
=> ( ( k1_funct_1 @ A @ C )
= D ) ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(940,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k6_pre_topc @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
thf(5174,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k6_pre_topc @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(3151,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) @ C )
<=> ( ( r2_hidden @ B @ C )
& ( r1_tarski @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_setwiseo) ).
thf(2011,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) @ C )
=> ( ( r2_hidden @ B @ C )
& ( r1_tarski @ A @ C ) ) )
& ( ( ( r2_hidden @ B @ C )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(604,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v14_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ E @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) ) ) )
=> ( r3_lattices @ C @ E @ ( k3_lattice2 @ A @ C @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_lattice2) ).
thf(3857,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v14_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ E @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) ) ) )
=> ( r3_lattices @ C @ E @ ( k3_lattice2 @ A @ C @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(994,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( r2_hidden @ B @ ( k1_lopclset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_lopclset) ).
thf(5406,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( r2_hidden @ B @ ( k1_lopclset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(899,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ E )
=> ( ( k1_funct_1 @ C @ F )
= ( k1_funct_1 @ D @ F ) ) ) )
=> ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ C @ E ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_lattice2) ).
thf(5012,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ E )
=> ( ( k1_funct_1 @ C @ F )
= ( k1_funct_1 @ D @ F ) ) ) )
=> ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ C @ E ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1317,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
<=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v11_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_lattice2) ).
thf(6760,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v11_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v10_lattices @ ( k1_lattice2 @ A ) )
& ( v11_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1093,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_borsuk_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( A
= ( k3_tarski @ D ) )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_borsuk_1) ).
thf(5875,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_borsuk_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( A
= ( k3_tarski @ D ) )
& ( r2_hidden @ D @ C ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
& ( A
= ( k3_tarski @ D ) )
& ( r2_hidden @ D @ C ) )
=> ( r2_hidden @ A @ ( a_2_0_borsuk_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( m2_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_realset1) ).
thf(4589,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( ( m2_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) )
=> ( m2_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1214,axiom,
? [A: $i] : ( l2_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(6406,plain,
? [A: $i] : ( l2_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(452,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_3) ).
thf(3169,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(1196,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(6296,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(4480,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(478,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(3265,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(1136,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_pre_topc) ).
thf(6047,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( m1_subset_1 @ ( u1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( m1_realset1 @ C @ A @ B )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_realset1) ).
thf(2646,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( m1_realset1 @ C @ A @ B )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
=> ( m1_realset1 @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(552,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(3635,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(2164,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(1002,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(5438,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1163,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v16_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_filter_0) ).
thf(6139,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v12_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v16_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(1143,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_lattices) ).
thf(6064,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v17_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v11_lattices @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(6058,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(1263,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(6588,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(998,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) )
& ( m1_pre_topc @ ( k3_pre_topc @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pre_topc) ).
thf(5416,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) )
& ( m1_pre_topc @ ( k3_pre_topc @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).
thf(4370,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(580,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_tops_1) ).
thf(3767,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) )
=> ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(794,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(4576,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(235,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
=> ( ( k2_tops_1 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_tops_1) ).
thf(2307,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
=> ( ( k2_tops_1 @ A @ ( k1_tops_1 @ A @ B ) )
= ( k2_tops_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(427,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_setwiseo) ).
thf(3054,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).
thf(4059,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1225,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(6442,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(359,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k1_tops_1 @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_tops_1) ).
thf(2773,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k1_tops_1 @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(894,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( k3_tarski @ ( k5_subset_1 @ B @ C @ D ) )
= ( k3_xboole_0 @ ( k3_tarski @ C ) @ ( k3_tarski @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_borsuk_1) ).
thf(4999,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
=> ( ( k3_tarski @ ( k5_subset_1 @ B @ C @ D ) )
= ( k3_xboole_0 @ ( k3_tarski @ C ) @ ( k3_tarski @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(2264,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r2_hidden @ C @ A )
| ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(476,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
thf(3261,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( v3_pre_topc @ ( k1_tops_1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(1038,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r3_lattice4 @ A @ B @ C )
<=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice4) ).
thf(5611,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r3_lattice4 @ A @ B @ C )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) ) )
& ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k5_lattices @ A ) )
= ( k5_lattices @ B ) )
=> ( r3_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(3827,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k4_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
thf(5002,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1129,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v2_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(6032,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v2_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(756,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(4434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_3) ).
thf(1666,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1256,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(6565,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(3371,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(759,axiom,
( ( k2_funct_4 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funct_5) ).
thf(4449,plain,
( ( k2_funct_4 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(1296,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k12_lopclset @ A )
= ( k6_lopclset @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lopclset) ).
thf(6696,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k12_lopclset @ A )
= ( k6_lopclset @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(1184,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(6232,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(263,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_1) ).
thf(2396,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(650,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_funct_4 @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k1_funct_4) ).
thf(4016,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k1_funct_4 @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(2805,plain,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(547,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(3603,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(1335,axiom,
( ~ ( v3_struct_0 @ k22_borsuk_1 )
& ( v1_pre_topc @ k22_borsuk_1 )
& ( v2_pre_topc @ k22_borsuk_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_borsuk_1) ).
thf(6820,plain,
( ~ ( v3_struct_0 @ k22_borsuk_1 )
& ( v1_pre_topc @ k22_borsuk_1 )
& ( v2_pre_topc @ k22_borsuk_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_3) ).
thf(2249,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1033,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v13_lattices @ A )
& ( r3_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattice4) ).
thf(5579,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v13_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v13_lattices @ A )
& ( r3_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(1023,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_pre_topc) ).
thf(5512,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(868,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ B @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_tops_1) ).
thf(4878,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ B @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1318,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
=> ( r1_filter_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_filter_1) ).
thf(6773,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r1_filter_1 @ A @ B )
=> ( r1_filter_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(891,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(4989,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_xboole_1) ).
thf(2133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ B )
& ! [D: $i] :
( ( ( r1_tarski @ A @ D )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ B @ D ) ) )
=> ( B
= ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(2147,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
& ( r2_hidden @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(5266,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(1008,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k4_lattice4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice4) ).
thf(5455,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k4_lattice4 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(1502,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1083,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v2_pre_topc @ A )
<=> ( ( r2_hidden @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( u1_pre_topc @ A ) )
=> ( r2_hidden @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( u1_pre_topc @ A ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( u1_pre_topc @ A ) )
& ( r2_hidden @ C @ ( u1_pre_topc @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( u1_pre_topc @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_pre_topc) ).
thf(5815,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( ( v2_pre_topc @ A )
=> ( ( r2_hidden @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( u1_pre_topc @ A ) )
=> ( r2_hidden @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( u1_pre_topc @ A ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( u1_pre_topc @ A ) )
& ( r2_hidden @ C @ ( u1_pre_topc @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( u1_pre_topc @ A ) ) ) ) ) ) )
& ( ( ( r2_hidden @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ ( u1_pre_topc @ A ) )
=> ( r2_hidden @ ( k5_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ ( u1_pre_topc @ A ) ) ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( u1_pre_topc @ A ) )
& ( r2_hidden @ C @ ( u1_pre_topc @ A ) ) )
=> ( r2_hidden @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ ( u1_pre_topc @ A ) ) ) ) ) )
=> ( v2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(778,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(4521,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) ) )
& ( ! [B: $i,C: $i] :
( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
& ( ( k1_funct_1 @ A @ B )
= ( k1_funct_1 @ A @ C ) ) )
=> ( B = C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_realset1) ).
thf(3989,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(845,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( r2_borsuk_1 @ A @ B )
<=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ( v5_pre_topc @ C @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k23_borsuk_1 ) )
= D )
& ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k24_borsuk_1 ) ) @ ( u1_struct_0 @ B ) )
& ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ k22_borsuk_1 ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ E ) )
= D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_borsuk_1) ).
thf(4785,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ( ( ( r2_borsuk_1 @ A @ B )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ( v5_pre_topc @ C @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k23_borsuk_1 ) )
= D )
& ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k24_borsuk_1 ) ) @ ( u1_struct_0 @ B ) )
& ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ k22_borsuk_1 ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ E ) )
= D ) ) ) ) ) ) )
& ( ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ( v5_pre_topc @ C @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) @ A )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k23_borsuk_1 ) )
= D )
& ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ k24_borsuk_1 ) ) @ ( u1_struct_0 @ B ) )
& ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ k22_borsuk_1 ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ k22_borsuk_1 ) ) @ ( u1_struct_0 @ A ) @ C @ ( k8_borsuk_1 @ A @ k22_borsuk_1 @ D @ E ) )
= D ) ) ) ) ) )
=> ( r2_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(773,axiom,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).
thf(4499,plain,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(722,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lopclset) ).
thf(4284,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(1619,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1238,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( C
= ( k8_borsuk_1 @ A @ B @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_borsuk_1) ).
thf(6496,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( C
= ( k8_borsuk_1 @ A @ B @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(1096,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m1_filter_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
<=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_filter_0) ).
thf(5893,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) ) ) ) ) )
=> ( m1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(5507,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(920,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_lattice2) ).
thf(5102,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1175,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(6178,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).
thf(3471,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ D ) )
& ( r1_xboole_0 @ C @ A )
& ( r1_xboole_0 @ D @ B ) )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_xboole_1) ).
thf(1883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( k2_xboole_0 @ A @ B )
= ( k2_xboole_0 @ C @ D ) )
& ( r1_xboole_0 @ C @ A )
& ( r1_xboole_0 @ D @ B ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(661,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ D @ C ) ) @ ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_1) ).
thf(4044,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ D @ C ) ) @ ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1102,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ E ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k5_filter_0 @ A @ D @ E ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k5_filter_0 @ A @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_0) ).
thf(5924,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [E: $i] :
( ( ~ ( v1_xboole_0 @ E )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ E ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ B @ C ) @ ( k5_filter_0 @ A @ D @ E ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ B ) @ ( k5_filter_0 @ A @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) )
& ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_4) ).
thf(3198,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) )
& ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(483,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
<=> ( v2_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tops_1) ).
thf(3297,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) )
& ( ( v2_tops_1 @ ( k6_pre_topc @ A @ B ) @ A )
=> ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(901,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).
thf(5021,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k2_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(614,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_funct_1) ).
thf(3894,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(702,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lattices) ).
thf(4187,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(419,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(3028,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(674,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k1_pre_topc @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_pre_topc) ).
thf(4080,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k1_pre_topc @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tops_1) ).
thf(5285,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1300,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k1_lopclset @ A )
= ( a_1_0_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lopclset) ).
thf(6709,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k1_lopclset @ A )
= ( a_1_0_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_subset_1) ).
thf(1423,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(487,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_tops_1) ).
thf(3307,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) )
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1071,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
<=> ( r2_hidden @ B @ ( u1_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_pre_topc) ).
thf(5769,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( r2_hidden @ B @ ( u1_pre_topc @ A ) ) )
& ( ( r2_hidden @ B @ ( u1_pre_topc @ A ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).
thf(3958,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k3_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(6303,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k3_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k3_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(279,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_qc_lang1) ).
thf(2464,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(1057,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(5702,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(975,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_tops_1 @ A @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C )
& ( r2_hidden @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_tops_1) ).
thf(5302,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ B @ ( k1_tops_1 @ A @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C )
& ( r2_hidden @ B @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ C )
& ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ B @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(1602,plain,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1276,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v17_lattices @ ( k6_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_lopclset) ).
thf(6629,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v17_lattices @ ( k6_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(690,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ D )
=> ( r3_lattices @ A @ ( k3_lattice2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_lattice2) ).
thf(4140,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ D )
=> ( r3_lattices @ A @ ( k3_lattice2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(321,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_tops_1) ).
thf(2628,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(592,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v2_tops_1 @ B @ A ) )
=> ( ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(3810,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v2_tops_1 @ B @ A ) )
=> ( ( v2_tops_1 @ B @ A )
& ( v3_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1012,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_filter_0) ).
thf(5465,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ B )
= ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_realset1) ).
thf(4608,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] :
( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
thf(2663,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1134,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k1_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_tops_1) ).
thf(6043,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k1_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(1194,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k11_borsuk_1 @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_borsuk_1) ).
thf(6292,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k11_borsuk_1 @ A @ B @ C ) @ ( k11_borsuk_1 @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(572,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
thf(3718,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_pre_topc @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(609,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k9_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(3877,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k9_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(786,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_relat_1) ).
thf(4553,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_funct_1) ).
thf(3546,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(903,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ B @ C ) ) )
=> ( r2_hidden @ D @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_borsuk_1) ).
thf(5038,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ B @ C ) ) )
=> ( r2_hidden @ D @ ( u1_struct_0 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(749,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) )
= ( k6_pre_topc @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_tops_1) ).
thf(4402,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) )
= ( k6_pre_topc @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(536,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(3535,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).
thf(2344,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ~ ( ( ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(237,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
<=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_tops_1) ).
thf(2313,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ B @ C )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) ) )
& ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1106,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(5936,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(213,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_4 @ A @ B ) ) @ ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_4) ).
thf(2228,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_4 @ A @ B ) ) @ ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(3033,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(3408,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
= ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(1740,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k4_subset_1 @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_xboole_1) ).
thf(1910,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_xboole_1) ).
thf(2300,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
<=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(2157,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
=> ~ ( r2_hidden @ B @ A ) )
& ( ~ ( r2_hidden @ B @ A )
=> ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_realset1) ).
thf(2946,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(4974,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1294,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_0) ).
thf(6691,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v11_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(1267,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( k2_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) @ B @ C )
= ( k3_lopclset @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lopclset) ).
thf(6603,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [E: $i] :
( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( k2_lattices @ ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) @ B @ C )
= ( k3_lopclset @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k7_subset_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).
thf(3381,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k7_subset_1 @ A @ B @ C )
= ( k7_subset_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(663,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( v2_funct_1 @ C ) )
=> ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_funct_1) ).
thf(4048,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ A @ B )
& ( v2_funct_1 @ C ) )
=> ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(534,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
thf(3518,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k1_relat_1 @ B )
= A )
& ( ( k1_relat_1 @ C )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(436,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ ( k4_lattice4 @ A @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ ( k4_lattice4 @ A @ B ) )
& ( ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ C @ ( k5_lattice4 @ A ) )
= ( k2_lattice4 @ A @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattice4) ).
thf(3119,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ C @ ( k4_lattice4 @ A @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ ( k4_lattice4 @ A @ B ) )
& ( ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ C @ ( k5_lattice4 @ A ) )
= ( k2_lattice4 @ A @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1156,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_1) ).
thf(6111,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).
thf(3916,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(682,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(4109,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(1111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k8_borsuk_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_borsuk_1) ).
thf(5951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k8_borsuk_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(1305,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_filter_0) ).
thf(6728,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k1_filter_0 @ A )
= ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(575,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( C != k1_xboole_0 )
=> ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
& ( v1_funct_2 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
& ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_funct_4) ).
thf(3731,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( C != k1_xboole_0 )
=> ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
& ( v1_funct_2 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
& ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(635,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(3968,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(686,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(4123,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ A @ C )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1327,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( u1_struct_0 @ ( k6_lopclset @ A ) )
= ( k1_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_lopclset) ).
thf(6795,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( u1_struct_0 @ ( k6_lopclset @ A ) )
= ( k1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(619,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i,D: $i] :
( ( ( g1_pre_topc @ A @ B )
= ( g1_pre_topc @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_pre_topc) ).
thf(3909,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i,D: $i] :
( ( ( g1_pre_topc @ A @ B )
= ( g1_pre_topc @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(1097,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_filter_0 @ ( k3_filter_0 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_filter_0) ).
thf(5904,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_filter_0 @ ( k3_filter_0 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(3482,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(953,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k5_lattices @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_lattices) ).
thf(5221,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ ( k5_lattices @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(183,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
thf(2100,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_4 @ B @ C ) ) )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
| ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funct_4) ).
thf(3413,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_4 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
| ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
| ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_4 @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(960,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) )
& ( v2_pre_topc @ ( k3_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_pre_topc) ).
thf(5238,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) )
& ( v2_pre_topc @ ( k3_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(336,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
<=> ( ( k6_pre_topc @ A @ B )
= ( k2_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tops_1) ).
thf(2685,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
=> ( ( k6_pre_topc @ A @ B )
= ( k2_pre_topc @ A ) ) )
& ( ( ( k6_pre_topc @ A @ B )
= ( k2_pre_topc @ A ) )
=> ( v1_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(343,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
= ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_relat_1) ).
thf(2709,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
= ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1079,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(5798,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
& ( ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(338,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(2692,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(36,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( m2_subset_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_lopclset) ).
thf(1498,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( m2_subset_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(339,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) ) )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_tops_1) ).
thf(2694,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k6_pre_topc @ A @ C ) ) )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(858,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(4845,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( l1_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1000,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v14_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( ( k6_lattices @ ( k5_filter_1 @ A @ B ) )
= ( k6_filter_1 @ A @ B @ ( k6_lattices @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_1) ).
thf(5428,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v14_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) )
& ( ( k6_lattices @ ( k5_filter_1 @ A @ B ) )
= ( k6_filter_1 @ A @ B @ ( k6_lattices @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(567,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( v1_tops_1 @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_tops_1) ).
thf(3704,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( v1_tops_1 @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).
thf(3386,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v1_xboole_0 @ ( k18_borsuk_1 @ A @ B @ C ) )
& ( m1_eqrel_1 @ ( k18_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k18_borsuk_1) ).
thf(2726,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A )
& ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ~ ( v1_xboole_0 @ ( k18_borsuk_1 @ A @ B @ C ) )
& ( m1_eqrel_1 @ ( k18_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(1100,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(5919,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(709,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k3_lattices @ ( k1_lattice2 @ A ) @ D @ E ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k4_lattices @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_lattice2) ).
thf(4227,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( B = D )
& ( C = E ) )
=> ( ( ( k4_lattices @ A @ B @ C )
= ( k3_lattices @ ( k1_lattice2 @ A ) @ D @ E ) )
& ( ( k3_lattices @ A @ B @ C )
= ( k4_lattices @ ( k1_lattice2 @ A ) @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1119,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r2_hidden @ ( k6_lattices @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_filter_0) ).
thf(5978,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( r2_hidden @ ( k6_lattices @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(2537,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(1362,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k12_filter_0 @ A @ B )
= ( k10_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_filter_0) ).
thf(6919,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k12_filter_0 @ A @ B )
= ( k10_filter_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(1274,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k7_filter_0 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_0) ).
thf(6624,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k7_filter_0 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(455,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v3_realset2 @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_realset2) ).
thf(3176,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v3_realset2 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B = C ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( B = C ) ) )
=> ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k2_setwiseo @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_setwiseo) ).
thf(1397,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k2_setwiseo @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(731,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k9_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(4320,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k9_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ E @ B )
& ( D
= ( k1_funct_1 @ A @ E ) ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k9_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_realset1) ).
thf(4518,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(443,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
& ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(3143,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
& ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(721,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v3_pre_topc @ C @ A ) )
=> ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_tops_1) ).
thf(4276,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v3_pre_topc @ C @ A ) )
=> ( C = k1_xboole_0 ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r1_tarski @ C @ B )
& ( v3_pre_topc @ C @ A ) )
=> ( C = k1_xboole_0 ) ) )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1099,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_funct_1 @ ( k9_lopclset @ A ) )
& ( v1_funct_2 @ ( k9_lopclset @ A ) @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) )
& ( m2_relset_1 @ ( k9_lopclset @ A ) @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_lopclset) ).
thf(5915,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_funct_1 @ ( k9_lopclset @ A ) )
& ( v1_funct_2 @ ( k9_lopclset @ A ) @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) )
& ( m2_relset_1 @ ( k9_lopclset @ A ) @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(912,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_tops_1) ).
thf(5080,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(921,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k5_filter_0 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_filter_0) ).
thf(5107,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k5_filter_0 @ A @ B @ C ) )
& ( r1_tarski @ C @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(697,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( k6_pre_topc @ A @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_tops_1) ).
thf(4167,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( k6_pre_topc @ A @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r1_tarski @ C @ A )
& ( r1_tarski @ C @ B )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(4389,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ~ ( ( r1_tarski @ C @ A )
& ( r1_tarski @ C @ B )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(1090,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(5865,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ B )
& ( r2_hidden @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_relat_1) ).
thf(3643,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(836,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(4736,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k10_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc18_finseq_1) ).
thf(4530,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k10_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(582,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relat_1) ).
thf(3775,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(442,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(3141,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(880,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_filter_0 @ C @ B )
& ( m1_filter_0 @ D @ B ) )
=> ( ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).
thf(4951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_filter_0 @ C @ B )
& ( m1_filter_0 @ D @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A = E )
& ? [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
& ? [G: $i] :
( ( m1_subset_1 @ G @ ( u1_struct_0 @ B ) )
& ( r3_lattices @ B @ ( k4_lattices @ B @ F @ G ) @ E )
& ( r2_hidden @ F @ C )
& ( r2_hidden @ G @ D ) ) ) )
=> ( r2_hidden @ A @ ( a_3_1_filter_0 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1054,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(5694,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ C )
=> ( ( r1_tarski @ A @ D )
=> ( m2_relset_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(3000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ B @ C )
=> ( ( r1_tarski @ A @ D )
=> ( m2_relset_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(796,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 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_subset_1) ).
thf(4582,plain,
! [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 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1157,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v13_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_filter_0) ).
thf(6116,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v13_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_xboole_1) ).
thf(2561,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(1265,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k3_pre_topc @ A @ B ) )
& ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_pre_topc) ).
thf(6593,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ~ ( v3_struct_0 @ ( k3_pre_topc @ A @ B ) )
& ( v1_pre_topc @ ( k3_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(1121,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
<=> ( v14_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_lattice2) ).
thf(5992,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v13_lattices @ A )
=> ( v14_lattices @ ( k1_lattice2 @ A ) ) )
& ( ( v14_lattices @ ( k1_lattice2 @ A ) )
=> ( v13_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(574,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(3728,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(752,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).
thf(4421,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ! [E: $i] :
( ( r2_hidden @ E @ A )
=> ( ( k1_funct_1 @ C @ E )
= ( k1_funct_1 @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(729,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).
thf(4315,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_xboole_0 @ B @ C )
<=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(1414,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
& ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_xboole_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(211,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k2_funct_1 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(2196,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k2_funct_1 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k2_relat_1 @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
& ( D
= ( k1_funct_1 @ B @ C ) ) ) ) ) )
=> ( B
= ( k2_funct_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
& ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(1842,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
& ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1030,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice2) ).
thf(5547,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k1_lattice2 @ A ) )
& ( v3_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(1700,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1169,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_0) ).
thf(6164,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ B @ C )
= ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ C @ E ) @ D )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_lattice2) ).
thf(1937,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ C @ E ) @ D )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_xboole_1) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(813,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_filter_0 @ A @ B )
= ( a_2_0_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_filter_0) ).
thf(4648,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_filter_0 @ A @ B )
= ( a_2_0_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(665,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_connsp_2 @ E @ A @ C )
=> ! [F: $i] :
( ( m1_connsp_2 @ F @ B @ D )
=> ( m1_connsp_2 @ ( k7_borsuk_1 @ A @ B @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k8_borsuk_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_borsuk_1) ).
thf(4054,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_connsp_2 @ E @ A @ C )
=> ! [F: $i] :
( ( m1_connsp_2 @ F @ B @ D )
=> ( m1_connsp_2 @ ( k7_borsuk_1 @ A @ B @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k8_borsuk_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(1239,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_filter_0) ).
thf(6501,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_filter_0 @ A @ B ) @ ( k3_filter_0 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(2108,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(1889,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k2_funct_2 @ A @ B @ C @ D )
= ( k9_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(542,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( B
= ( k2_relat_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(3555,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( B
= ( k2_relat_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( C
= ( k1_funct_1 @ A @ D ) ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(1644,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1189,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( v1_tops_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_tops_1) ).
thf(6275,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
& ( r1_tarski @ B @ C ) )
=> ( v1_tops_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).
thf(2681,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ C )
<=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_subset_1) ).
thf(1530,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) )
& ( ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) )
=> ( r1_tarski @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1181,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_zfmisc_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(6207,plain,
! [A: $i,B: $i] :
( ( ( B
= ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ( r1_tarski @ C @ A ) )
& ( ( r1_tarski @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
=> ( B
= ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(1347,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_filter_1) ).
thf(6876,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v3_struct_0 @ ( k5_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k5_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k5_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k5_filter_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k12_mcart_1) ).
thf(2581,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( k12_mcart_1 @ A @ B @ C @ D )
= ( k2_zfmisc_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(114,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ ( k1_lattice2 @ B ) ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ ( k1_lattice2 @ B ) ) ) )
=> ( ( D = E )
=> ( ( ( k2_lattice2 @ A @ B @ C @ D )
= ( k3_lattice2 @ A @ ( k1_lattice2 @ B ) @ C @ E ) )
& ( ( k3_lattice2 @ A @ B @ C @ D )
= ( k2_lattice2 @ A @ ( k1_lattice2 @ B ) @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattice2) ).
thf(1799,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ ( k1_lattice2 @ B ) ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ ( k1_lattice2 @ B ) ) ) )
=> ( ( D = E )
=> ( ( ( k2_lattice2 @ A @ B @ C @ D )
= ( k3_lattice2 @ A @ ( k1_lattice2 @ B ) @ C @ E ) )
& ( ( k3_lattice2 @ A @ B @ C @ D )
= ( k2_lattice2 @ A @ ( k1_lattice2 @ B ) @ C @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(4120,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_xboole_1) ).
thf(1852,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).
thf(2697,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(405,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_tops_1) ).
thf(2968,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ B ) @ ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(1314,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_relat_1 @ ( k9_filter_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_filter_1) ).
thf(6752,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v1_relat_1 @ ( k9_filter_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(979,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_0) ).
thf(5317,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1161,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( ( r2_hidden @ ( k3_tarski @ C ) @ ( u1_pre_topc @ A ) )
<=> ( r2_hidden @ C @ ( u1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_borsuk_1) ).
thf(6134,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ( ( ( r2_hidden @ ( k3_tarski @ C ) @ ( u1_pre_topc @ A ) )
=> ( r2_hidden @ C @ ( u1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) )
& ( ( r2_hidden @ C @ ( u1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) )
=> ( r2_hidden @ ( k3_tarski @ C ) @ ( u1_pre_topc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(274,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
=> ( ( v4_tops_1 @ ( k1_tops_1 @ A @ B ) @ A )
& ( v4_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_tops_1) ).
thf(2450,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
=> ( ( v4_tops_1 @ ( k1_tops_1 @ A @ B ) @ A )
& ( v4_tops_1 @ ( k6_pre_topc @ A @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(558,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lopclset) ).
thf(3654,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(1015,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(5481,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(1154,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( C
= ( k3_pre_topc @ A @ B ) )
<=> ( ( k2_pre_topc @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_pre_topc) ).
thf(6097,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( m1_pre_topc @ C @ A ) )
=> ( ( ( C
= ( k3_pre_topc @ A @ B ) )
=> ( ( k2_pre_topc @ C )
= B ) )
& ( ( ( k2_pre_topc @ C )
= B )
=> ( C
= ( k3_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(989,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_subset_1 @ ( k1_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lopclset) ).
thf(5374,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_subset_1 @ ( k1_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(934,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k6_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k6_lattices @ A ) @ ( k6_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_filter_1) ).
thf(5149,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v14_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( k6_lattices @ ( k8_filter_1 @ A @ B ) )
= ( k10_filter_1 @ A @ B @ ( k6_lattices @ A ) @ ( k6_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k10_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_funct_1) ).
thf(2304,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k10_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(260,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(2387,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k2_relat_1 @ A )
= ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
& ( ( k1_relat_1 @ A )
= ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(121,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
thf(1831,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(578,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(3743,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(1045,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_0) ).
thf(5639,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k5_filter_0 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(928,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(5134,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_filter_0) ).
thf(5234,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k4_filter_0 @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
& ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g3_lattices) ).
thf(1668,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ( v3_lattices @ ( g3_lattices @ A @ B @ C ) )
& ( l3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_xboole_1) ).
thf(1974,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_subset_1) ).
thf(2505,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(711,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(4237,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(511,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_lattice4 @ C @ B @ A )
& ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ F ) ) )
=> ( r3_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice4) ).
thf(3390,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( v1_lattice4 @ C @ B @ A )
& ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ F ) ) )
=> ( r3_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(853,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_4 @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_4) ).
thf(4829,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_4 @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_lattice4) ).
thf(3222,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(875,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
= ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_2) ).
thf(4934,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
= ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(286,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ( v3_realset2 @ A )
<=> ? [B: $i] :
( ( u1_struct_0 @ A )
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_group_6) ).
thf(2497,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ( ( ( v3_realset2 @ A )
=> ? [B: $i] :
( ( u1_struct_0 @ A )
= ( k1_tarski @ B ) ) )
& ( ? [B: $i] :
( ( u1_struct_0 @ A )
= ( k1_tarski @ B ) )
=> ( v3_realset2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1228,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( m1_pre_topc @ B @ A )
<=> ( ( r1_tarski @ ( k2_pre_topc @ B ) @ ( k2_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ C @ ( u1_pre_topc @ B ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_pre_topc) ).
thf(6450,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ( ( ( m1_pre_topc @ B @ A )
=> ( ( r1_tarski @ ( k2_pre_topc @ B ) @ ( k2_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ C @ ( u1_pre_topc @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) )
=> ( r2_hidden @ C @ ( u1_pre_topc @ B ) ) ) ) ) ) )
& ( ( ( r1_tarski @ ( k2_pre_topc @ B ) @ ( k2_pre_topc @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ C @ ( u1_pre_topc @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ A ) )
& ( C
= ( k3_xboole_0 @ D @ ( k2_pre_topc @ B ) ) ) )
=> ( r2_hidden @ C @ ( u1_pre_topc @ B ) ) ) ) ) )
=> ( m1_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(1124,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_filter_0) ).
thf(6005,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( v1_filter_0 @ B @ A )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) )
=> ( v1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(951,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_pre_topc @ ( k1_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_tops_1) ).
thf(5217,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v3_pre_topc @ ( k1_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(377,axiom,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(2862,plain,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(689,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_relat_1) ).
thf(4135,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 )
& ( ( k5_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(1323,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_filter_0 @ A @ ( k1_filter_0 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_filter_0) ).
thf(6784,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_filter_0 @ A @ ( k1_filter_0 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(693,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(4152,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( ( k5_setwiseo @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_setwiseo) ).
thf(1720,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( ( k5_setwiseo @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1035,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(5603,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(988,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_0) ).
thf(5369,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) ) )
& ( ( ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) )
= ( k5_lattices @ A ) )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r2_hidden @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(6152,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r2_hidden @ B @ A )
=> ( ( ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r2_hidden @ B @ D ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ C )
=> ( r2_hidden @ B @ D ) )
=> ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(824,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattices) ).
thf(4689,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) )
= ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k21_borsuk_1 @ A @ B @ C )
= ( k16_borsuk_1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k21_borsuk_1) ).
thf(4069,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k21_borsuk_1 @ A @ B @ C )
= ( k16_borsuk_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ ( k10_relat_1 @ C @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_borsuk_1) ).
thf(3005,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ ( k10_relat_1 @ C @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(2272,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(504,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
<=> ( ~ ( v3_struct_0 @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_pre_topc) ).
thf(3364,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) )
=> ( ~ ( v3_struct_0 @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) ) )
& ( ( ~ ( v3_struct_0 @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ D @ A )
& ( r2_hidden @ C @ D )
& ( r1_xboole_0 @ B @ D ) ) ) )
=> ( r2_hidden @ C @ ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_3) ).
thf(2140,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(676,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relat_1) ).
thf(4086,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( l1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_borsuk_1) ).
thf(2756,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( l1_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(451,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) @ B ) ) )
=> ( ( D = k1_xboole_0 )
| ( r3_lattices @ A @ ( k2_lattice2 @ C @ A @ D @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice2) ).
thf(3162,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) @ B ) ) )
=> ( ( D = k1_xboole_0 )
| ( r3_lattices @ A @ ( k2_lattice2 @ C @ A @ D @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(462,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) )
= ( k1_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_tops_1) ).
thf(3201,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) )
= ( k1_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(102,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(1759,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1172,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) )
& ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_pre_topc) ).
thf(6171,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( v1_pre_topc @ ( g1_pre_topc @ A @ B ) )
& ( l1_pre_topc @ ( g1_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(4352,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ A @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(812,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(4644,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1167,axiom,
m1_subset_1 @ k24_borsuk_1 @ ( u1_struct_0 @ k22_borsuk_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k24_borsuk_1) ).
thf(6160,plain,
m1_subset_1 @ k24_borsuk_1 @ ( u1_struct_0 @ k22_borsuk_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) )
=> ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).
thf(2883,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ D ) )
=> ( ( v1_funct_1 @ E )
& ( m2_relset_1 @ E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1302,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_filter_1) ).
thf(6716,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_4) ).
thf(2963,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(1207,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattice4) ).
thf(6378,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(999,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( C
= ( k6_borsuk_1 @ A @ B ) )
<=> ( ( ( u1_struct_0 @ C )
= ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_pre_topc @ C )
= ( a_3_0_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_borsuk_1) ).
thf(5419,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( ( v1_pre_topc @ C )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( ( C
= ( k6_borsuk_1 @ A @ B ) )
=> ( ( ( u1_struct_0 @ C )
= ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_pre_topc @ C )
= ( a_3_0_borsuk_1 @ A @ B @ C ) ) ) )
& ( ( ( ( u1_struct_0 @ C )
= ( k2_zfmisc_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
& ( ( u1_pre_topc @ C )
= ( a_3_0_borsuk_1 @ A @ B @ C ) ) )
=> ( C
= ( k6_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(1092,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_lopclset @ A ) @ ( k4_lattices @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lopclset) ).
thf(5872,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ ( k8_lopclset @ A ) @ ( k4_lattices @ A @ B @ C ) )
= ( k3_xboole_0 @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(785,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).
thf(4550,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
& ! [C: $i] :
~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(923,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(5112,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(1434,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_lattice2) ).
thf(1857,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(935,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( a_3_0_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_0) ).
thf(5153,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( a_3_0_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(2926,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
<=> ( ( k4_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(2702,plain,
! [A: $i,B: $i] :
( ( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ A @ B )
= A ) )
& ( ( ( k4_xboole_0 @ A @ B )
= A )
=> ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(301,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( D
= ( k3_tarski @ C ) )
=> ( ( k3_subset_1 @ A @ D )
= ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_borsuk_1) ).
thf(2546,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ( D
= ( k3_tarski @ C ) )
=> ( ( k3_subset_1 @ A @ D )
= ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(2043,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
& ( v1_funct_2 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
& ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_4) ).
thf(3183,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
& ( v1_funct_2 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
& ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(882,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( k2_relat_1 @ ( k2_funct_4 @ C ) )
= ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_4) ).
thf(4966,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( k2_relat_1 @ ( k2_funct_4 @ C ) )
= ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(841,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) )
=> ( ( k3_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) )
= ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_3) ).
thf(4765,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) )
=> ( ( k3_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) )
= ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(544,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ D )
=> ( r3_lattices @ A @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ C ) @ ( k2_lattice2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice2) ).
thf(3592,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ D )
=> ( r3_lattices @ A @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ C ) @ ( k2_lattice2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1332,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_filter_1 @ A )
= ( a_1_0_filter_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_1) ).
thf(6812,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_filter_1 @ A )
= ( a_1_0_filter_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( r2_hidden @ D @ B )
<=> ~ ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).
thf(2089,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ( r2_hidden @ D @ B )
=> ~ ( r2_hidden @ D @ C ) )
& ( ~ ( r2_hidden @ D @ C )
=> ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(458,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_borsuk_1) ).
thf(3190,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ C )
= ( k3_lopclset @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lopclset) ).
thf(5126,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k3_lopclset @ A @ B @ C )
= ( k3_lopclset @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1371,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_filter_0) ).
thf(6950,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_xboole_1) ).
thf(1906,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
thf(2729,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1363,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k5_lattices @ A ) )
= ( k6_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lattice4) ).
thf(6922,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lattices @ A @ ( k5_lattices @ A ) )
= ( k6_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(1297,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( v14_lattices @ A )
& ( v14_lattices @ B ) )
<=> ( v14_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_1) ).
thf(6699,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( v14_lattices @ A )
& ( v14_lattices @ B ) )
=> ( v14_lattices @ ( k8_filter_1 @ A @ B ) ) )
& ( ( v14_lattices @ ( k8_filter_1 @ A @ B ) )
=> ( ( v14_lattices @ A )
& ( v14_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
& ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(4874,plain,
! [A: $i,B: $i] :
( ( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
& ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_borsuk_1) ).
thf(3491,plain,
! [A: $i,B: $i,C: $i] :
( ( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( l1_struct_0 @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_funct_1 @ ( k3_borsuk_1 @ A @ B @ C ) )
& ( v1_funct_2 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ ( k3_borsuk_1 @ A @ B @ C ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1149,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pre_topc) ).
thf(6084,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_subset_1 @ ( k1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(98,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_3 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_3) ).
thf(1747,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_3 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1261,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k4_lattice4 @ A @ B )
= ( a_2_0_lattice4 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice4) ).
thf(6578,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k4_lattice4 @ A @ B )
= ( a_2_0_lattice4 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( v1_pre_topc @ D )
& ( v2_pre_topc @ D )
& ( l1_pre_topc @ D ) )
=> ( ( r2_hidden @ A @ ( a_3_0_borsuk_1 @ B @ C @ D ) )
<=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ D ) ) ) )
& ( A
= ( k5_setfam_1 @ ( u1_struct_0 @ D ) @ E ) )
& ( r1_tarski @ E @ ( a_2_1_borsuk_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_borsuk_1) ).
thf(6243,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( v1_pre_topc @ D )
& ( v2_pre_topc @ D )
& ( l1_pre_topc @ D ) )
=> ( ( ( r2_hidden @ A @ ( a_3_0_borsuk_1 @ B @ C @ D ) )
=> ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ D ) ) ) )
& ( A
= ( k5_setfam_1 @ ( u1_struct_0 @ D ) @ E ) )
& ( r1_tarski @ E @ ( a_2_1_borsuk_1 @ B @ C ) ) ) )
& ( ? [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ D ) ) ) )
& ( A
= ( k5_setfam_1 @ ( u1_struct_0 @ D ) @ E ) )
& ( r1_tarski @ E @ ( a_2_1_borsuk_1 @ B @ C ) ) )
=> ( r2_hidden @ A @ ( a_3_0_borsuk_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(774,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(4503,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( l1_lattices @ A )
& ( l2_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1250,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(6546,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(564,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( m1_subset_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_setwiseo) ).
thf(3696,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( m1_subset_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(4365,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(961,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ ( k3_filter_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_filter_0) ).
thf(5241,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ~ ( v1_xboole_0 @ D )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ D @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ C ) ) ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ B ) @ ( k3_filter_0 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(496,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).
thf(3343,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(103,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_tops_1) ).
thf(1764,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(439,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_funct_4 @ ( k2_funct_4 @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_4) ).
thf(3130,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_funct_4 @ ( k2_funct_4 @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(1139,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( v3_filter_0 @ ( k5_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_filter_1) ).
thf(6053,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( v3_filter_0 @ ( k5_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(1062,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) )
= ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_tops_1) ).
thf(5722,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) )
= ( k2_tops_1 @ A @ ( k2_tops_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k2_relat_1 @ B ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_3) ).
thf(4685,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k2_relat_1 @ B ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(741,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
=> ( r1_tarski @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(4380,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
=> ( r1_tarski @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(865,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t177_relat_1) ).
thf(4872,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C )
& ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(2904,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ A @ C )
& ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(78,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_zfmisc_1) ).
thf(1680,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1080,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( v1_filter_0 @ C @ A )
& ~ ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
& ( r2_hidden @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lopclset) ).
thf(5808,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( v1_filter_0 @ C @ A )
& ~ ( r2_hidden @ C @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ B ) )
& ( r2_hidden @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(733,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(4354,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A )
= ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_3) ).
thf(2033,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A )
= ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(930,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_filter_0) ).
thf(5138,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(1271,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v14_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_0) ).
thf(6615,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( v14_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( ( k2_partfun1 @ A @ B @ C @ E )
= ( k2_partfun1 @ A @ B @ D @ E ) )
=> ( ( k2_funct_2 @ A @ B @ C @ E )
= ( k2_funct_2 @ A @ B @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice2) ).
thf(2149,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( ( k2_partfun1 @ A @ B @ C @ E )
= ( k2_partfun1 @ A @ B @ D @ E ) )
=> ( ( k2_funct_2 @ A @ B @ C @ E )
= ( k2_funct_2 @ A @ B @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(804,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(4613,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m2_relset_1 @ D @ C @ A )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
=> ( m2_relset_1 @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1336,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
<=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v11_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_filter_1) ).
thf(6824,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v11_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v11_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_xboole_1) ).
thf(2253,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_4) ).
thf(3871,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k1_funct_4 @ C @ D )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(815,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k8_funct_2 @ A @ B @ C @ E ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_group_6) ).
thf(4657,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( v2_funct_1 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k8_funct_2 @ A @ B @ C @ E ) )
=> ( D = E ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( k8_funct_2 @ A @ B @ C @ D )
= ( k8_funct_2 @ A @ B @ C @ E ) )
=> ( D = E ) ) ) )
=> ( v2_funct_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(1113,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_pre_topc) ).
thf(5960,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1037,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k11_filter_0 @ A @ B )
= ( k10_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_filter_0) ).
thf(5608,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( ( k11_filter_0 @ A @ B )
= ( k10_filter_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1229,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( r2_lattice4 @ A @ B @ C )
<=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_lattice4) ).
thf(6469,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( r2_lattice4 @ A @ B @ C )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) ) )
& ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k6_lattices @ A ) )
= ( k6_lattices @ B ) )
=> ( r2_lattice4 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(576,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k1_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ ( k1_relat_1 @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_funct_3) ).
thf(3738,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k1_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ ( k1_relat_1 @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(612,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).
thf(3888,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(293,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_tops_1) ).
thf(2524,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) )
= ( k1_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_1) ).
thf(4453,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1055,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(5698,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C ) )
=> ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k1_funct_4 @ C @ D ) )
& ( m2_relset_1 @ ( k1_funct_4 @ C @ D ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_funct_4) ).
thf(3187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( v1_funct_1 @ ( k1_funct_4 @ C @ D ) )
& ( m2_relset_1 @ ( k1_funct_4 @ C @ D ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k2_funct_2 @ A @ B @ C @ A )
= ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).
thf(1833,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( k2_funct_2 @ A @ B @ C @ A )
= ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( v2_funct_1 @ C )
<=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).
thf(2970,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( v2_funct_1 @ C )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ C @ E ) ) )
=> ( D = E ) )
=> ( v2_funct_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(625,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(3925,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
| ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(1348,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ ( k8_filter_1 @ A @ B ) @ ( k8_filter_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_filter_1) ).
thf(6881,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ ( k8_filter_1 @ A @ B ) @ ( k8_filter_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(364,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ C ) @ D )
= ( k4_filter_0 @ A @ B @ ( k4_filter_0 @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_filter_1) ).
thf(2789,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ C ) @ D )
= ( k4_filter_0 @ A @ B @ ( k4_filter_0 @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(328,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_filter_0) ).
thf(2657,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ ( k2_filter_0 @ A @ B ) )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(728,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_mcart_1) ).
thf(4309,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1108,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k4_lattice4 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice4) ).
thf(5940,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k4_lattice4 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(872,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(4926,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(1114,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(5962,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(919,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v1_pre_topc @ A )
=> ( A
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_pre_topc) ).
thf(5099,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ( ( v1_pre_topc @ A )
=> ( A
= ( g1_pre_topc @ ( u1_struct_0 @ A ) @ ( u1_pre_topc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(1126,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k5_lattices @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattices) ).
thf(6019,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k5_lattices @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(607,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(3868,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(1237,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(6493,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(142,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tops_1) ).
thf(1916,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1345,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_lopclset @ A ) )
& ( v1_pre_topc @ ( k11_lopclset @ A ) )
& ( v2_pre_topc @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lopclset) ).
thf(6870,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k11_lopclset @ A ) )
& ( v1_pre_topc @ ( k11_lopclset @ A ) )
& ( v2_pre_topc @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_xboole_1) ).
thf(2225,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1272,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_lopclset @ A ) )
& ( v10_lattices @ ( k6_lopclset @ A ) )
& ( l3_lattices @ ( k6_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lopclset) ).
thf(6617,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ~ ( v3_struct_0 @ ( k6_lopclset @ A ) )
& ( v10_lattices @ ( k6_lopclset @ A ) )
& ( l3_lattices @ ( k6_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(5488,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(474,axiom,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(3255,plain,
? [A: $i] :
( ( l1_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(1262,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( k10_lopclset @ B ) )
<=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ B ) ) @ ( k9_lopclset @ B ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lopclset) ).
thf(6581,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ~ ( v3_realset2 @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( k10_lopclset @ B ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ B ) ) @ ( k9_lopclset @ B ) @ C )
= A ) ) )
& ( ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ B ) ) @ ( k9_lopclset @ B ) @ C )
= A ) )
=> ( r2_hidden @ A @ ( k10_lopclset @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(100,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(1752,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(6,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattice4 @ A @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_lattice4) ).
thf(1388,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattice4 @ A @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(480,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k5_finsub_1 @ A )
= ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
thf(3272,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k5_finsub_1 @ A )
= ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(1183,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_lattices) ).
thf(6229,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(4032,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(11,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattice4 @ A @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lattice4) ).
thf(1403,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k1_lattice4 @ A @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1354,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lopclset) ).
thf(6898,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) @ ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_3) ).
thf(2959,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) @ ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( C != k1_xboole_0 )
=> ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_4) ).
thf(3213,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( C != k1_xboole_0 )
=> ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).
thf(1428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
& ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( k1_funct_1 @ D @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1115,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_borsuk_1) ).
thf(5965,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( v1_borsuk_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(769,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ E ) ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_lattice4) ).
thf(4485,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ( r3_lattices @ A @ ( k4_lattices @ A @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ ( k4_filter_0 @ B @ D @ E ) ) ) @ ( k8_funct_2 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ A ) @ C @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(210,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_lattices @ A @ ( k2_lattice4 @ A @ B ) )
= ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k5_lattice4 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice4) ).
thf(2193,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_lattices @ A @ ( k2_lattice4 @ A @ B ) )
= ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k5_lattice4 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(581,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_eqrel_1 @ ( k15_borsuk_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_borsuk_1) ).
thf(3773,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( m1_eqrel_1 @ ( k15_borsuk_1 @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(4096,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(1245,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(6532,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(354,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(2753,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_xboole_1) ).
thf(2055,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1279,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
<=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_1) ).
thf(6636,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) ) )
& ( ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v10_lattices @ ( k8_filter_1 @ A @ B ) )
& ( v17_lattices @ ( k8_filter_1 @ A @ B ) )
& ( l3_lattices @ ( k8_filter_1 @ A @ B ) ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(1159,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k5_lattices @ A )
= ( k6_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_lattice2) ).
thf(6123,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k5_lattices @ A )
= ( k6_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1065,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_filter_1) ).
thf(5735,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( l3_lattices @ B ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_1 @ A @ B ) )
& ( v3_lattices @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(720,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ A ) @ B )
=> ( ( r2_hidden @ C @ D )
=> ( D
= ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_borsuk_1) ).
thf(4273,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ A ) @ B )
=> ( ( r2_hidden @ C @ D )
=> ( D
= ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1075,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(5784,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(239,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relat_1) ).
thf(2319,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1125,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k6_lattices @ A ) @ B )
= ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattices) ).
thf(6016,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k6_lattices @ A ) @ B )
= ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(1213,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(6403,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(1014,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lattice4) ).
thf(5471,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) )
=> ( r2_hidden @ A @ ( k4_lattice4 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k9_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(2891,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k9_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(433,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( k6_pre_topc @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ C )
<=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_pre_topc) ).
thf(3077,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( C
= ( k6_pre_topc @ A @ B ) )
=> ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) ) )
& ( ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( r2_hidden @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ D @ C )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) ) )
& ( ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( v3_pre_topc @ E @ A )
& ( r2_hidden @ D @ E )
& ( r1_xboole_0 @ B @ E ) ) )
=> ( r2_hidden @ D @ C ) ) ) )
=> ( C
= ( k6_pre_topc @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(1285,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k13_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k13_lopclset) ).
thf(6667,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k13_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(683,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k1_funct_1 @ ( k17_borsuk_1 @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_borsuk_1) ).
thf(4112,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k1_funct_1 @ ( k17_borsuk_1 @ B @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1287,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( a_2_0_lopclset @ A @ B ) @ ( k7_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_lopclset) ).
thf(6673,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r1_tarski @ ( a_2_0_lopclset @ A @ B ) @ ( k7_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( v2_borsuk_1 @ ( k20_borsuk_1 @ A @ B @ C ) @ A )
& ( m1_borsuk_1 @ ( k20_borsuk_1 @ A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k20_borsuk_1) ).
thf(3651,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( v2_borsuk_1 @ ( k20_borsuk_1 @ A @ B @ C ) @ A )
& ( m1_borsuk_1 @ ( k20_borsuk_1 @ A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1088,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k9_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_filter_0) ).
thf(5859,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_filter_0 @ E @ A )
=> ( ( ( r2_hidden @ ( k9_filter_0 @ A @ B @ C ) @ E )
& ( r2_hidden @ ( k9_filter_0 @ A @ C @ D ) @ E ) )
=> ( r2_hidden @ ( k9_filter_0 @ A @ B @ D ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(692,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_relat_1) ).
thf(4149,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(560,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_xboole_0 @ ( k1_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_tops_1) ).
thf(3663,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_xboole_0 @ ( k1_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(706,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) )
& ( v2_funct_1 @ B ) )
=> ( ( k3_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) )
= ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_3) ).
thf(4218,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) )
& ( v2_funct_1 @ B ) )
=> ( ( k3_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) )
= ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_1) ).
thf(1635,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(395,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( B
= ( k5_lattice4 @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C )
= ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice4) ).
thf(2935,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ B @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( ( B
= ( k5_lattice4 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C )
= ( k7_lattices @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C )
= ( k7_lattices @ A @ C ) ) )
=> ( B
= ( k5_lattice4 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) )
=> ( ( r1_tarski @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k2_funct_2 @ A @ C @ D @ ( k3_tarski @ B ) )
= ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_3) ).
thf(3002,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) )
=> ( ( r1_tarski @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k2_funct_2 @ A @ C @ D @ ( k3_tarski @ B ) )
= ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ D ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(852,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(4822,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(545,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k2_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_tops_1) ).
thf(3594,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) @ ( k2_tops_1 @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_tops_1 @ A @ B ) @ ( k2_tops_1 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(793,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) )
& ( v2_funct_1 @ A ) )
=> ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_1) ).
thf(4573,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) )
& ( v2_funct_1 @ A ) )
=> ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(915,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(5086,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_tarski @ A @ C )
& ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1251,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( r1_tarski @ C @ ( k18_borsuk_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_borsuk_1) ).
thf(6549,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( r1_tarski @ C @ ( k18_borsuk_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k2_lopclset @ A @ B @ C )
= ( k2_lopclset @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_lopclset) ).
thf(6334,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k2_lopclset @ A @ B @ C )
= ( k2_lopclset @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(67,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( k10_setwiseo @ A @ B @ ( k5_setwiseo @ A @ D @ E ) @ C )
= ( k5_setwiseo @ B @ ( k10_setwiseo @ A @ B @ D @ C ) @ ( k10_setwiseo @ A @ B @ E @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_setwiseo) ).
thf(1638,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( k10_setwiseo @ A @ B @ ( k5_setwiseo @ A @ D @ E ) @ C )
= ( k5_setwiseo @ B @ ( k10_setwiseo @ A @ B @ D @ C ) @ ( k10_setwiseo @ A @ B @ E @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(500,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_4) ).
thf(3355,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1142,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v3_lattice4 @ C @ B @ A )
=> ( ( v3_filter_0 @ A )
& ( r1_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lattice4) ).
thf(6061,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v3_filter_0 @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v3_lattice4 @ C @ B @ A )
=> ( ( v3_filter_0 @ A )
& ( r1_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1232,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
thf(6478,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k1_tops_1 @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).
thf(2521,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( ( k2_relat_1 @ C )
= ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).
thf(2119,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t179_relat_1) ).
thf(3996,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(1806,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ A @ B )
& ( A != C ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( A != C ) )
=> ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(1333,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( ( r1_filter_1 @ A @ B )
& ( r1_filter_1 @ B @ C ) )
=> ( r1_filter_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_1) ).
thf(6815,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( l3_lattices @ C ) )
=> ( ( ( r1_filter_1 @ A @ B )
& ( r1_filter_1 @ B @ C ) )
=> ( r1_filter_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(1042,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_subset_1 @ ( k7_borsuk_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_borsuk_1) ).
thf(5631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( m1_subset_1 @ ( k7_borsuk_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_zfmisc_1) ).
thf(2116,plain,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(766,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(4477,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(949,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(5212,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(1259,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(6572,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( k2_funct_4 @ ( k2_funct_4 @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_funct_4) ).
thf(4929,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( k2_funct_4 @ ( k2_funct_4 @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(1368,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_0) ).
thf(6942,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] : ( m1_filter_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(1321,axiom,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(6779,plain,
? [A: $i] :
( ( l2_struct_0 @ A )
& ~ ( v3_struct_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(473,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_setwiseo) ).
thf(3251,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_relat_1) ).
thf(3155,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(594,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_0) ).
thf(3815,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ B @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ B @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(180,axiom,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(2084,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(259,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_funct_3 @ A ) )
& ( v1_funct_2 @ ( k3_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
& ( m2_relset_1 @ ( k3_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funct_3) ).
thf(2383,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_funct_3 @ A ) )
& ( v1_funct_2 @ ( k3_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
& ( m2_relset_1 @ ( k3_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ! [C: $i] :
( ( m1_filter_1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_1) ).
thf(2493,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ! [C: $i] :
( ( m1_filter_1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ ( k5_relat_1 @ B @ C ) ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_3) ).
thf(2987,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ ( k5_relat_1 @ B @ C ) ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(423,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ D @ C )
<=> ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) ) ) )
& ( ( k6_pre_topc @ A @ B )
= ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_pre_topc) ).
thf(3038,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( r2_hidden @ D @ C )
=> ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) ) )
& ( ( ( v4_pre_topc @ D @ A )
& ( r1_tarski @ B @ D ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ( k6_pre_topc @ A @ B )
= ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).
thf(2422,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(726,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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(4305,plain,
! [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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(1019,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( C
= ( k3_filter_0 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_filter_0) ).
thf(5491,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( ( C
= ( k3_filter_0 @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) )
& ( ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) )
=> ( C
= ( k3_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(801,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
thf(4601,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( ( k1_relat_1 @ A )
= ( k1_relat_1 @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(396,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ( ( k10_setwiseo @ A @ B @ ( k1_setwiseo @ A ) @ C )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_setwiseo) ).
thf(2943,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ( ( k10_setwiseo @ A @ B @ ( k1_setwiseo @ A ) @ C )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(569,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(3710,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(917,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
<=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k10_filter_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_filter_0) ).
thf(5093,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( ( r1_filter_0 @ A @ D @ B @ C )
=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k10_filter_0 @ A @ D ) ) )
& ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k10_filter_0 @ A @ D ) )
=> ( r1_filter_0 @ A @ D @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(694,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(4154,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(1193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(6289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(532,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
<=> ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k1_tops_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_tops_1) ).
thf(3500,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k1_tops_1 @ A @ B ) ) ) )
& ( ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k1_tops_1 @ A @ B ) ) )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(1052,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v12_lattices @ A )
=> ( v12_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_filter_0) ).
thf(5689,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v12_lattices @ A )
=> ( v12_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(992,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(5381,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(1078,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_borsuk_1) ).
thf(5795,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_borsuk_1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).
thf(1690,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_struct_0 @ A @ B )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(430,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(3066,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(1178,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m2_subset_1 @ ( k2_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lopclset) ).
thf(6196,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m2_subset_1 @ ( k2_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
thf(3384,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1117,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_filter_0) ).
thf(5972,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k9_filter_0 @ A @ B @ C )
= ( k9_filter_0 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k2_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(1571,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k2_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1039,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ B )
<=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_filter_0) ).
thf(5616,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
=> ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) )
& ( ~ ( r2_hidden @ ( k7_lattices @ A @ C ) @ B )
=> ( r2_hidden @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
<=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
thf(4509,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) )
=> ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m2_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( m2_connsp_2 @ ( k10_borsuk_1 @ A @ B @ C @ D @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ ( k1_struct_0 @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_borsuk_1) ).
thf(1439,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m2_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( m2_connsp_2 @ ( k10_borsuk_1 @ A @ B @ C @ D @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ ( k1_struct_0 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ B @ ( k1_funct_1 @ ( k2_funct_1 @ B ) @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ ( k2_funct_1 @ B ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
thf(2180,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) )
=> ( ( A
= ( k1_funct_1 @ B @ ( k1_funct_1 @ ( k2_funct_1 @ B ) @ A ) ) )
& ( A
= ( k1_funct_1 @ ( k5_relat_1 @ ( k2_funct_1 @ B ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(370,axiom,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(2812,plain,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(318,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( v2_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ C )
& ( D != k1_xboole_0 )
& ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_tops_1) ).
thf(2605,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( ( v2_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ C )
& ( D != k1_xboole_0 )
& ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ B @ D ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r1_tarski @ D @ C )
& ( D != k1_xboole_0 )
& ( v3_pre_topc @ D @ A )
& ( r1_xboole_0 @ B @ D ) ) ) ) )
=> ( v2_tops_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(320,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_tops_1) ).
thf(2625,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ B )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(913,axiom,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(5082,plain,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(186,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v5_tops_1 @ B @ A )
<=> ( B
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_tops_1) ).
thf(2111,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v5_tops_1 @ B @ A )
=> ( B
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) )
& ( ( B
= ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) )
=> ( v5_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1217,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v3_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(6414,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_xboole_0 @ B )
=> ( v3_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(1334,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lopclset @ A )
= ( a_1_1_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_lopclset) ).
thf(6817,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k7_lopclset @ A )
= ( a_1_1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(1460,plain,
! [A: $i] :
( ( k2_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(897,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_tops_1) ).
thf(5007,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k6_pre_topc @ A @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1085,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v1_filter_0 @ B @ A )
<=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_0) ).
thf(5838,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( v1_filter_0 @ B @ A )
=> ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) ) )
& ( ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ C )
=> ( ( C
= ( u1_struct_0 @ A ) )
| ( B = C ) ) ) ) )
=> ( v1_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(467,axiom,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_relat_1) ).
thf(3219,plain,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(826,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ k1_xboole_0 @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_4) ).
thf(4694,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ k1_xboole_0 @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(2267,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(834,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_lattices @ A @ ( k2_lattice2 @ C @ A @ D @ E ) @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice2) ).
thf(4731,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ( r3_lattices @ A @ ( k2_lattice2 @ C @ A @ D @ E ) @ B )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(654,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v6_compts_1 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_borsuk_1) ).
thf(4028,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( v6_compts_1 @ ( k1_struct_0 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(93,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_lattices @ A @ ( k1_lattice4 @ A @ B ) )
= ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k5_lattice4 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_lattice4) ).
thf(1731,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k7_lattices @ A @ ( k1_lattice4 @ A @ B ) )
= ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ ( k5_lattice4 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_2) ).
thf(4264,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(626,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(3932,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(889,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
& ( v3_tops_1 @ C @ A ) )
=> ( v3_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_tops_1) ).
thf(4985,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_tops_1 @ B @ A )
& ( v3_tops_1 @ C @ A ) )
=> ( v3_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).
thf(1862,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ C @ A )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(703,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).
thf(4208,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ C )
= ( k1_filter_1 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k1_filter_1) ).
thf(6747,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ C )
= ( k1_filter_1 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
<=> ( B
= ( k1_subset_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).
thf(2410,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
=> ( B
= ( k1_subset_1 @ A ) ) )
& ( ( B
= ( k1_subset_1 @ A ) )
=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(549,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
<=> ( v3_pre_topc @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pre_topc) ).
thf(3614,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( v3_pre_topc @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) @ A ) )
& ( ( v3_pre_topc @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) @ A )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(362,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2785,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( m1_subset_1 @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_mcart_1) ).
thf(2593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
=> ( m1_subset_1 @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C )
& ! [E: $i,F: $i] :
( ( ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) )
=> ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) ) )
& ( ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) )
=> ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_2) ).
thf(3451,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ A )
& ( m2_relset_1 @ D @ B @ A ) )
=> ( ( ( ( k2_relat_1 @ C )
= B )
& ( v2_funct_1 @ C )
& ! [E: $i,F: $i] :
( ( ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) )
=> ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) ) )
& ( ( ( r2_hidden @ F @ A )
& ( ( k1_funct_1 @ C @ F )
= E ) )
=> ( ( r2_hidden @ E @ B )
& ( ( k1_funct_1 @ D @ E )
= F ) ) ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( D
= ( k2_funct_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(1289,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_lattice4) ).
thf(6678,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m2_lattice4 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(860,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_mcart_1) ).
thf(4850,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1339,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k1_filter_1) ).
thf(6847,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(1330,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_tarski @ ( k10_lopclset @ A ) @ ( k1_lopclset @ ( k11_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l49_lopclset) ).
thf(6802,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_tarski @ ( k10_lopclset @ A ) @ ( k1_lopclset @ ( k11_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(605,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k16_borsuk_1 @ A @ B ) )
& ( v1_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_borsuk_1) ).
thf(3861,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( v3_struct_0 @ ( k16_borsuk_1 @ A @ B ) )
& ( v1_pre_topc @ ( k16_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k16_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(392,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(2928,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(1257,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v11_lattices @ A )
=> ( v11_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_filter_0) ).
thf(6568,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v11_lattices @ A )
=> ( v11_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
& ~ ( r2_hidden @ C @ A )
& ~ ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_setwiseo) ).
thf(2461,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
& ~ ( r2_hidden @ C @ A )
& ~ ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(996,axiom,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(5410,plain,
! [A: $i,B: $i] :
( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(1010,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k6_lattices @ A ) )
= ( k7_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_lopclset) ).
thf(5459,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k6_lattices @ A ) )
= ( k7_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(1283,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_filter_1 @ A @ ( k12_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_lopclset) ).
thf(6660,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_filter_1 @ A @ ( k12_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(118,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(1820,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1206,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_lopclset @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k10_lopclset @ A ) )
=> ( v3_pre_topc @ B @ ( k11_lopclset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l38_lopclset) ).
thf(6376,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k11_lopclset @ A ) ) ) )
=> ( ( r2_hidden @ B @ ( k10_lopclset @ A ) )
=> ( v3_pre_topc @ B @ ( k11_lopclset @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m1_filter_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_1) ).
thf(1688,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m1_filter_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(2401,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(1003,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v15_lattices @ A )
<=> ( ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattices) ).
thf(5442,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v15_lattices @ A )
=> ( ( v13_lattices @ A )
& ( v14_lattices @ A ) ) )
& ( ( ( v13_lattices @ A )
& ( v14_lattices @ A ) )
=> ( v15_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1269,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( m1_subset_1 @ ( k5_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattices) ).
thf(6609,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( m1_subset_1 @ ( k5_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(3110,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_1) ).
thf(3806,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).
thf(2797,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ B )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ k1_xboole_0 @ A )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_xboole_1) ).
thf(2244,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(829,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_tops_1) ).
thf(4703,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v4_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(974,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k5_lattices @ A ) @ B )
= ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_lattices) ).
thf(5299,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k5_lattices @ A ) @ B )
= ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1176,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lattice2) ).
thf(6180,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ B @ C )
= C ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(916,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
thf(5089,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
& ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(670,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( r2_hidden @ ( k1_struct_0 @ A @ D ) @ ( k18_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_borsuk_1) ).
thf(4067,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( r2_hidden @ ( k1_struct_0 @ A @ D ) @ ( k18_borsuk_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t181_relat_1) ).
thf(2984,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1040,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( B
!= ( k5_lattices @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_filter_0) ).
thf(5619,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( B
!= ( k5_lattices @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r2_hidden @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(538,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ D ) @ C ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ D @ C ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_filter_1) ).
thf(3539,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ C @ D ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ B @ D ) @ C ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ B @ ( k3_lattices @ A @ D @ C ) ) )
& ( r3_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) @ ( k4_filter_0 @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(358,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k5_relat_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_relat_1) ).
thf(2770,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k5_relat_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(854,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(4832,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1204,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_pre_topc) ).
thf(6345,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1260,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_lattice2 @ A )
<=> ( ( v3_filter_0 @ A )
& ( v13_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lattice2) ).
thf(6574,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v1_lattice2 @ A )
=> ( ( v3_filter_0 @ A )
& ( v13_lattices @ A ) ) )
& ( ( ( v3_filter_0 @ A )
& ( v13_lattices @ A ) )
=> ( v1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(1358,axiom,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
thf(6907,plain,
? [A: $i] :
( ( l3_lattices @ A )
& ~ ( v3_struct_0 @ A )
& ( v3_lattices @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ D )
& ( m2_relset_1 @ E @ A @ D ) )
=> ( ( ( r1_tarski @ B @ A )
& ( r1_tarski @ ( k2_funct_2 @ A @ D @ E @ B ) @ C ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ D @ E @ B ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ D @ E @ B ) @ B @ C )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ D @ E @ B ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_cat_1) ).
thf(2051,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( v1_xboole_0 @ D )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ D )
& ( m2_relset_1 @ E @ A @ D ) )
=> ( ( ( r1_tarski @ B @ A )
& ( r1_tarski @ ( k2_funct_2 @ A @ D @ E @ B ) @ C ) )
=> ( ( v1_funct_1 @ ( k2_partfun1 @ A @ D @ E @ B ) )
& ( v1_funct_2 @ ( k2_partfun1 @ A @ D @ E @ B ) @ B @ C )
& ( m2_relset_1 @ ( k2_partfun1 @ A @ D @ E @ B ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).
thf(2550,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).
thf(2481,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(1308,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k7_lattices @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_lattices) ).
thf(6738,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k7_lattices @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(740,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(4373,plain,
! [A: $i] :
( ( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( v1_xboole_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1188,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v2_lattice4 @ C @ A @ B )
<=> ( ( k2_relat_1 @ C )
= ( u1_struct_0 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice4) ).
thf(6270,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v2_lattice4 @ C @ A @ B )
=> ( ( k2_relat_1 @ C )
= ( u1_struct_0 @ B ) ) )
& ( ( ( k2_relat_1 @ C )
= ( u1_struct_0 @ B ) )
=> ( v2_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(1024,axiom,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(5516,plain,
! [A: $i,B: $i] :
( ( ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k1_tops_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(450,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ A @ B )
= ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(3159,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k5_setfam_1 @ A @ B )
= ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(255,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k2_funct_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k2_funct_1 @ B ) @ ( k2_funct_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_1) ).
thf(2369,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k2_funct_1 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k2_funct_1 @ B ) @ ( k2_funct_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(736,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) )
& ( r2_hidden @ E @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ C @ E ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ E ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_1) ).
thf(4362,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) )
& ( r2_hidden @ E @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ C @ E ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) )
& ( r2_hidden @ ( k4_lattices @ A @ C @ E ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k11_filter_0 @ A @ B ) @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(393,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(2931,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(905,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k1_struct_0 @ A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_borsuk_1) ).
thf(5042,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ~ ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) ) @ ( k17_borsuk_1 @ A @ ( k18_borsuk_1 @ A @ B @ C ) ) @ D )
= ( k1_struct_0 @ A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(166,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
<=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
thf(2022,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
=> ( v2_funct_1 @ A ) )
& ( ( v2_funct_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(3310,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(568,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( r3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
<=> ( ( r3_lattices @ A @ C @ D )
& ( r3_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_1) ).
thf(3706,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ( r3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
=> ( ( r3_lattices @ A @ C @ D )
& ( r3_lattices @ B @ E @ F ) ) )
& ( ( ( r3_lattices @ A @ C @ D )
& ( r3_lattices @ B @ E @ F ) )
=> ( r3_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_2_borsuk_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ C ) )
& ( A = D )
& ( r2_hidden @ ( k3_tarski @ D ) @ ( u1_pre_topc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_borsuk_1) ).
thf(5725,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_2_borsuk_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ C ) )
& ( A = D )
& ( r2_hidden @ ( k3_tarski @ D ) @ ( u1_pre_topc @ B ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ C ) )
& ( A = D )
& ( r2_hidden @ ( k3_tarski @ D ) @ ( u1_pre_topc @ B ) ) )
=> ( r2_hidden @ A @ ( a_2_2_borsuk_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(378,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v6_group_1 @ A )
<=> ( v1_finset_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_group_1) ).
thf(2867,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v6_group_1 @ A )
=> ( v1_finset_1 @ ( u1_struct_0 @ A ) ) )
& ( ( v1_finset_1 @ ( u1_struct_0 @ A ) )
=> ( v6_group_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1231,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_3 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_funct_3) ).
thf(6476,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_3 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(611,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ F @ C )
=> ( r3_lattices @ A @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ D @ F ) @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ F ) ) ) )
=> ( ( C = k1_xboole_0 )
| ( r3_lattices @ A @ ( k2_lattice2 @ B @ A @ C @ D ) @ ( k2_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_lattice2) ).
thf(3881,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ F @ C )
=> ( r3_lattices @ A @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ D @ F ) @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ F ) ) ) )
=> ( ( C = k1_xboole_0 )
| ( r3_lattices @ A @ ( k2_lattice2 @ B @ A @ C @ D ) @ ( k2_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(753,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(4426,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(746,axiom,
? [A: $i] : ( l1_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(4394,plain,
? [A: $i] : ( l1_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(3193,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ B @ A )
=> ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(800,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t182_relat_1) ).
thf(4598,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).
thf(1420,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
& ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
=> ( ( B != k1_xboole_0 )
=> ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(640,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(3981,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(2234,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(444,axiom,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(3146,plain,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(3921,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
thf(2597,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).
thf(5652,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
& ( A
= ( k4_filter_0 @ B @ D @ E ) )
& ( r2_hidden @ D @ C )
& ( r2_hidden @ E @ C ) )
=> ( r2_hidden @ A @ ( a_2_0_lattice4 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(1224,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(6440,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_1) ).
thf(5435,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(63,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k3_funct_3 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k3_funct_3 @ B ) @ ( k3_funct_3 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_3) ).
thf(1626,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k3_funct_3 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k3_funct_3 @ B ) @ ( k3_funct_3 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(750,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(4405,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ B )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( r2_hidden @ C @ A )
& ( r2_hidden @ C @ B ) )
& ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1351,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_lopclset) ).
thf(6890,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k9_lopclset @ A )
= ( k8_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( k1_relat_1 @ ( k2_funct_4 @ C ) )
= ( k2_zfmisc_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_4) ).
thf(3936,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( k1_relat_1 @ ( k2_funct_4 @ C ) )
= ( k2_zfmisc_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(1248,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k2_pre_topc @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_pre_topc) ).
thf(6540,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k2_pre_topc @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(1095,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_filter_0) ).
thf(5886,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( k3_lattices @ A @ B @ C )
= ( k3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( k4_lattices @ A @ B @ C )
= ( k4_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(1249,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_lattices) ).
thf(6542,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v15_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ A )
& ( v13_lattices @ A )
& ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
thf(2665,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(716,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k1_funct_3 @ A ) )
& ( v1_funct_2 @ ( k1_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
& ( m2_relset_1 @ ( k1_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_3) ).
thf(4260,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k1_funct_3 @ A ) )
& ( v1_funct_2 @ ( k1_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
& ( m2_relset_1 @ ( k1_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(4813,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1177,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v2_filter_0 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
<=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_0) ).
thf(6185,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ( v2_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B )
=> ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ C @ B )
| ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) )
=> ( v2_filter_0 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(1990,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B )
& ( m1_subset_1 @ D @ A ) )
=> ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(425,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k4_lopclset @ A ) )
& ( v1_funct_2 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lopclset) ).
thf(3048,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k4_lopclset @ A ) )
& ( v1_funct_2 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ ( k4_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(862,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ ( k9_filter_0 @ A @ B @ C ) ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k12_filter_0 @ A @ ( k2_filter_0 @ A @ C ) ) @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k12_filter_0 @ A @ ( k2_filter_0 @ A @ C ) ) @ B ) )
=> ( r3_lattices @ A @ D @ ( k3_lattices @ A @ B @ ( k9_filter_0 @ A @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_filter_1) ).
thf(4859,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ ( k9_filter_0 @ A @ B @ C ) ) @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k12_filter_0 @ A @ ( k2_filter_0 @ A @ C ) ) @ B ) )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( k2_filter_1 @ ( u1_struct_0 @ A ) @ ( k12_filter_0 @ A @ ( k2_filter_0 @ A @ C ) ) @ B ) )
=> ( r3_lattices @ A @ D @ ( k3_lattices @ A @ B @ ( k9_filter_0 @ A @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v2_funct_1 @ D )
& ( r2_hidden @ C @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_2) ).
thf(2333,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( ( v2_funct_1 @ D )
& ( r2_hidden @ C @ A ) )
=> ( ( B = k1_xboole_0 )
| ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(222,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(2256,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_relat_1 @ A )
= ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(2564,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(986,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_filter_0) ).
thf(5358,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( B
!= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ~ ( ( r1_tarski @ B @ C )
& ( v1_filter_0 @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(831,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ C ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_filter_0) ).
thf(4722,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ D @ C ) )
=> ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(956,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_funct_1) ).
thf(5229,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(1061,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(5716,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(345,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( v13_lattices @ A )
<=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_lattices) ).
thf(2715,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( ( v13_lattices @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) ) )
& ( ? [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) )
=> ( v13_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1211,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_lopclset @ A ) )
=> ( v4_pre_topc @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lopclset) ).
thf(6399,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_lopclset @ A ) )
=> ( v4_pre_topc @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(1273,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v17_lattices @ A )
& ( r4_lattice4 @ B @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_lattice4) ).
thf(6621,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v17_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( ( v17_lattices @ A )
& ( r4_lattice4 @ B @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(50,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_relat_1) ).
thf(1566,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k3_relat_1 @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k3_relat_1 @ A ) @ ( k3_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1069,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( m3_lattice4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_lattice4) ).
thf(5748,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( m3_lattice4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k7_lattices @ A @ C ) @ B ) ) ) ) )
=> ( m3_lattice4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(939,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k6_lattices @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_filter_0) ).
thf(5171,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ ( k6_lattices @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(631,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v12_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ B @ D )
=> ( ( k1_lattices @ A @ B @ ( k2_lattices @ A @ C @ D ) )
= ( k2_lattices @ A @ ( k1_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_lattices) ).
thf(3949,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v12_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ B @ D )
=> ( ( k1_lattices @ A @ B @ ( k2_lattices @ A @ C @ D ) )
= ( k2_lattices @ A @ ( k1_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r1_lattices @ A @ B @ D )
=> ( ( k1_lattices @ A @ B @ ( k2_lattices @ A @ C @ D ) )
= ( k2_lattices @ A @ ( k1_lattices @ A @ B @ C ) @ D ) ) ) ) ) )
=> ( v12_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(374,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(2831,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1004,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(5446,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(307,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( A
= ( k2_relat_1 @ B ) )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).
thf(2567,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( A
= ( k2_relat_1 @ B ) )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1007,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(5452,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ B @ C ) ) ) ) )
=> ( ( r2_hidden @ A @ ( a_3_1_borsuk_1 @ B @ C @ D ) )
<=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k7_borsuk_1 @ B @ C @ E @ F ) )
& ( r1_tarski @ ( k7_borsuk_1 @ B @ C @ E @ F ) @ D )
& ( v3_pre_topc @ E @ B )
& ( v3_pre_topc @ F @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_borsuk_1) ).
thf(5047,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C )
& ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ B @ C ) ) ) ) )
=> ( ( ( r2_hidden @ A @ ( a_3_1_borsuk_1 @ B @ C @ D ) )
=> ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k7_borsuk_1 @ B @ C @ E @ F ) )
& ( r1_tarski @ ( k7_borsuk_1 @ B @ C @ E @ F ) @ D )
& ( v3_pre_topc @ E @ B )
& ( v3_pre_topc @ F @ C ) ) )
& ( ? [E: $i,F: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k7_borsuk_1 @ B @ C @ E @ F ) )
& ( r1_tarski @ ( k7_borsuk_1 @ B @ C @ E @ F ) @ D )
& ( v3_pre_topc @ E @ B )
& ( v3_pre_topc @ F @ C ) )
=> ( r2_hidden @ A @ ( a_3_1_borsuk_1 @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(554,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relat_1) ).
thf(3640,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ~ ( r2_hidden @ D @ B )
<=> ( r2_hidden @ D @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).
thf(1516,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ( ( ~ ( r2_hidden @ D @ B )
=> ( r2_hidden @ D @ C ) )
& ( ( r2_hidden @ D @ C )
=> ~ ( r2_hidden @ D @ B ) ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(490,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) )
& ( ( ( v2_pre_topc @ A )
& ( ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_pre_topc) ).
thf(3315,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) )
& ( ( ( v2_pre_topc @ A )
& ( ( k6_pre_topc @ A @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(657,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).
thf(4035,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1291,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k1_filter_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_filter_1) ).
thf(6683,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k1_filter_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(735,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ F @ D )
& ( r3_lattices @ A @ B @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) ) )
=> ( r3_lattices @ A @ B @ ( k2_lattice2 @ C @ A @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice2) ).
thf(4360,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ F @ D )
& ( r3_lattices @ A @ B @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) ) )
=> ( r3_lattices @ A @ B @ ( k2_lattice2 @ C @ A @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1103,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ B @ ( k6_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattices) ).
thf(5927,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r3_lattices @ A @ B @ ( k6_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(771,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ C ) @ B )
= ( k4_filter_0 @ A @ C @ B ) )
& ( ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ B @ C ) )
= ( k4_filter_0 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_filter_1) ).
thf(4490,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k4_filter_0 @ A @ ( k3_lattices @ A @ B @ C ) @ B )
= ( k4_filter_0 @ A @ C @ B ) )
& ( ( k4_filter_0 @ A @ B @ ( k4_lattices @ A @ B @ C ) )
= ( k4_filter_0 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(435,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
<=> ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(3112,plain,
! [A: $i,B: $i] :
( ( ( r1_xboole_0 @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 ) )
& ( ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( r1_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_tops_1 @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_tops_1) ).
thf(2661,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_tops_1 @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1138,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
=> ( r1_filter_0 @ A @ D @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_filter_0) ).
thf(6051,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r1_filter_0 @ A @ D @ B @ C )
=> ( r1_filter_0 @ A @ D @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(876,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_relat_1) ).
thf(4937,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(1365,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k7_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_lopclset) ).
thf(6934,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_subset_1 @ ( k7_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_subset_1) ).
thf(1611,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
= ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_xboole_1) ).
thf(2060,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1350,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_pre_topc) ).
thf(6885,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ A )
& ( v1_pre_topc @ A )
& ( v2_pre_topc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( k10_setwiseo @ A @ B @ ( k5_setwiseo @ A @ E @ ( k2_setwiseo @ A @ D ) ) @ C )
= ( k5_setwiseo @ B @ ( k10_setwiseo @ A @ B @ E @ C ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_setwiseo) ).
thf(1400,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
=> ( ( k10_setwiseo @ A @ B @ ( k5_setwiseo @ A @ E @ ( k2_setwiseo @ A @ D ) ) @ C )
= ( k5_setwiseo @ B @ ( k10_setwiseo @ A @ B @ E @ C ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(1743,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m2_realset1 @ C @ A @ B )
=> ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(877,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).
thf(4939,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= k1_xboole_0 )
=> ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_subset_1) ).
thf(1605,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_xboole_0 @ B @ C )
& ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
=> ( B
= ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(2588,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_lattices @ A @ B @ C ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(2732,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_0) ).
thf(5484,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ~ ( v1_xboole_0 @ ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(333,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ( ( k3_lattices @ ( k6_lopclset @ A ) @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_lopclset) ).
thf(2678,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ( ( k3_lattices @ ( k6_lopclset @ A ) @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(291,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(2518,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( ~ ( r2_hidden @ C @ B )
=> ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(811,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(4641,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(204,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(2175,plain,
! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k19_borsuk_1 @ A @ B @ C )
= ( k18_borsuk_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k19_borsuk_1) ).
thf(4287,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k19_borsuk_1 @ A @ B @ C )
= ( k18_borsuk_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(107,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(1780,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(266,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_tops_1) ).
thf(2407,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k1_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(3058,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= ( k2_zfmisc_1 @ C @ D ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1266,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(6596,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ A @ C )
& ! [D: $i] :
( ( ( r1_tarski @ D @ B )
& ( r1_tarski @ D @ C ) )
=> ( r1_tarski @ D @ A ) ) )
=> ( A
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(34,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_partfun1) ).
thf(1484,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ~ ( ! [C: $i] :
( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ A @ C )
= ( k1_funct_1 @ B @ C ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k2_xboole_0 @ A @ B )
!= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(799,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
=> ( r3_lattices @ A @ D @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_filter_0) ).
thf(4593,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) @ C )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
=> ( r3_lattices @ A @ D @ ( k3_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(2888,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1209,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(6389,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(1191,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v16_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattices @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_lattices) ).
thf(6280,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v16_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattices @ A @ C @ B ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ? [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( r2_lattices @ A @ C @ B ) ) )
=> ( v16_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(679,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k5_lopclset @ A ) )
& ( v1_funct_2 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lopclset) ).
thf(4092,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v1_funct_1 @ ( k5_lopclset @ A ) )
& ( v1_funct_2 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ ( k5_lopclset @ A ) @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(429,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_0) ).
thf(3063,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k4_lattices @ A @ B @ D ) @ C )
& ( r3_lattices @ A @ ( k4_lattices @ A @ D @ B ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( m2_subset_1 @ ( k2_lopclset @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lopclset) ).
thf(6037,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( m2_subset_1 @ ( k2_lopclset @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(651,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ ( k2_lattice4 @ A @ B ) @ ( k2_lattice4 @ A @ C ) )
= ( k2_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice4) ).
thf(4020,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_lattices @ A @ ( k2_lattice4 @ A @ B ) @ ( k2_lattice4 @ A @ C ) )
= ( k2_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1219,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k5_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattices) ).
thf(6421,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ B )
= ( k5_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice2) ).
thf(1785,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1110,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_filter_0) ).
thf(5948,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( r2_hidden @ B @ D )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
& ( r2_hidden @ ( k3_lattices @ A @ C @ B ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(589,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(3801,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
& ( ( ( k2_relat_1 @ A )
= k1_xboole_0 )
=> ( ( k1_relat_1 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(602,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
thf(3847,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ! [D: $i] :
( ( ( r2_hidden @ D @ B )
& ( r1_tarski @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(4982,plain,
! [A: $i,B: $i,C: $i] :
( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(909,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k1_funct_3 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
& ! [C: $i] :
( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k9_relat_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_3) ).
thf(5062,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k1_funct_3 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
& ! [C: $i] :
( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k9_relat_1 @ A @ C ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
& ! [C: $i] :
( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k9_relat_1 @ A @ C ) ) ) )
=> ( B
= ( k1_funct_3 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(418,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) )
= ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_1) ).
thf(3019,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k7_lattices @ A @ ( k4_filter_0 @ A @ B @ C ) )
= ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k3_lattices @ A @ ( k4_lattices @ A @ B @ ( k7_lattices @ A @ C ) ) @ ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ B @ ( k7_lattices @ A @ C ) ) )
& ( ( k7_lattices @ A @ ( k9_filter_0 @ A @ B @ C ) )
= ( k9_filter_0 @ A @ ( k7_lattices @ A @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(2747,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) )
=> ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(3448,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(966,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
& ( B = D )
& ( C = E ) )
=> ( r3_lattices @ A @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_lattice2) ).
thf(5262,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k1_lattice2 @ A ) ) )
=> ( ( ( r3_lattices @ ( k1_lattice2 @ A ) @ D @ E )
& ( B = D )
& ( C = E ) )
=> ( r3_lattices @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).
thf(3305,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(595,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
<=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finset_1) ).
thf(3818,plain,
! [A: $i] :
( ( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) )
& ( ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(562,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( k1_funct_4 @ B @ C )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funct_4) ).
thf(3691,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( k1_funct_4 @ B @ C )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(3791,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(526,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v11_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( r2_hidden @ G @ B )
=> ( ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ G )
= ( k4_lattices @ C @ F @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ E @ G ) ) ) ) )
=> ( ( k4_lattices @ C @ F @ ( k2_lattice2 @ A @ C @ B @ E ) )
= ( k2_lattice2 @ A @ C @ B @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_lattice2) ).
thf(3475,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v11_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ( ! [G: $i] :
( ( m1_subset_1 @ G @ A )
=> ( ( r2_hidden @ G @ B )
=> ( ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ G )
= ( k4_lattices @ C @ F @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ E @ G ) ) ) ) )
=> ( ( k4_lattices @ C @ F @ ( k2_lattice2 @ A @ C @ B @ E ) )
= ( k2_lattice2 @ A @ C @ B @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(842,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( m1_lattice4 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice4) ).
thf(4768,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( m1_lattice4 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ( ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k3_lattices @ A @ D @ E ) )
= ( k3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ ( k4_lattices @ A @ D @ E ) )
= ( k4_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ E ) ) ) ) ) )
=> ( m1_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(596,axiom,
? [A: $i] : ( l1_struct_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(3823,plain,
? [A: $i] : ( l1_struct_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(1197,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
thf(6298,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(1122,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( r3_lattices @ A @ B @ C )
<=> ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_filter_0) ).
thf(5995,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ ( k8_filter_0 @ A @ D ) ) )
=> ( ( ( B = E )
& ( C = F ) )
=> ( ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F ) )
& ( ( r3_lattices @ ( k8_filter_0 @ A @ D ) @ E @ F )
=> ( r3_lattices @ A @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(3127,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ B )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(1901,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_tarski @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(539,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) @ ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_tops_1) ).
thf(3544,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) @ ( k1_tops_1 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k6_filter_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k5_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_1) ).
thf(6174,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k6_filter_1 @ A @ B @ C ) @ ( u1_struct_0 @ ( k5_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(688,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( r1_xboole_0 @ B @ C ) )
=> ( C
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_pre_topc) ).
thf(4132,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
& ( r1_xboole_0 @ B @ C ) )
=> ( C
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1280,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_lattice4) ).
thf(6653,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v2_filter_0 @ ( k1_filter_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_xboole_1) ).
thf(2322,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(502,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ~ ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ C @ B ) @ A )
= ( k1_funct_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_4) ).
thf(3359,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ~ ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ C @ B ) @ A )
= ( k1_funct_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).
thf(3329,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(454,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ A @ ( k1_funct_4 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_4) ).
thf(3174,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ A @ ( k1_funct_4 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1006,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v14_lattices @ A )
=> ( v14_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_filter_0) ).
thf(5450,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( v14_lattices @ A )
=> ( v14_lattices @ ( k8_filter_0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(603,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_funct_1 @ ( k5_lattice4 @ A ) )
& ( v1_funct_2 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice4) ).
thf(3853,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v1_funct_1 @ ( k5_lattice4 @ A ) )
& ( v1_funct_2 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ ( k5_lattice4 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(696,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_3 @ B ) ) )
=> ( ( k1_funct_1 @ ( k1_funct_3 @ B ) @ A )
= ( k9_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_3) ).
thf(4164,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_3 @ B ) ) )
=> ( ( k1_funct_1 @ ( k1_funct_3 @ B ) @ A )
= ( k9_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(571,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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(3715,plain,
! [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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(104,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(1766,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(257,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(2379,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(1187,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( m2_lattice4 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_lattice4) ).
thf(6262,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( m2_lattice4 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B ) )
=> ( ( r2_hidden @ ( k4_lattices @ A @ C @ D ) @ B )
& ( r2_hidden @ ( k3_lattices @ A @ C @ D ) @ B ) ) ) ) )
=> ( m2_lattice4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(1319,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( v2_funct_1 @ ( k9_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lopclset) ).
thf(6775,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( v2_funct_1 @ ( k9_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(892,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( v3_tops_1 @ B @ A )
<=> ( B
= ( k2_tops_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_tops_1) ).
thf(4991,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( ( ( v3_tops_1 @ B @ A )
=> ( B
= ( k2_tops_1 @ A @ B ) ) )
& ( ( B
= ( k2_tops_1 @ A @ B ) )
=> ( v3_tops_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(1043,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_pre_topc) ).
thf(5633,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(1051,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k2_lopclset @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_lopclset) ).
thf(5685,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( ( k2_lopclset @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
thf(2030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
= ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1361,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_tarski @ ( k10_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_lopclset) ).
thf(6917,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( r1_tarski @ ( k10_lopclset @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(633,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(3961,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
& ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(856,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
= ( k1_funct_4 @ A @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_funct_4) ).
thf(4838,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
= ( k1_funct_4 @ A @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(416,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) )
=> ( ( B
= ( k4_lopclset @ A ) )
<=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( k2_binop_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ B @ C @ D )
= ( k2_lopclset @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lopclset) ).
thf(3007,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) )
& ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) ) @ ( k1_lopclset @ A ) ) )
=> ( ( ( B
= ( k4_lopclset @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( k2_binop_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ B @ C @ D )
= ( k2_lopclset @ A @ C @ D ) ) ) ) )
& ( ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ! [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) )
=> ( ( k2_binop_1 @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ ( k1_lopclset @ A ) @ B @ C @ D )
= ( k2_lopclset @ A @ C @ D ) ) ) )
=> ( B
= ( k4_lopclset @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ D @ A @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k2_lattice2 @ A @ B @ C @ D ) @ ( u1_struct_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice2) ).
thf(2247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ D @ A @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k2_lattice2 @ A @ B @ C @ D ) @ ( u1_struct_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(933,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_lattices) ).
thf(5147,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k7_lattices @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(947,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_tops_1) ).
thf(5208,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k1_tops_1 @ A @ B ) @ ( k1_tops_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(148,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) @ D )
= ( k4_lattices @ A @ ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_lattice4) ).
thf(1934,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ C ) ) @ D )
= ( k4_lattices @ A @ ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ B @ D ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(398,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) ) )
=> ( ( v2_funct_1 @ B )
& ( v2_funct_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_funct_1) ).
thf(2948,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( ( k2_relat_1 @ B )
= ( k1_relat_1 @ A ) ) )
=> ( ( v2_funct_1 @ B )
& ( v2_funct_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1203,axiom,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(6337,plain,
! [A: $i] :
? [B: $i] :
( ( r2_hidden @ A @ B )
& ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r1_tarski @ D @ C ) )
=> ( r2_hidden @ D @ B ) )
& ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( r2_hidden @ ( k1_zfmisc_1 @ C ) @ B ) )
& ! [C: $i] :
~ ( ( r1_tarski @ C @ B )
& ~ ( r2_tarski @ C @ B )
& ~ ( r2_hidden @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(1849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(2558,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(636,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) )
<=> ( r3_lattices @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_filter_0) ).
thf(3970,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) )
=> ( r3_lattices @ A @ C @ B ) )
& ( ( r3_lattices @ A @ C @ B )
=> ( r2_hidden @ B @ ( k2_filter_0 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(1145,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k6_pre_topc @ B @ D )
= ( k3_xboole_0 @ ( k6_pre_topc @ A @ C ) @ ( k2_pre_topc @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_pre_topc) ).
thf(6073,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( C = D )
=> ( ( k6_pre_topc @ B @ D )
= ( k3_xboole_0 @ ( k6_pre_topc @ A @ C ) @ ( k2_pre_topc @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(954,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_filter_0) ).
thf(5223,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( a_3_1_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
& ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattices) ).
thf(3124,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ( ~ ( v3_struct_0 @ ( g3_lattices @ A @ B @ C ) )
& ( v3_lattices @ ( g3_lattices @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).
thf(2145,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
=> ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1020,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_filter_0 @ A @ B )
= ( k2_filter_0 @ A @ C ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_filter_1) ).
thf(5504,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_filter_0 @ A @ B )
= ( k2_filter_0 @ A @ C ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(2357,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(99,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ B @ A )
& ( m2_relset_1 @ C @ B @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ( ( ( k2_funct_2 @ B @ A @ C @ D )
= k1_xboole_0 )
=> ( D = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_setwiseo) ).
thf(1749,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ B @ A )
& ( m2_relset_1 @ C @ B @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
=> ( ( ( k2_funct_2 @ B @ A @ C @ D )
= k1_xboole_0 )
=> ( D = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(662,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( v2_tops_1 @ C @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v2_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_tops_1) ).
thf(4046,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( v2_tops_1 @ C @ A )
& ( v4_pre_topc @ C @ A ) )
=> ( v2_tops_1 @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(874,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_borsuk_1 @ C @ B ) )
=> ( m1_borsuk_1 @ ( k19_borsuk_1 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k19_borsuk_1) ).
thf(4932,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( m1_borsuk_1 @ C @ B ) )
=> ( m1_borsuk_1 @ ( k19_borsuk_1 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(510,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_tops_1) ).
thf(3388,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
=> ( v3_tops_1 @ ( k2_tops_1 @ A @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(755,axiom,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(4431,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( v1_funct_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) )
& ( v1_funct_2 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B )
& ( m2_relset_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_lattice2) ).
thf(2511,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ B )
& ( m2_relset_1 @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( v1_funct_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) )
& ( v1_funct_2 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B )
& ( m2_relset_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k3_tarski @ ( k5_setfam_1 @ A @ B ) )
= ( k3_tarski @ ( a_2_0_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_borsuk_1) ).
thf(4634,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( k3_tarski @ ( k5_setfam_1 @ A @ B ) )
= ( k3_tarski @ ( a_2_0_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(955,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ! [G: $i] :
( ( m1_filter_0 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( u1_struct_0 @ A ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( u1_struct_0 @ A ) )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r1_filter_0 @ C @ G @ D @ E )
& ( r1_filter_0 @ C @ G @ E @ F ) )
=> ( r1_filter_0 @ C @ G @ D @ F ) )
& ( ( ( r1_filter_0 @ A @ B @ H @ I )
& ( r1_filter_0 @ A @ B @ I @ J ) )
=> ( r1_filter_0 @ A @ B @ H @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_filter_0) ).
thf(5226,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v3_filter_0 @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ C ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ C ) )
=> ! [G: $i] :
( ( m1_filter_0 @ G @ C )
=> ! [H: $i] :
( ( m1_subset_1 @ H @ ( u1_struct_0 @ A ) )
=> ! [I: $i] :
( ( m1_subset_1 @ I @ ( u1_struct_0 @ A ) )
=> ! [J: $i] :
( ( m1_subset_1 @ J @ ( u1_struct_0 @ A ) )
=> ( ( ( ( r1_filter_0 @ C @ G @ D @ E )
& ( r1_filter_0 @ C @ G @ E @ F ) )
=> ( r1_filter_0 @ C @ G @ D @ F ) )
& ( ( ( r1_filter_0 @ A @ B @ H @ I )
& ( r1_filter_0 @ A @ B @ I @ J ) )
=> ( r1_filter_0 @ A @ B @ H @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(1150,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k7_filter_0 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_filter_0) ).
thf(6086,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k7_filter_0 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ C ) @ ( k2_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relset_1) ).
thf(1881,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( r1_tarski @ ( k3_relat_1 @ C ) @ ( k2_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1168,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(6161,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ! [D: $i] :
( ( m1_subset_1 @ D @ B )
=> ( r2_hidden @ D @ C ) )
=> ( r1_tarski @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(620,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ? [B: $i,C: $i] : ( r1_tarski @ ( k1_relat_1 @ ( k2_funct_4 @ A ) ) @ ( k2_zfmisc_1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_funct_4) ).
thf(3914,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ? [B: $i,C: $i] : ( r1_tarski @ ( k1_relat_1 @ ( k2_funct_4 @ A ) ) @ ( k2_zfmisc_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(310,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
=> ( v2_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
thf(2584,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
=> ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(715,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ B @ ( k10_relat_1 @ C @ A ) ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_setwiseo) ).
thf(4257,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ B @ ( k10_relat_1 @ C @ A ) ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
| ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(4671,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_xboole_0 @ A @ B )
| ( r1_xboole_0 @ C @ D ) )
=> ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_funct_1) ).
thf(4819,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k10_filter_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k8_filter_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_1) ).
thf(6301,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k10_filter_1 @ A @ B @ C @ D ) @ ( u1_struct_0 @ ( k8_filter_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(1326,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( v11_lattices @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_lattice4) ).
thf(6793,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v11_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ B @ A )
=> ( ( v2_lattice4 @ C @ B @ A )
=> ( v11_lattices @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(60,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tops_1) ).
thf(1617,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v1_tops_1 @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ A @ B )
& ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ~ ( ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ C @ B ) )
& ~ ( ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_0) ).
thf(1940,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ A @ B )
& ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ~ ( ( r2_hidden @ C @ A )
& ~ ( r2_hidden @ C @ B ) )
& ~ ( ( r2_hidden @ C @ B )
& ~ ( r2_hidden @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(4548,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( B
= ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(2458,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( B
= ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(1649,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ! [C: $i] :
( ( m1_realset1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(802,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(4606,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(833,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v6_compts_1 @ D @ B )
=> ! [E: $i] :
( ( m2_connsp_2 @ E @ ( k6_borsuk_1 @ B @ A ) @ ( k7_borsuk_1 @ B @ A @ D @ ( k1_struct_0 @ A @ C ) ) )
=> ? [F: $i] :
( ( m2_connsp_2 @ F @ B @ D )
& ? [G: $i] :
( ( m1_connsp_2 @ G @ A @ C )
& ( r1_tarski @ ( k10_borsuk_1 @ B @ A @ D @ C @ F @ G ) @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_borsuk_1) ).
thf(4727,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( v6_compts_1 @ D @ B )
=> ! [E: $i] :
( ( m2_connsp_2 @ E @ ( k6_borsuk_1 @ B @ A ) @ ( k7_borsuk_1 @ B @ A @ D @ ( k1_struct_0 @ A @ C ) ) )
=> ? [F: $i] :
( ( m2_connsp_2 @ F @ B @ D )
& ? [G: $i] :
( ( m1_connsp_2 @ G @ A @ C )
& ( r1_tarski @ ( k10_borsuk_1 @ B @ A @ D @ C @ F @ G ) @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_partfun1) ).
thf(4945,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(453,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_1) ).
thf(3171,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k1_relat_1 @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
thf(1913,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(535,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(3533,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(1022,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relat_1) ).
thf(5510,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1367,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( v3_lattice4 @ C @ A @ B )
<=> ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice4) ).
thf(6938,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_lattice4 @ C @ A @ B )
=> ( ( ( v3_lattice4 @ C @ A @ B )
=> ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) ) )
& ( ( ( v1_lattice4 @ C @ A @ B )
& ( v2_lattice4 @ C @ A @ B ) )
=> ( v3_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ F @ G )
= ( k2_binop_1 @ A @ B @ C @ E @ F @ G ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_binop_1) ).
thf(1453,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ B )
=> ( ( k2_binop_1 @ A @ B @ C @ D @ F @ G )
= ( k2_binop_1 @ A @ B @ C @ E @ F @ G ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(561,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( A != k1_xboole_0 )
=> ( ( m1_eqrel_1 @ B @ A )
<=> ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( m1_eqrel_1 @ B @ A )
<=> ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(3665,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( A != k1_xboole_0 )
=> ( ( ( m1_eqrel_1 @ B @ A )
=> ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) )
& ( ( ( ( k5_setfam_1 @ A @ B )
= A )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( r2_hidden @ C @ B )
=> ( ( C != k1_xboole_0 )
& ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( r2_hidden @ D @ B )
& ( C != D )
& ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) )
=> ( m1_eqrel_1 @ B @ A ) ) ) )
& ( ( A = k1_xboole_0 )
=> ( ( ( m1_eqrel_1 @ B @ A )
=> ( B = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( m1_eqrel_1 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(1304,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lopclset) ).
thf(6726,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k7_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(810,axiom,
? [A: $i] : ( l2_lattices @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(4639,plain,
? [A: $i] : ( l2_lattices @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(356,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( r2_hidden @ E @ ( k10_setwiseo @ A @ B @ D @ C ) )
<=> ? [F: $i] :
( ( m1_subset_1 @ F @ A )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ E @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_setwiseo) ).
thf(2760,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
& ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
=> ! [E: $i] :
( ( ( r2_hidden @ E @ ( k10_setwiseo @ A @ B @ D @ C ) )
=> ? [F: $i] :
( ( m1_subset_1 @ F @ A )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ E @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) ) )
& ( ? [F: $i] :
( ( m1_subset_1 @ F @ A )
& ( r2_hidden @ F @ D )
& ( r2_hidden @ E @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) )
=> ( r2_hidden @ E @ ( k10_setwiseo @ A @ B @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1192,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) )
= ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_lattices) ).
thf(6286,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k7_lattices @ A @ ( k3_lattices @ A @ B @ C ) )
= ( k4_lattices @ A @ ( k7_lattices @ A @ B ) @ ( k7_lattices @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(390,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 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(2924,plain,
! [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 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( ( k5_setwiseo @ A @ B @ C )
= ( k5_setwiseo @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_setwiseo) ).
thf(1839,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( ( k5_setwiseo @ A @ B @ C )
= ( k5_setwiseo @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).
thf(4651,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
=> ( ( ( B = k1_xboole_0 )
& ( A != k1_xboole_0 ) )
| ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ C )
& ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(551,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_1) ).
thf(3620,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) ) )
& ( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
& ( ( k1_relat_1 @ B )
= ( k1_relat_1 @ C ) )
& ( ( k5_relat_1 @ B @ A )
= ( k5_relat_1 @ C @ A ) ) )
=> ( B = C ) ) ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( r2_hidden @ A @ ( a_2_1_borsuk_1 @ B @ C ) )
<=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k12_mcart_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ B ) )
& ( r2_hidden @ E @ ( u1_pre_topc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_borsuk_1) ).
thf(5981,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( v2_pre_topc @ C )
& ( l1_pre_topc @ C ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_borsuk_1 @ B @ C ) )
=> ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k12_mcart_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ B ) )
& ( r2_hidden @ E @ ( u1_pre_topc @ C ) ) ) )
& ( ? [D: $i,E: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
& ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( u1_struct_0 @ C ) ) )
& ( A
= ( k12_mcart_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ C ) @ D @ E ) )
& ( r2_hidden @ D @ ( u1_pre_topc @ B ) )
& ( r2_hidden @ E @ ( u1_pre_topc @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_1_borsuk_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(1227,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k6_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).
thf(6447,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k6_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(942,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).
thf(5179,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A = D )
& ( r3_lattices @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_2_0_filter_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(1316,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( v3_lattice4 @ ( k13_lopclset @ A ) @ A @ ( k12_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_lopclset) ).
thf(6758,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( v3_lattice4 @ ( k13_lopclset @ A ) @ A @ ( k12_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(154,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
thf(1966,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
=> ( ( ( k1_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) )
& ( ( k2_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
= ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1215,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(6408,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(1133,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(6041,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).
thf(1553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ D )
= ( k1_tarski @ A ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
thf(1949,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( k1_tarski @ A )
= ( k2_xboole_0 @ B @ C ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B = k1_xboole_0 )
& ( C
= ( k1_tarski @ A ) ) )
& ~ ( ( B
= ( k1_tarski @ A ) )
& ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(379,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( k2_partfun1 @ A @ B @ D @ C )
= ( k2_partfun1 @ A @ B @ E @ C ) )
<=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice2) ).
thf(2870,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( ( ( k2_partfun1 @ A @ B @ D @ C )
= ( k2_partfun1 @ A @ B @ E @ C ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ F ) ) ) ) )
& ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ C )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ F ) ) ) )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= ( k2_partfun1 @ A @ B @ E @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).
thf(2828,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k9_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(2310,plain,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1162,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( v1_relat_1 @ ( k10_filter_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_filter_0) ).
thf(6137,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A ) )
=> ( v1_relat_1 @ ( k10_filter_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(1105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(5934,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
=> ( m1_subset_1 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(844,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
<=> ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_tops_1) ).
thf(4780,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) )
& ( ( ( k2_tops_1 @ A @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_xboole_1) ).
thf(2325,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
= ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(701,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
thf(4185,plain,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(673,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(4078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(976,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(5308,plain,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_xboole_1) ).
thf(1448,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
=> ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_xboole_1) ).
thf(2490,plain,
! [A: $i,B: $i,C: $i] :
( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_xboole_1) ).
thf(2187,plain,
! [A: $i,B: $i] :
( ( ( k2_xboole_0 @ A @ B )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(647,axiom,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(4006,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(491,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( v2_funct_1 @ B )
<=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).
thf(3320,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( ( v2_funct_1 @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ A )
& ( ( k1_funct_1 @ B @ C )
= ( k1_funct_1 @ B @ D ) ) )
=> ( C = D ) )
=> ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(764,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( B
= ( k5_lattices @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattices) ).
thf(4463,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_lattices @ A ) )
=> ( ( v13_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( B
= ( k5_lattices @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k2_lattices @ A @ B @ C )
= B )
& ( ( k2_lattices @ A @ C @ B )
= B ) ) )
=> ( B
= ( k5_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(698,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(4170,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(1310,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_subset_1 @ ( k1_pre_topc @ A ) @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_lopclset) ).
thf(6743,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_subset_1 @ ( k1_pre_topc @ A ) @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(982,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_tops_1) ).
thf(5332,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( r2_hidden @ C @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ D @ A )
& ( r1_tarski @ D @ B )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ C @ B ) ) )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(360,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ F @ C )
=> ( r3_lattices @ A @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ D @ F ) @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ F ) ) ) )
=> ( ( C = k1_xboole_0 )
| ( r3_lattices @ A @ ( k3_lattice2 @ B @ A @ C @ D ) @ ( k3_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_lattice2) ).
thf(2775,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( r2_hidden @ F @ C )
=> ( r3_lattices @ A @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ D @ F ) @ ( k8_funct_2 @ B @ ( u1_struct_0 @ A ) @ E @ F ) ) ) )
=> ( ( C = k1_xboole_0 )
| ( r3_lattices @ A @ ( k3_lattice2 @ B @ A @ C @ D ) @ ( k3_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( ( k5_setwiseo @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setwiseo) ).
thf(1734,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
=> ( ( k5_setwiseo @ A @ B @ C )
= ( k2_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(365,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_tops_1) ).
thf(2792,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_tops_1 @ B @ A )
=> ( v2_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(389,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) )
=> ( A
= ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_1) ).
thf(2907,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( ( k1_relat_1 @ C )
= A )
& ( ( k1_relat_1 @ D )
= A )
& ( ( k5_relat_1 @ B @ C )
= ( k5_relat_1 @ B @ D ) ) )
=> ( C = D ) ) ) ) )
=> ( A
= ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1356,axiom,
? [A: $i] : ( l1_pre_topc @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(6903,plain,
? [A: $i] : ( l1_pre_topc @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(5,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ C @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) ) @ ( k5_lattice4 @ A ) )
= ( k4_lattices @ A @ ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ C @ ( k5_lattice4 @ A ) ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_lattice4) ).
thf(1385,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ C @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) ) @ ( k5_lattice4 @ A ) )
= ( k4_lattices @ A @ ( k3_lattice2 @ ( u1_struct_0 @ A ) @ A @ C @ ( k5_lattice4 @ A ) ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(528,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ B @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) ) ) )
=> ( ( D = k1_xboole_0 )
| ( r3_lattices @ A @ B @ ( k3_lattice2 @ C @ A @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_lattice2) ).
thf(3484,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( r3_lattices @ A @ B @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) ) ) )
=> ( ( D = k1_xboole_0 )
| ( r3_lattices @ A @ B @ ( k3_lattice2 @ C @ A @ D @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(984,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(5351,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(494,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_1) ).
thf(3336,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(64,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v14_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ( ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ D @ B )
= ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ E @ B ) )
=> ( ( k3_lattice2 @ A @ C @ B @ D )
= ( k3_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_lattice2) ).
thf(1629,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v14_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ( ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ D @ B )
= ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ E @ B ) )
=> ( ( k3_lattice2 @ A @ C @ B @ D )
= ( k3_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1082,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( m1_subset_1 @ ( k6_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_lattices) ).
thf(5813,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( m1_subset_1 @ ( k6_lattices @ A ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_xboole_1) ).
thf(1854,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ C ) )
=> ( r1_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(470,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( v11_lattices @ A )
<=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k1_lattices @ A @ C @ D ) )
= ( k1_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ ( k2_lattices @ A @ B @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_lattices) ).
thf(3235,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v11_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k1_lattices @ A @ C @ D ) )
= ( k1_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ ( k2_lattices @ A @ B @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k2_lattices @ A @ B @ ( k1_lattices @ A @ C @ D ) )
= ( k1_lattices @ A @ ( k2_lattices @ A @ B @ C ) @ ( k2_lattices @ A @ B @ D ) ) ) ) ) )
=> ( v11_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1070,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m3_lattice4 @ C @ A )
=> ( ( C
= ( k3_lattice4 @ A @ B ) )
<=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_lattice4) ).
thf(5756,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m3_lattice4 @ C @ A )
=> ( ( ( C
= ( k3_lattice4 @ A @ B ) )
=> ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) ) )
& ( ( ( r1_tarski @ B @ C )
& ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( r1_tarski @ B @ D )
=> ( r1_tarski @ C @ D ) ) ) )
=> ( C
= ( k3_lattice4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(441,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(3136,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( k5_finsub_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finsub_1) ).
thf(4969,plain,
! [A: $i,B: $i] :
( ( k5_finsub_1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(1329,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_filter_1) ).
thf(6799,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( r1_filter_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).
thf(1646,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( ( r1_tarski @ B @ C )
& ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(978,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( v1_filter_0 @ B @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_lopclset) ).
thf(5315,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ~ ( ( v1_filter_0 @ B @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1146,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(6077,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(2167,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k2_xboole_0 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(846,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_4 @ A ) )
& ( v1_funct_1 @ ( k2_funct_4 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_4) ).
thf(4806,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_4 @ A ) )
& ( v1_funct_1 @ ( k2_funct_4 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_subset_1) ).
thf(1476,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ( ( k6_subset_1 @ A @ B @ C )
= ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( B != k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= ( k6_setfam_1 @ A @ B ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_setfam_1) ).
thf(1674,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( B != k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= ( k6_setfam_1 @ A @ B ) ) )
& ( ( B = k1_xboole_0 )
=> ( ( k8_setfam_1 @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1268,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_1) ).
thf(6607,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(1235,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_pre_topc) ).
thf(6489,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( r2_hidden @ B @ ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(805,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_relat_1 @ ( k17_borsuk_1 @ A @ B ) )
= ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_borsuk_1) ).
thf(4615,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_relat_1 @ ( k17_borsuk_1 @ A @ B ) )
= ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(2251,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
& ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
=> ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(597,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_finset_1 @ A )
=> ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(3825,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( v1_finset_1 @ A )
=> ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(1293,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_0) ).
thf(6689,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v3_filter_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k20_borsuk_1 @ A @ B @ C )
= ( k18_borsuk_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k20_borsuk_1) ).
thf(4666,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( k20_borsuk_1 @ A @ B @ C )
= ( k18_borsuk_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(1128,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v14_lattices @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_filter_0) ).
thf(6030,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( m1_filter_0 @ ( k6_domain_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1352,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k6_lopclset @ A )
= ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lopclset) ).
thf(6893,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k6_lopclset @ A )
= ( g3_lattices @ ( k1_lopclset @ A ) @ ( k4_lopclset @ A ) @ ( k5_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(296,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k1_funct_4 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_4) ).
thf(2532,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k1_funct_4 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(1508,plain,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(944,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( v14_lattices @ A )
<=> ( v13_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_lattice2) ).
thf(5191,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( ( v14_lattices @ A )
=> ( v13_lattices @ ( k1_lattice2 @ A ) ) )
& ( ( v13_lattices @ ( k1_lattice2 @ A ) )
=> ( v14_lattices @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(372,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ D @ B )
=> ( ( k1_tops_1 @ B @ D )
= D ) )
& ( ( ( k1_tops_1 @ A @ C )
= C )
=> ( v3_pre_topc @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_1) ).
thf(2823,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_pre_topc @ D @ B )
=> ( ( k1_tops_1 @ B @ D )
= D ) )
& ( ( ( k1_tops_1 @ A @ C )
= C )
=> ( v3_pre_topc @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(660,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_relat_1) ).
thf(4042,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(783,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) )
= ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) ) ) ) ) )
=> ( v11_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_lattices) ).
thf(4542,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) )
= ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) ) ) ) ) )
=> ( v11_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(855,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v14_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ E @ F ) ) ) )
=> ( r3_lattices @ C @ ( k3_lattice2 @ A @ C @ B @ D ) @ ( k3_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_lattice2) ).
thf(4834,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v14_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ E @ F ) ) ) )
=> ( r3_lattices @ C @ ( k3_lattice2 @ A @ C @ B @ D ) @ ( k3_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(772,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v4_pre_topc @ C @ A ) ) )
=> ( v4_pre_topc @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_pre_topc) ).
thf(4495,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ C @ B )
=> ( v4_pre_topc @ C @ A ) ) )
=> ( v4_pre_topc @ ( k6_setfam_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(962,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k5_lattices @ A ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_lopclset) ).
thf(5243,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( k1_zfmisc_1 @ ( k7_lopclset @ A ) ) @ ( k9_lopclset @ A ) @ ( k5_lattices @ A ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(830,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
& ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ D ) )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( E
= ( k12_mcart_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ G ) )
& ( v3_pre_topc @ F @ A )
& ( v3_pre_topc @ G @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_borsuk_1) ).
thf(4705,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( ( ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
& ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ D ) )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( E
= ( k12_mcart_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ G ) )
& ( v3_pre_topc @ F @ A )
& ( v3_pre_topc @ G @ B ) ) ) ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) ) )
& ( C
= ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ D ) )
& ! [E: $i] :
~ ( ( r2_hidden @ E @ D )
& ! [F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [G: $i] :
( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ~ ( ( E
= ( k12_mcart_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ F @ G ) )
& ( v3_pre_topc @ F @ A )
& ( v3_pre_topc @ G @ B ) ) ) ) ) )
=> ( v3_pre_topc @ C @ ( k6_borsuk_1 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(191,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k17_borsuk_1 @ A @ B )
= ( k2_borsuk_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_borsuk_1) ).
thf(2130,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( k17_borsuk_1 @ A @ B )
= ( k2_borsuk_1 @ ( u1_struct_0 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ C @ A ) @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_xboole_1) ).
thf(2416,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k2_xboole_0 @ ( k4_xboole_0 @ C @ A ) @ B )
= ( k4_xboole_0 @ ( k2_xboole_0 @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(584,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(3780,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ A )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( k4_xboole_0 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(4900,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( k4_xboole_0 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) ) )
& ( ( ( r2_hidden @ D @ A )
& ~ ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(48,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k2_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_pre_topc) ).
thf(1558,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) )
= ( k2_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(198,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( v5_pre_topc @ ( k3_borsuk_1 @ B @ A @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_borsuk_1) ).
thf(2152,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( v5_pre_topc @ ( k3_borsuk_1 @ B @ A @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(760,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_relat_1) ).
thf(4451,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(1101,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(5922,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
& ( m1_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
=> ( m1_subset_1 @ ( k10_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_setwiseo) ).
thf(2394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
& ( m1_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
=> ( m1_subset_1 @ ( k10_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(563,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t170_relat_1) ).
thf(3694,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(938,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( r2_hidden @ B @ A ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( m1_subset_1 @ B @ A )
<=> ( v1_xboole_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(5162,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( r2_hidden @ B @ A ) )
& ( ( r2_hidden @ B @ A )
=> ( m1_subset_1 @ B @ A ) ) ) )
& ( ( v1_xboole_0 @ A )
=> ( ( ( m1_subset_1 @ B @ A )
=> ( v1_xboole_0 @ B ) )
& ( ( v1_xboole_0 @ B )
=> ( m1_subset_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(615,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v2_tops_1 @ B @ A )
<=> ( r1_tarski @ B @ ( k2_tops_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_tops_1) ).
thf(3896,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
=> ( r1_tarski @ B @ ( k2_tops_1 @ A @ B ) ) )
& ( ( r1_tarski @ B @ ( k2_tops_1 @ A @ B ) )
=> ( v2_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(1190,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(6277,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
& ( v1_xboole_0 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1091,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_lattice4 @ A @ ( k1_setwiseo @ ( u1_struct_0 @ A ) ) )
= ( k6_lattices @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattice4) ).
thf(5869,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k2_lattice4 @ A @ ( k1_setwiseo @ ( u1_struct_0 @ A ) ) )
= ( k6_lattices @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(932,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(5144,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(319,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B ) @ ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_3) ).
thf(2623,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B ) @ ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1179,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( r3_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_filter_0) ).
thf(6198,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( r3_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(839,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funct_1) ).
thf(4745,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ C ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
=> ( C
= ( k5_relat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(273,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_tops_1) ).
thf(2447,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ C ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1241,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k9_filter_1 @ A ) )
<=> ( r3_lattices @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_1) ).
thf(6516,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k9_filter_1 @ A ) )
=> ( r3_lattices @ A @ B @ C ) )
& ( ( r3_lattices @ A @ B @ C )
=> ( r2_hidden @ ( k1_domain_1 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) @ B @ C ) @ ( k9_filter_1 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(400,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( v3_struct_0 @ A )
<=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_struct_0) ).
thf(2956,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( ( v3_struct_0 @ A )
=> ( v1_xboole_0 @ ( u1_struct_0 @ A ) ) )
& ( ( v1_xboole_0 @ ( u1_struct_0 @ A ) )
=> ( v3_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(639,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
<=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_filter_1) ).
thf(3978,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) )
=> ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ B ) )
& ( ( r2_hidden @ ( k4_filter_0 @ A @ C @ D ) @ B )
=> ( r3_lattices @ ( k5_filter_1 @ A @ B ) @ ( k6_filter_1 @ A @ B @ C ) @ ( k6_filter_1 @ A @ B @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_xboole_1) ).
thf(2081,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(995,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_lopclset @ A ) )
=> ( v3_pre_topc @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lopclset) ).
thf(5408,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_lopclset @ A ) )
=> ( v3_pre_topc @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(1341,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k6_filter_0 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_filter_0) ).
thf(6854,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( m1_filter_0 @ ( k6_filter_0 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(610,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).
thf(3879,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(705,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
<=> ( ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ B )
& ( r1_tarski @ B @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_tops_1) ).
thf(4214,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_tops_1 @ B @ A )
=> ( ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ B )
& ( r1_tarski @ B @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) ) )
& ( ( ( r1_tarski @ ( k1_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ B )
& ( r1_tarski @ B @ ( k6_pre_topc @ A @ ( k1_tops_1 @ A @ B ) ) ) )
=> ( v4_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1158,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_filter_0 @ A @ B ) @ C ) ) )
& ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_filter_0 @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_filter_0) ).
thf(6118,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k3_filter_0 @ A @ B ) @ C ) ) )
& ( ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) )
= ( k3_filter_0 @ A @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ ( k3_filter_0 @ A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1074,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_pre_topc) ).
thf(5781,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ? [B: $i] :
( ( m1_pre_topc @ B @ A )
& ( v1_pre_topc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(1135,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k2_funct_4 @ A ) ) @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_4) ).
thf(6045,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k2_funct_4 @ A ) ) @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(904,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_relat_1) ).
thf(5040,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(214,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( v4_pre_topc @ D @ B )
& ( v4_tops_1 @ D @ B ) )
=> ( v5_tops_1 @ D @ B ) )
& ( ( v5_tops_1 @ C @ A )
=> ( ( v4_pre_topc @ C @ A )
& ( v4_tops_1 @ C @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_tops_1) ).
thf(2230,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( l1_pre_topc @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( ( ( v4_pre_topc @ D @ B )
& ( v4_tops_1 @ D @ B ) )
=> ( v5_tops_1 @ D @ B ) )
& ( ( v5_tops_1 @ C @ A )
=> ( ( v4_pre_topc @ C @ A )
& ( v4_tops_1 @ C @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
thf(2036,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
& ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(556,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ G )
& ( r2_hidden @ G @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_mcart_1) ).
thf(3645,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ G )
& ( r2_hidden @ G @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(136,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( B
!= ( k2_pre_topc @ A ) )
& ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
!= k1_xboole_0 )
& ( B
= ( k2_pre_topc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_pre_topc) ).
thf(1893,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ~ ( ( B
!= ( k2_pre_topc @ A ) )
& ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= k1_xboole_0 ) )
& ~ ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
!= k1_xboole_0 )
& ( B
= ( k2_pre_topc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(231,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) @ B ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_tops_1) ).
thf(2294,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_tops_1 @ A @ B )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) ) @ B ) @ ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k6_pre_topc @ A @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(350,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_mcart_1) ).
thf(2739,plain,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ C @ D )
& ( r2_hidden @ D @ E )
& ( r2_hidden @ E @ F )
& ( r2_hidden @ F @ B ) )
=> ( r1_xboole_0 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(681,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( B
= ( k6_lattices @ A ) )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattices) ).
thf(4098,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l2_lattices @ A ) )
=> ( ( v14_lattices @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ( B
= ( k6_lattices @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( k1_lattices @ A @ B @ C )
= B )
& ( ( k1_lattices @ A @ C @ B )
= B ) ) )
=> ( B
= ( k6_lattices @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(1226,axiom,
? [A: $i] :
( ( l1_pre_topc @ A )
& ( v1_pre_topc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pre_topc) ).
thf(6444,plain,
? [A: $i] :
( ( l1_pre_topc @ A )
& ( v1_pre_topc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
=> ( ( C = D )
| ( r1_xboole_0 @ C @ D ) ) )
=> ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t101_zfmisc_1) ).
thf(1994,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
& ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
=> ( ( C = D )
| ( r1_xboole_0 @ C @ D ) ) )
=> ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(945,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k8_lopclset @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( a_2_0_lopclset @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_lopclset) ).
thf(5194,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k8_lopclset @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( a_2_0_lopclset @ A @ C ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( u1_struct_0 @ A ) )
& ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( a_2_0_lopclset @ A @ C ) ) ) )
=> ( B
= ( k8_lopclset @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(971,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k6_pre_topc @ A @ B ) )
= ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_tops_1) ).
thf(5287,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k6_pre_topc @ A @ ( k6_pre_topc @ A @ B ) )
= ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(520,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k10_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
thf(3420,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k10_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k10_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).
thf(1614,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ k1_xboole_0 @ A )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(585,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( k1_tops_1 @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) )
= ( k7_borsuk_1 @ A @ B @ ( k1_tops_1 @ A @ C ) @ ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_borsuk_1) ).
thf(3785,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ( ( k1_tops_1 @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) )
= ( k7_borsuk_1 @ A @ B @ ( k1_tops_1 @ A @ C ) @ ( k1_tops_1 @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(2534,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ( k3_subset_1 @ A @ B )
= ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(1295,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_filter_1) ).
thf(6693,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_filter_0 @ B @ A )
& ( m1_filter_0 @ C @ A ) )
=> ( ( k1_filter_1 @ A @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(1364,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( B
= ( k11_lopclset @ A ) )
<=> ( ( ( u1_struct_0 @ B )
= ( k7_lopclset @ A ) )
& ( ( u1_pre_topc @ B )
= ( a_1_2_lopclset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lopclset) ).
thf(6925,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ( v1_pre_topc @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( ( B
= ( k11_lopclset @ A ) )
=> ( ( ( u1_struct_0 @ B )
= ( k7_lopclset @ A ) )
& ( ( u1_pre_topc @ B )
= ( a_1_2_lopclset @ A ) ) ) )
& ( ( ( ( u1_struct_0 @ B )
= ( k7_lopclset @ A ) )
& ( ( u1_pre_topc @ B )
= ( a_1_2_lopclset @ A ) ) )
=> ( B
= ( k11_lopclset @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(957,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k7_lattices @ A @ C ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_lattices) ).
thf(5232,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( r3_lattices @ A @ ( k7_lattices @ A @ C ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(1028,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( v1_filter_0 @ D @ A )
=> ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
<=> ( ( r2_hidden @ B @ D )
| ( r2_hidden @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lopclset) ).
thf(5537,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( v1_filter_0 @ D @ A )
=> ( ( ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D )
=> ( ( r2_hidden @ B @ D )
| ( r2_hidden @ C @ D ) ) )
& ( ( ( r2_hidden @ B @ D )
| ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(795,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k1_tops_1 @ A @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_tops_1) ).
thf(4579,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( k1_tops_1 @ A @ ( k2_pre_topc @ A ) )
= ( k2_pre_topc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(161,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_funct_1 @ ( k17_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k17_borsuk_1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
& ( v5_pre_topc @ ( k17_borsuk_1 @ A @ B ) @ A @ ( k16_borsuk_1 @ A @ B ) )
& ( m2_relset_1 @ ( k17_borsuk_1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k17_borsuk_1) ).
thf(2003,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_funct_1 @ ( k17_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k17_borsuk_1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
& ( v5_pre_topc @ ( k17_borsuk_1 @ A @ B ) @ A @ ( k16_borsuk_1 @ A @ B ) )
& ( m2_relset_1 @ ( k17_borsuk_1 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_relat_1) ).
thf(2142,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
= ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1298,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k12_lopclset @ A ) )
& ( v10_lattices @ ( k12_lopclset @ A ) )
& ( l3_lattices @ ( k12_lopclset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k12_lopclset) ).
thf(6703,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k12_lopclset @ A ) )
& ( v10_lattices @ ( k12_lopclset @ A ) )
& ( l3_lattices @ ( k12_lopclset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ A @ B )
<=> ( m1_subset_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(3658,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ! [C: $i] :
( ( ( m2_subset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ B ) )
& ( ( m1_subset_1 @ C @ B )
=> ( m2_subset_1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(943,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) )
<=> ( ( v1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_lopclset) ).
thf(5187,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) )
=> ( ( v1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) ) )
& ( ( ( v1_filter_0 @ C @ A )
& ( r2_hidden @ B @ C ) )
=> ( r2_hidden @ C @ ( k1_funct_1 @ ( k8_lopclset @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(687,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F )
= B ) ) )
=> ( ( D = k1_xboole_0 )
| ( ( k2_lattice2 @ C @ A @ D @ E )
= B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice2) ).
thf(4125,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F )
= B ) ) )
=> ( ( D = k1_xboole_0 )
| ( ( k2_lattice2 @ C @ A @ D @ E )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(1086,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(5852,plain,
! [A: $i,B: $i] :
( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
=> ( r1_tarski @ A @ B ) )
& ( ( r1_tarski @ A @ B )
=> ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(869,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ E @ F ) ) ) )
=> ( r3_lattices @ C @ ( k2_lattice2 @ A @ C @ B @ D ) @ ( k2_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_lattice2) ).
thf(4880,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ( ( r2_hidden @ F @ B )
=> ( r3_lattices @ C @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ D @ F ) @ ( k8_funct_2 @ A @ ( u1_struct_0 @ C ) @ E @ F ) ) ) )
=> ( r3_lattices @ C @ ( k2_lattice2 @ A @ C @ B @ D ) @ ( k2_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(850,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) )
= ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattices) ).
thf(4816,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( k4_lattices @ A @ ( k4_lattices @ A @ ( k3_lattices @ A @ B @ C ) @ ( k3_lattices @ A @ C @ D ) ) @ ( k3_lattices @ A @ D @ B ) )
= ( k3_lattices @ A @ ( k3_lattices @ A @ ( k4_lattices @ A @ B @ C ) @ ( k4_lattices @ A @ C @ D ) ) @ ( k4_lattices @ A @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(1140,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v1_lattice4 @ C @ A @ B )
<=> ( v2_funct_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_lattice4) ).
thf(6055,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v1_lattice4 @ C @ A @ B )
=> ( v2_funct_1 @ C ) )
& ( ( v2_funct_1 @ C )
=> ( v1_lattice4 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_funct_4) ).
thf(5009,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
= ( k1_funct_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(335,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_tops_1) ).
thf(2683,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ ( k2_tops_1 @ A @ ( k6_pre_topc @ A @ B ) ) @ ( k2_tops_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(926,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(5129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_funct_1) ).
thf(4399,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(823,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(4687,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(847,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(4809,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
=> ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).
thf(3865,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( r2_hidden @ C @ A )
=> ( ( B = k1_xboole_0 )
| ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(896,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) )
=> ( ( k10_relat_1 @ B @ ( k3_tarski @ A ) )
= ( k3_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_3) ).
thf(5004,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) )
=> ( ( k10_relat_1 @ B @ ( k3_tarski @ A ) )
= ( k3_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(848,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_tops_1) ).
thf(4811,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_pre_topc @ C @ A ) )
=> ( v3_pre_topc @ ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(506,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( v1_borsuk_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v4_pre_topc @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_borsuk_1) ).
thf(3373,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_pre_topc @ B @ A )
=> ( ( ( v1_borsuk_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v4_pre_topc @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( C
= ( u1_struct_0 @ B ) )
=> ( v4_pre_topc @ C @ A ) ) )
=> ( v1_borsuk_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(3,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ C @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) ) @ ( k5_lattice4 @ A ) )
= ( k3_lattices @ A @ ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ C @ ( k5_lattice4 @ A ) ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_lattice4) ).
thf(1380,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ C @ ( k2_setwiseo @ ( u1_struct_0 @ A ) @ B ) ) @ ( k5_lattice4 @ A ) )
= ( k3_lattices @ A @ ( k2_lattice2 @ ( u1_struct_0 @ A ) @ A @ C @ ( k5_lattice4 @ A ) ) @ ( k7_lattices @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(371,axiom,
! [A: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ A )
& ( A = k1_xboole_0 ) )
& ~ ( ( A != k1_xboole_0 )
& ( r1_xboole_0 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(2815,plain,
! [A: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ A )
& ( A = k1_xboole_0 ) )
& ~ ( ( A != k1_xboole_0 )
& ( r1_xboole_0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ D @ C ) @ E )
= E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice2) ).
thf(2008,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ D @ C ) @ E )
= E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(857,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).
thf(4841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) )
=> ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1026,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(5522,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(44,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ D @ C )
= ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ E @ C ) )
=> ( ( C = k1_xboole_0 )
| ( ( k3_lattice2 @ B @ A @ C @ D )
= ( k3_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_lattice2) ).
thf(1527,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ B ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ D @ B @ ( u1_struct_0 @ A ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ B @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ B @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ D @ C )
= ( k2_partfun1 @ B @ ( u1_struct_0 @ A ) @ E @ C ) )
=> ( ( C = k1_xboole_0 )
| ( ( k3_lattice2 @ B @ A @ C @ D )
= ( k3_lattice2 @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(440,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(3132,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( v3_pre_topc @ B @ A )
& ( v4_pre_topc @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(1027,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_lattice4) ).
thf(5527,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ? [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
& ( C
= ( k3_lattices @ A @ ( k7_lattices @ A @ D ) @ E ) )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ E @ B ) ) )
=> ( r2_hidden @ C @ ( k4_lattice4 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(1164,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_relset_1 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_filter_0) ).
thf(6150,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( m2_relset_1 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
& ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_4) ).
thf(4357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
& ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(762,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ B )
= B ) )
& ( ( ( v2_pre_topc @ A )
& ( ( k6_pre_topc @ A @ B )
= B ) )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).
thf(4455,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( ( k6_pre_topc @ A @ B )
= B ) )
& ( ( ( v2_pre_topc @ A )
& ( ( k6_pre_topc @ A @ B )
= B ) )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1322,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_lattice4 @ ( k13_lopclset @ A ) @ A @ ( k12_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k13_lopclset) ).
thf(6782,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ( m1_lattice4 @ ( k13_lopclset @ A ) @ A @ ( k12_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(323,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ D ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_filter_0) ).
thf(2636,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r3_lattices @ A @ B @ C )
=> ( ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ C @ D ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ B @ D ) @ ( k3_lattices @ A @ D @ C ) )
& ( r3_lattices @ A @ ( k3_lattices @ A @ D @ B ) @ ( k3_lattices @ A @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(1056,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( m2_connsp_2 @ E @ A @ C )
=> ! [F: $i] :
( ( m2_connsp_2 @ F @ B @ D )
=> ( m2_connsp_2 @ ( k7_borsuk_1 @ A @ B @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_borsuk_1) ).
thf(5700,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
=> ! [E: $i] :
( ( m2_connsp_2 @ E @ A @ C )
=> ! [F: $i] :
( ( m2_connsp_2 @ F @ B @ D )
=> ( m2_connsp_2 @ ( k7_borsuk_1 @ A @ B @ E @ F ) @ ( k6_borsuk_1 @ A @ B ) @ ( k7_borsuk_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1246,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relat_1) ).
thf(6535,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(353,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( v3_tops_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_tops_1) ).
thf(2751,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v2_tops_1 @ B @ A )
& ( v4_pre_topc @ B @ A ) )
=> ( v3_tops_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(1195,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_lattice4) ).
thf(6294,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m3_lattice4 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) )
=> ( r2_hidden @ ( k3_lattices @ A @ B @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(765,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).
thf(4474,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ A )
& ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1067,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_hidden @ D @ ( k18_borsuk_1 @ A @ B @ C ) )
& ~ ( r2_hidden @ D @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r2_hidden @ E @ ( k2_pre_topc @ B ) )
& ( D
= ( k1_struct_0 @ A @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_borsuk_1) ).
thf(5741,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_eqrel_1 @ C @ ( u1_struct_0 @ B ) ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( r2_hidden @ D @ ( k18_borsuk_1 @ A @ B @ C ) )
& ~ ( r2_hidden @ D @ C )
& ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ A ) )
=> ~ ( ~ ( r2_hidden @ E @ ( k2_pre_topc @ B ) )
& ( D
= ( k1_struct_0 @ A @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(254,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_pre_topc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_pre_topc) ).
thf(2366,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ( ( k2_pre_topc @ A )
= ( k3_subset_1 @ ( u1_struct_0 @ A ) @ ( k1_pre_topc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
=> ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(3196,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
& ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
=> ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(950,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_borsuk_1) ).
thf(5215,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ ( u1_struct_0 @ ( k6_borsuk_1 @ A @ B ) ) @ ( k11_borsuk_1 @ A @ B @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1046,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( C
= ( k7_lattices @ A @ B ) )
<=> ( r2_lattices @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattices) ).
thf(5642,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v11_lattices @ A )
& ( v16_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ( ( ( C
= ( k7_lattices @ A @ B ) )
=> ( r2_lattices @ A @ C @ B ) )
& ( ( r2_lattices @ A @ C @ B )
=> ( C
= ( k7_lattices @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(922,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(5110,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1247,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(6537,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(725,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relat_1) ).
thf(4303,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(790,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
=> ( ( k1_tops_1 @ A @ ( k2_tops_1 @ A @ B ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_tops_1) ).
thf(4565,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_tops_1 @ B @ A )
=> ( ( k1_tops_1 @ A @ ( k2_tops_1 @ A @ B ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(843,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).
thf(4777,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(1171,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m2_subset_1 @ ( k1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lopclset) ).
thf(6169,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m2_subset_1 @ ( k1_pre_topc @ A ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(937,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r8_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_filter_0) ).
thf(5159,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ( r8_relat_2 @ ( k10_filter_0 @ A @ B ) @ ( u1_struct_0 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
| ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(1495,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
| ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( v1_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( l1_pre_topc @ ( k6_borsuk_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_borsuk_1) ).
thf(5709,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B ) )
=> ( ( v1_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( v2_pre_topc @ ( k6_borsuk_1 @ A @ B ) )
& ( l1_pre_topc @ ( k6_borsuk_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).
thf(3347,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(704,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) @ ( k17_borsuk_1 @ A @ B ) @ D )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_borsuk_1) ).
thf(4210,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
& ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ ( k16_borsuk_1 @ A @ B ) ) @ ( k17_borsuk_1 @ A @ B ) @ D )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(972,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_lattices @ A @ C @ D )
& ( r2_lattices @ B @ E @ F ) )
<=> ( r2_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_filter_1) ).
thf(5290,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( u1_struct_0 @ B ) )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ ( u1_struct_0 @ B ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v15_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( v15_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( ( r2_lattices @ A @ C @ D )
& ( r2_lattices @ B @ E @ F ) )
=> ( r2_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r2_lattices @ ( k8_filter_1 @ A @ B ) @ ( k10_filter_1 @ A @ B @ C @ E ) @ ( k10_filter_1 @ A @ B @ D @ F ) )
=> ( ( r2_lattices @ A @ C @ D )
& ( r2_lattices @ B @ E @ F ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_partfun1) ).
thf(1693,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( v2_funct_1 @ C )
=> ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
& ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(5019,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(675,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(4083,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1084,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ( ( k4_lattices @ ( k6_lopclset @ A ) @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_lopclset) ).
thf(5835,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k6_lopclset @ A ) ) )
=> ( ( k4_lattices @ ( k6_lopclset @ A ) @ B @ C )
= ( k3_xboole_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(2070,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(997,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( v1_lattice4 @ E @ A @ B )
=> ( ( r3_lattices @ A @ C @ D )
<=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_lattice4) ).
thf(5413,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ! [E: $i] :
( ( m1_lattice4 @ E @ A @ B )
=> ( ( v1_lattice4 @ E @ A @ B )
=> ( ( ( r3_lattices @ A @ C @ D )
=> ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) ) )
& ( ( r3_lattices @ B @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ C ) @ ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ E @ D ) )
=> ( r3_lattices @ A @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1011,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_filter_0) ).
thf(5462,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( v15_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(1561,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m2_relset_1 @ C @ A @ B )
=> ( m1_relset_1 @ C @ A @ B ) )
& ( ( m1_relset_1 @ C @ A @ B )
=> ( m2_relset_1 @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(2961,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( v1_relat_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( v1_pre_topc @ ( k21_borsuk_1 @ A @ B @ C ) )
& ( v1_borsuk_1 @ ( k21_borsuk_1 @ A @ B @ C ) @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) )
& ( m1_pre_topc @ ( k21_borsuk_1 @ A @ B @ C ) @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k21_borsuk_1) ).
thf(1710,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A )
& ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( v1_pre_topc @ ( k21_borsuk_1 @ A @ B @ C ) )
& ( v1_borsuk_1 @ ( k21_borsuk_1 @ A @ B @ C ) @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) )
& ( m1_pre_topc @ ( k21_borsuk_1 @ A @ B @ C ) @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1208,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v17_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_filter_0) ).
thf(6380,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ~ ( v3_struct_0 @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v10_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( v17_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) )
& ( l3_lattices @ ( k8_filter_0 @ A @ ( k2_filter_0 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(265,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ( ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ D @ B )
= ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ E @ B ) )
=> ( ( k2_lattice2 @ A @ C @ B @ D )
= ( k2_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_lattice2) ).
thf(2404,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ! [C: $i] :
( ( ~ ( v3_struct_0 @ C )
& ( v10_lattices @ C )
& ( v13_lattices @ C )
& ( l3_lattices @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ D @ A @ ( u1_struct_0 @ C ) ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ ( u1_struct_0 @ C ) )
& ( m2_relset_1 @ E @ A @ ( u1_struct_0 @ C ) ) )
=> ( ( ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ D @ B )
= ( k2_partfun1 @ A @ ( u1_struct_0 @ C ) @ E @ B ) )
=> ( ( k2_lattice2 @ A @ C @ B @ D )
= ( k2_lattice2 @ A @ C @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(864,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( v3_borsuk_1 @ C @ A @ B )
<=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_borsuk_1) ).
thf(4865,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) )
& ( m2_relset_1 @ C @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) )
=> ( ( ( v3_borsuk_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= D ) ) ) )
& ( ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( r2_hidden @ D @ ( u1_struct_0 @ B ) )
=> ( ( k8_funct_2 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) @ C @ D )
= D ) ) )
=> ( v3_borsuk_1 @ C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(420,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(3030,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
= ( k2_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(991,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k6_lattices @ A )
= ( k5_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_lattice2) ).
thf(5378,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ( ( k6_lattices @ A )
= ( k5_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(424,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattices @ A @ ( k1_lattice4 @ A @ B ) @ ( k1_lattice4 @ A @ C ) )
= ( k1_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_lattice4) ).
thf(3045,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_lattices @ A @ ( k1_lattice4 @ A @ B ) @ ( k1_lattice4 @ A @ C ) )
= ( k1_lattice4 @ A @ ( k5_setwiseo @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(941,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( a_2_1_lattice4 @ A @ B )
= ( k3_lattice4 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice4) ).
thf(5176,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m2_lattice4 @ B @ A ) )
=> ( ( ( r2_hidden @ ( k5_lattices @ A ) @ B )
& ( r2_hidden @ ( k6_lattices @ A ) @ B ) )
=> ( ( a_2_1_lattice4 @ A @ B )
= ( k3_lattice4 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(981,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( r2_hidden @ A @ ( a_1_0_filter_1 @ B ) )
<=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ D ) )
& ( r3_lattices @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
thf(5322,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_1_0_filter_1 @ B ) )
=> ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ D ) )
& ( r3_lattices @ B @ C @ D ) ) )
& ( ? [C: $i,D: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ B ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_domain_1 @ ( u1_struct_0 @ B ) @ ( u1_struct_0 @ B ) @ C @ D ) )
& ( r3_lattices @ B @ C @ D ) )
=> ( r2_hidden @ A @ ( a_1_0_filter_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(175,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= C )
=> ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_pre_topc) ).
thf(2063,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B )
= C )
=> ( ( k2_pre_topc @ A )
= ( k4_subset_1 @ ( u1_struct_0 @ A ) @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(730,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_struct_0) ).
thf(4318,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( l1_struct_0 @ A )
& ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) ) )
=> ( m1_subset_1 @ ( k1_struct_0 @ A @ B ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(1240,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( ( v1_filter_0 @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_filter_0) ).
thf(6503,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ~ ( ( B != C )
& ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ~ ( ( v1_filter_0 @ D @ A )
& ( ( ( r2_hidden @ B @ D )
& ~ ( r2_hidden @ C @ D ) )
| ( ~ ( r2_hidden @ B @ D )
& ( r2_hidden @ C @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k2_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k2_borsuk_1 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k2_borsuk_1 @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_borsuk_1) ).
thf(2353,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ( ( v1_funct_1 @ ( k2_borsuk_1 @ A @ B ) )
& ( v1_funct_2 @ ( k2_borsuk_1 @ A @ B ) @ A @ B )
& ( m2_relset_1 @ ( k2_borsuk_1 @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1346,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_borsuk_1 @ ( k15_borsuk_1 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_borsuk_1) ).
thf(6874,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( m1_borsuk_1 @ ( k15_borsuk_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
thf(3362,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1200,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) )
& ( r1_tarski @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_lattice4) ).
thf(6329,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_filter_0 @ B @ A )
=> ! [C: $i] :
( ( m1_filter_0 @ C @ A )
=> ( ( r1_tarski @ B @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) )
& ( r1_tarski @ C @ ( k3_filter_0 @ A @ ( k1_finsub_1 @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(1044,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_pre_topc) ).
thf(5637,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k6_pre_topc @ A @ B ) @ ( k6_pre_topc @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(775,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ A @ k1_xboole_0 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_4) ).
thf(4506,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ A @ k1_xboole_0 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_relat_1) ).
thf(3392,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ! [D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( r1_tarski @ C @ D )
& ( r1_tarski @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m2_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( ( k10_borsuk_1 @ A @ B @ C @ D @ E @ F )
= ( k2_zfmisc_1 @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_borsuk_1) ).
thf(1925,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
& ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( m2_connsp_2 @ E @ A @ C )
& ( m1_connsp_2 @ F @ B @ D ) )
=> ( ( k10_borsuk_1 @ A @ B @ C @ D @ E @ F )
= ( k2_zfmisc_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( m2_subset_1 @ ( k3_lopclset @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lopclset) ).
thf(5236,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_lopclset @ A ) )
& ( m1_subset_1 @ C @ ( k1_lopclset @ A ) ) )
=> ( m2_subset_1 @ ( k3_lopclset @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) @ ( k1_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1155,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( ( k3_filter_0 @ A @ B )
= ( k1_filter_0 @ A ) )
& ( ( k3_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_0) ).
thf(6104,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v13_lattices @ A )
& ( l3_lattices @ A )
& ( r2_hidden @ ( k5_lattices @ A ) @ B ) )
=> ( ( ( k3_filter_0 @ A @ B )
= ( k1_filter_0 @ A ) )
& ( ( k3_filter_0 @ A @ B )
= ( u1_struct_0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ B ) )
=> ( ( r2_hidden @ A @ ( a_2_3_borsuk_1 @ B @ C ) )
<=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_struct_0 @ B @ D ) )
& ~ ( r2_hidden @ D @ ( u1_struct_0 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_borsuk_1) ).
thf(6126,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v2_pre_topc @ B )
& ( l1_pre_topc @ B )
& ~ ( v3_struct_0 @ C )
& ( m1_pre_topc @ C @ B ) )
=> ( ( ( r2_hidden @ A @ ( a_2_3_borsuk_1 @ B @ C ) )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_struct_0 @ B @ D ) )
& ~ ( r2_hidden @ D @ ( u1_struct_0 @ C ) ) ) )
& ( ? [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ B ) )
& ( A
= ( k1_struct_0 @ B @ D ) )
& ~ ( r2_hidden @ D @ ( u1_struct_0 @ C ) ) )
=> ( r2_hidden @ A @ ( a_2_3_borsuk_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(287,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v4_pre_topc @ B @ A )
<=> ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
thf(2502,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v4_pre_topc @ B @ A )
=> ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v3_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v4_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(190,axiom,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
thf(2127,plain,
! [A: $i] :
( ( l1_struct_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B )
= ( k6_subset_1 @ ( u1_struct_0 @ A ) @ ( k2_pre_topc @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
=> ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( r2_hidden @ E @ B )
<=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).
thf(1977,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
=> ( ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ( ( ( r2_hidden @ E @ B )
=> ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) ) )
& ( ( ( r2_hidden @ E @ C )
& ~ ( r2_hidden @ E @ D ) )
=> ( r2_hidden @ E @ B ) ) ) )
=> ( B
= ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(2966,plain,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(1313,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( u1_struct_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_filter_0) ).
thf(6750,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ( m1_filter_0 @ ( u1_struct_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(566,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( v2_funct_1 @ A )
=> ( r1_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) @ ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_3) ).
thf(3701,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( v2_funct_1 @ A )
=> ( r1_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) @ ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(317,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k1_funct_4 @ A @ B )
= B )
& ( ( k1_funct_4 @ B @ A )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_funct_4) ).
thf(2600,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k1_funct_4 @ A @ B )
= B )
& ( ( k1_funct_4 @ B @ A )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(386,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v3_pre_topc @ ( k2_pre_topc @ A ) @ A )
& ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_tops_1) ).
thf(2898,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ( ( v3_pre_topc @ ( k2_pre_topc @ A ) @ A )
& ( v4_pre_topc @ ( k2_pre_topc @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
thf(3411,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v4_pre_topc @ ( k6_pre_topc @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(884,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattice4) ).
thf(4972,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ( m1_subset_1 @ B @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( m1_subset_1 @ ( k2_lattice4 @ A @ B ) @ ( u1_struct_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1118,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(5975,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(890,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(4987,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_subset_1) ).
thf(1500,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(3245,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != k1_xboole_0 )
& ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
| ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
& ~ ( r1_tarski @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(712,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(4239,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) )
& ( ! [B: $i] :
~ ( r2_hidden @ B @ A )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(289,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ D )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_borsuk_1) ).
thf(2507,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_eqrel_1 @ B @ A ) )
=> ! [C: $i] :
( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
=> ? [D: $i] :
( ( m1_subset_1 @ D @ A )
& ( ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ D )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1148,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k6_pre_topc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
thf(6082,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( r1_tarski @ B @ ( k6_pre_topc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(952,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_filter_0) ).
thf(5219,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v3_filter_0 @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_filter_0 @ D @ A )
=> ( ( ( r2_hidden @ B @ D )
& ( r2_hidden @ ( k4_filter_0 @ A @ B @ C ) @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(1013,axiom,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).
thf(5468,plain,
! [A: $i] :
( ( l3_lattices @ A )
=> ( ( v3_lattices @ ( k1_lattice2 @ A ) )
& ( l3_lattices @ ( k1_lattice2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(628,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(3939,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_xboole_1) ).
thf(1597,plain,
! [A: $i,B: $i,C: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
= ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(577,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_relat_1) ).
thf(3740,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(21,axiom,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ B @ A )
<=> ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
thf(1431,plain,
! [A: $i] :
( ( l1_pre_topc @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
=> ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) )
& ( ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A )
=> ( v3_pre_topc @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1359,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ( m2_lattice4 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice4) ).
thf(6911,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ? [B: $i] :
( ( m2_lattice4 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(990,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(5376,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(513,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
<=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_tops_1) ).
thf(3394,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v1_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C ) ) ) )
& ( ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ~ ( ( C != k1_xboole_0 )
& ( v3_pre_topc @ C @ A )
& ( r1_xboole_0 @ B @ C ) ) )
=> ( v1_tops_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).
thf(2484,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
~ ( ( r2_hidden @ F @ A )
& ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(2699,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(1505,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(719,axiom,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tops_1) ).
thf(4271,plain,
! [A: $i,B: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A )
& ( v3_pre_topc @ B @ A )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( v4_pre_topc @ ( k3_subset_1 @ ( u1_struct_0 @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(226,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( r2_borsuk_1 @ A @ B )
=> ( r2_borsuk_1 @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) @ ( k21_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_borsuk_1) ).
thf(2270,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( ~ ( v3_struct_0 @ B )
& ( v1_borsuk_1 @ B @ A )
& ( m1_pre_topc @ B @ A ) )
=> ! [C: $i] :
( ( ( v2_borsuk_1 @ C @ B )
& ( m1_borsuk_1 @ C @ B ) )
=> ( ( r2_borsuk_1 @ A @ B )
=> ( r2_borsuk_1 @ ( k16_borsuk_1 @ A @ ( k20_borsuk_1 @ A @ B @ C ) ) @ ( k21_borsuk_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(677,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_filter_0) ).
thf(4088,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( u1_struct_0 @ A ) )
=> ( ( ( r3_lattices @ A @ B @ C )
& ( r3_lattices @ A @ B @ D ) )
=> ( r3_lattices @ A @ B @ ( k4_lattices @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(707,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ C @ A )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_tops_1) ).
thf(4221,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v1_tops_1 @ B @ A )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( v3_pre_topc @ C @ A )
=> ( ( k6_pre_topc @ A @ C )
= ( k6_pre_topc @ A @ ( k5_subset_1 @ ( u1_struct_0 @ A ) @ C @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(1282,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k10_lopclset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lopclset) ).
thf(6658,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v17_lattices @ A )
& ~ ( v3_realset2 @ A )
& ( l3_lattices @ A ) )
=> ~ ( v1_xboole_0 @ ( k10_lopclset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(256,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(2372,plain,
! [A: $i,B: $i] :
( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
=> ( r2_hidden @ A @ B ) )
& ( ( r2_hidden @ A @ B )
=> ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1220,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k6_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k2_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice4) ).
thf(6424,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( v14_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m2_lattice4 @ B @ A )
=> ( ( r2_hidden @ ( k6_lattices @ A ) @ B )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ ( k5_finsub_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( r1_tarski @ C @ B )
=> ( r2_hidden @ ( k2_lattice4 @ A @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
thf(4674,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A )
=> ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(380,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(2879,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(910,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finset_1) ).
thf(5073,plain,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(797,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_setwiseo) ).
thf(4584,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ~ ( ( B != k1_xboole_0 )
& ! [C: $i] :
( ( m1_subset_1 @ C @ A )
=> ~ ( r2_hidden @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1047,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_filter_0) ).
thf(5649,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ! [C: $i] :
( ( ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) ) )
=> ( ( k5_filter_0 @ A @ B @ C )
= ( k5_filter_0 @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(1737,plain,
! [A: $i,B: $i] :
( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
= ( k2_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(515,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(3405,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(2297,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( A != k1_xboole_0 )
=> ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_xboole_1) ).
thf(2087,plain,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(573,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F )
= B ) ) )
=> ( ( D = k1_xboole_0 )
| ( ( k3_lattice2 @ C @ A @ D @ E )
= B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_lattice2) ).
thf(3721,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ! [F: $i] :
( ( m1_subset_1 @ F @ C )
=> ( ( r2_hidden @ F @ D )
=> ( ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F )
= B ) ) )
=> ( ( D = k1_xboole_0 )
| ( ( k3_lattice2 @ C @ A @ D @ E )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(205,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
& ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(2177,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
& ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_xboole_1) ).
thf(1417,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(780,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(4533,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(617,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_relat_1) ).
thf(3901,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A )
=> ( ( k9_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ B @ ( k4_xboole_0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(2690,plain,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ B @ ( k4_xboole_0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ~ ( ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).
thf(1463,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) )
=> ! [E: $i] :
~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
& ! [F: $i] :
( ( m1_subset_1 @ F @ A )
=> ~ ( ( r2_hidden @ F @ C )
& ( E
= ( k1_funct_1 @ D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(412,axiom,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ F @ D )
& ( r3_lattices @ A @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) @ B ) )
=> ( r3_lattices @ A @ ( k3_lattice2 @ C @ A @ D @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_lattice2) ).
thf(2998,plain,
! [A: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k5_finsub_1 @ C ) )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ C @ ( u1_struct_0 @ A ) )
& ( m2_relset_1 @ E @ C @ ( u1_struct_0 @ A ) ) )
=> ( ? [F: $i] :
( ( m1_subset_1 @ F @ C )
& ( r2_hidden @ F @ D )
& ( r3_lattices @ A @ ( k8_funct_2 @ C @ ( u1_struct_0 @ A ) @ E @ F ) @ B ) )
=> ( r3_lattices @ A @ ( k3_lattice2 @ C @ A @ D @ E ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_setwiseo) ).
thf(1769,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
=> ( ( r2_hidden @ A @ B )
| ( A = C ) ) )
& ( ( ( r2_hidden @ A @ B )
| ( A = C ) )
=> ( r2_hidden @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(886,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(4977,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(275,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(2453,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(666,axiom,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_tops_1 @ B @ A ) )
=> ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_tops_1) ).
thf(4056,plain,
! [A: $i] :
( ( ( v2_pre_topc @ A )
& ( l1_pre_topc @ A ) )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( u1_struct_0 @ A ) ) )
=> ( ( ( v3_pre_topc @ B @ A )
& ( v3_tops_1 @ B @ A ) )
=> ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
thf(3052,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
<=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
thf(2170,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) )
& ( ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ D @ A @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k3_lattice2 @ A @ B @ C @ D ) @ ( u1_struct_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice2) ).
thf(2351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B )
& ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
& ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ ( u1_struct_0 @ B ) )
& ( m1_relset_1 @ D @ A @ ( u1_struct_0 @ B ) ) )
=> ( m1_subset_1 @ ( k3_lattice2 @ A @ B @ C @ D ) @ ( u1_struct_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(410,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_4 @ A @ B )
= ( k1_funct_4 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_4) ).
thf(2993,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_4 @ A @ B )
= ( k1_funct_4 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(2191,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1353,axiom,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m1_lattice4 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_lattice4) ).
thf(6896,plain,
! [A: $i,B: $i] :
( ( ~ ( v3_struct_0 @ A )
& ( v10_lattices @ A )
& ( l3_lattices @ A )
& ~ ( v3_struct_0 @ B )
& ( v10_lattices @ B )
& ( l3_lattices @ B ) )
=> ? [C: $i] : ( m1_lattice4 @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
= ( k2_zfmisc_1 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(3035,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
= ( k2_zfmisc_1 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(7943,plain,
$false,
inference(e,[status(thm)],[5810,2630,2336,5320,1899,3581,2427,5205,6845,1686,4560,4447,1718,3944,1411,5365,6167,1469,4571,5857,2341,5136,6530,4062,2072,5260,3798,6712,4183,4290,3698,2787,2595,3830,6431,2544,5778,6555,2331,4682,5733,6954,4877,1818,5582,5131,2363,2644,3549,3417,6798,1728,6426,3498,5348,6022,6791,5141,1406,6944,3813,2381,6883,2527,4391,3153,2953,2590,5297,6900,1569,4697,1971,3402,1533,5691,1793,1437,4487,6480,1608,4090,6401,4011,4884,4026,6634,5713,1919,4247,6804,4980,2360,1705,3017,5550,1788,1426,4234,1671,3745,4739,1756,5906,6675,3332,2316,3446,2933,6089,3338,6655,5257,6416,2712,6851,4856,6551,6680,2901,3313,6570,4142,1391,3947,5938,2886,6754,4948,3597,3350,6914,6251,3994,5486,1782,5518,1441,4266,2020,4679,4618,3777,4030,1724,4963,2067,6483,4156,5269,4249,1887,4386,6707,4743,5883,2667,6095,3495,5274,1826,4023,2466,4428,3891,5553,4637,1409,3204,5953,4539,3263,4439,3976,2328,2735,4563,3275,6034,6039,2339,4692,4224,1871,6723,4761,3617,1860,3612,3148,1511,2274,2185,3280,6662,6332,6519,1992,5706,4568,3353,2745,2571,3713,1922,6049,3998,3840,6626,2767,1479,3919,3216,6936,1931,5746,1778,4669,6071,2420,5605,4862,3638,1514,6905,6611,6396,4368,5942,1641,3835,4383,1815,4460,2989,5076,1963,6734,2852,3268,4008,3258,3788,5792,2456,2237,6002,2782,2650,6523,3973,5541,5156,5457,4556,6562,2017,5682,5787,6081,4411,1946,4396,5663,1664,2794,3966,1714,6227,4173,5084,3075,4072,1450,6670,5027,5861,1373,2996,2893,1632,2469,4733,2259,6410,3473,3983,6745,1682,4847,4050,2122,6176,4724,2291,1383,6841,3357,2540,5311,6559,3923,2555,3300,4115,6438,5738,6631,5384,6491,6863,4038,2103,3226,5629,5970,6474,5045,5059,6591,3986,5929,2058,3537,1928,3068,5448,5353,2833,2281,6685,5210,6777,5096,3505,6947,5772,3808,1796,2530,1622,2424,6347,1394,4996,3157,5246,4307,4040,4536,3243,2809,1600,6156,3211,2392,2154,3906,6787,4628,1696,6860,2586,4483,4065,3899,6856,3303,6731,5117,2641,6741,6092,6200,4700,1651,5174,3151,2011,3857,5406,5012,6760,5875,4589,6406,3169,6296,4480,3265,6047,2646,3635,2164,5438,6139,6064,6058,6588,5416,4370,3767,4576,2307,3054,4059,6442,2773,4999,2264,3261,5611,3827,5002,6032,4434,1666,6565,3371,4449,6696,6232,2396,4016,2805,3603,6820,2249,5579,5512,4878,6773,4989,2133,2147,5266,5455,1502,5815,4521,3989,4785,4499,4284,1619,6496,5893,5507,5102,6178,3471,1883,4044,5924,3198,3297,5021,3894,4187,3028,4080,5285,6709,1423,3307,5769,3958,6303,2464,5702,5302,1602,6629,4140,2628,3810,5465,4608,2663,6043,6292,3718,3877,4553,3546,5038,4402,3535,2344,2313,5936,2228,3033,3408,1740,1910,2300,2157,2946,4974,6691,6603,3381,4048,3518,3119,6111,3916,4109,5951,6728,3731,3968,4123,6795,3909,5904,3482,5221,2100,3413,5238,2685,2709,5798,2692,1498,2694,4845,5428,3704,3386,2726,5919,4227,5978,2537,6919,6624,3176,1397,4320,4518,3143,4276,5915,5080,5107,4167,4389,5865,3643,4736,4530,3775,3141,4951,5694,3000,4582,6116,2561,6593,5992,3728,4421,4315,1414,2196,1842,5547,1700,6164,1937,1791,4648,4054,6501,2108,1889,3555,1644,6275,2681,1530,6207,6876,2581,1799,4120,1852,2697,2968,6752,5317,6134,2450,3654,5481,6097,5374,5149,2304,2387,1831,3743,5639,5134,5234,1668,1974,2505,4237,3390,4829,3222,4934,2497,6450,6005,5217,2862,4135,6784,4152,1720,5603,5369,6152,4689,4069,3005,2272,3364,2140,4086,2756,3162,3201,1759,6171,4352,4644,6160,2883,6716,2963,6378,5419,5872,4550,5112,1434,1857,5153,2926,2702,2546,2043,3183,4966,4765,3592,6812,2089,3190,5126,6950,1906,2729,6922,6699,4874,3491,6084,1747,6578,6243,4503,6546,3696,4365,5241,3343,1764,3130,6053,5722,4685,4380,4872,2904,1680,5808,4354,2033,5138,6615,2149,4613,6824,2253,3871,4657,5960,5608,6469,3738,3888,2524,4453,5698,3187,1833,2970,3925,6881,2789,2657,4309,5940,4926,5962,5099,6019,3868,6493,1916,6870,2225,6617,5488,3255,6581,1752,1388,3272,6229,4032,1403,6898,2959,3213,1428,5965,4485,2193,3773,4096,6532,2753,2055,6636,6123,5735,4273,5784,2319,6016,6403,5471,2891,3077,6667,4112,6673,3651,5859,4149,3663,4218,1635,2935,3002,4822,3594,4573,5086,6549,6334,1638,3355,6061,6478,2521,2119,3996,1806,6815,5631,2116,4477,5212,6572,4929,6942,6779,3251,3155,3815,2084,2383,2493,2987,3038,2422,4305,5491,4601,2943,3710,5093,4154,6289,3500,5689,5381,5795,1690,3066,6196,3384,5972,1571,5616,4509,1439,2180,2812,2605,2625,5082,2111,6414,6817,1460,5007,5838,3219,4694,2267,4731,4028,1731,4264,3932,4985,1862,4208,6747,2410,3614,2785,2593,3451,6678,4850,6847,6802,3861,2928,6568,2461,5410,5459,6660,1820,6376,1688,2401,5442,6609,3110,3806,2797,2244,4703,5299,6180,5089,4067,2984,5619,3539,2770,4832,6345,6574,6907,2051,2550,2481,6738,4373,6270,5516,3159,2369,4362,2931,5042,2022,3310,3706,5725,2867,6476,3881,4426,4394,3193,4598,1420,3981,2234,3146,3921,2597,5652,6440,5435,1626,4405,6890,3936,6540,5886,6542,2665,4260,4813,6185,1990,3048,4859,2333,2256,2564,5358,4722,5229,5716,2715,6399,6621,1566,5748,5171,3949,2831,5446,2567,5452,5047,3640,1516,3315,4035,6683,4360,5927,4490,3112,2661,6051,4937,6934,1611,2060,6885,1400,1743,4939,1605,2588,2732,5484,2678,2518,4641,2175,4287,1780,2407,3058,6596,1484,4593,2888,6389,6280,4092,3063,6037,4020,6421,1785,5948,3801,3847,4982,5062,3019,2747,3448,5262,3305,3818,3691,3791,3475,4768,3823,6298,5995,3127,1901,3544,6174,4132,6653,2322,3359,3329,3174,5450,3853,4164,3715,1766,2379,6262,6775,4991,5633,5685,2030,6917,3961,4838,3007,2247,5147,5208,1934,2948,6337,1849,2558,3970,6073,5223,3124,2145,5504,2357,1749,4046,4932,3388,4431,2511,4634,5226,6086,1881,6161,3914,2584,4257,4671,4819,6301,6793,1617,1940,4548,2458,1649,4606,4727,4945,3171,1913,3533,5510,6938,1453,3665,6726,4639,2760,6286,2924,1839,4651,3620,5981,6447,5179,6758,1966,6408,6041,1553,1949,2870,2828,2310,6137,5934,4780,2325,4185,4078,5308,1448,2490,2187,4006,3320,4463,4170,6743,5332,2775,1734,2792,2907,6903,1385,3484,5351,3336,1629,5813,1854,3235,5756,3136,4969,6799,1646,5315,6077,2167,4806,1476,1674,6607,6489,4615,2251,3825,6689,4666,6030,6893,2532,1508,5191,2823,4042,4542,4834,4495,5243,4705,2130,2416,3780,4900,1558,2152,4451,5922,2394,3694,5162,3896,6277,5869,5144,2623,6198,4745,2447,6516,2956,3978,2081,5408,6854,3879,4214,6118,5781,6045,5040,2230,2036,3645,1893,2294,2739,4098,6444,1994,5194,5287,3420,1614,3785,2534,6693,6925,5232,5537,4579,2003,2142,6703,3658,5187,4125,5852,4880,4816,6055,5009,2683,5129,4399,4687,4809,3865,5004,4811,3373,1380,2815,2008,4841,5522,1527,3132,5527,6150,4357,4455,6782,2636,5700,6535,2751,6294,4474,5741,2366,3196,5215,5642,5110,6537,4303,4565,4777,6169,5159,1495,5709,3347,4210,5290,1693,5019,4083,5835,2070,5413,5462,1561,2961,1710,6380,2404,4865,3030,5378,3045,5176,5322,2063,4318,6503,2353,6874,3362,6329,5637,4506,3392,1925,5236,6104,6126,2502,2127,1829,1977,2966,6750,3701,2600,2898,3411,4972,5975,4987,1500,3245,4239,2507,6082,5219,5468,3939,1597,3740,1431,6911,5376,3394,2484,2699,1505,4271,2270,4088,4221,6658,2372,6424,4674,2879,5073,4584,5649,1737,3405,2297,2087,3721,2177,1417,4533,3901,2690,1463,2998,1769,4977,2453,4056,3052,2170,2351,2993,2191,6896,3035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT292+2 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 14:08:28 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.93/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.88/1.42 % [INFO] Parsing done (530ms).
% 3.10/1.43 % [INFO] Running in sequential loop mode.
% 3.38/1.62 % [INFO] eprover registered as external prover.
% 3.38/1.63 % [INFO] cvc4 registered as external prover.
% 3.38/1.63 % [INFO] Scanning for conjecture ...
% 4.40/1.93 % [INFO] Found a conjecture and 6467 axioms. Running axiom selection ...
% 6.39/2.60 % [INFO] Axiom selection finished. Selected 1370 axioms (removed 5097 axioms).
% 8.09/3.15 % [INFO] Problem is first-order (TPTP FOF).
% 8.29/3.19 % [INFO] Type checking passed.
% 8.29/3.20 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 48.42/12.08 % External prover 'e' found a proof!
% 48.42/12.08 % [INFO] Killing All external provers ...
% 48.42/12.09 % Time passed: 11568ms (effective reasoning time: 10649ms)
% 48.42/12.09 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 48.42/12.09 % Axioms used in derivation (1370): t106_xboole_1, t72_xboole_1, t15_finset_1, t7_filter_0, t28_funct_3, t2_filter_0, t21_zfmisc_1, t175_relat_1, d13_filter_0, dt_k2_borsuk_1, t158_relat_1, t17_lattice4, rc2_lopclset, t38_funct_4, t45_lattice4, t51_filter_1, t42_xboole_1, dt_k1_funct_3, t34_subset_1, t34_funct_3, t30_lopclset, dt_k5_filter_1, t108_tops_1, t50_lattice4, t51_partfun1, redefinition_m2_relset_1, t20_filter_1, t44_xboole_1, t13_zfmisc_1, t24_filter_0, t10_lattice2, t13_relset_1, t70_setwiseo, cc1_tops_1, t181_relat_1, t15_lopclset, dt_k7_filter_0, fc8_tops_1, t177_relat_1, t19_xboole_1, t70_tops_1, t31_filter_0, t43_subset_1, d5_lopclset, t147_funct_1, t84_tops_1, t14_finset_1, t20_lattice4, t39_lattices, t76_lattice2, t67_tops_1, t26_lopclset, t17_xboole_1, t2_lopclset, dt_k1_filter_1, t78_filter_0, t42_subset_1, t36_lopclset, t43_lattice2, dt_m1_lattice4, t15_setwiseo, cc2_finset_1, t20_zfmisc_1, t76_tops_1, t36_funct_3, t35_subset_1, d1_tarski, dt_k2_lattice2, t135_zfmisc_1, t17_zfmisc_1, t54_tops_1, fc11_finseq_1, t148_funct_1, t25_relset_1, fc12_tops_1, t66_funct_2, t143_funct_1, t67_relat_1, t62_filter_0, t66_partfun1, t45_pre_topc, t154_relat_1, t13_funct_3, t70_funct_2, dt_k3_borsuk_1, t80_filter_0, t56_filter_1, l38_lopclset, t53_subset_1, t35_tops_1, t79_tops_1, rc4_finset_1, t35_filter_1, fc2_pre_topc, redefinition_k5_subset_1, t81_filter_0, d12_borsuk_1, t48_filter_1, d13_lattices, dt_k6_filter_1, d6_filter_0, idempotence_k3_lopclset, t97_tops_1, t105_zfmisc_1, t54_filter_1, t41_pre_topc, t140_zfmisc_1, fraenkel_a_1_0_filter_1, dt_k19_borsuk_1, redefinition_k12_mcart_1, t109_xboole_1, idempotence_k3_xboole_0, t1_boole, d6_lattice2, t62_relat_1, t7_subset_1, t2_realset1, t32_funct_2, t66_xboole_1, t23_xboole_1, fraenkel_a_2_1_borsuk_1, t36_lattice4, t15_filter_1, t79_funct_4, symmetry_r1_filter_1, t14_funct_4, t50_relat_1, t91_tops_1, dt_k2_tops_1, t29_filter_0, t24_lattice4, t73_xboole_1, t3_xboole_1, d4_lattice4, t137_funct_1, d3_subset_1, t57_lattice2, t51_borsuk_1, idempotence_k5_setwiseo, t7_lattice2, t113_xboole_1, rc7_finseq_1, t87_tops_1, t56_partfun1, t8_subset_1, existence_l1_lattices, t29_borsuk_1, t29_funct_3, t156_funct_1, t35_borsuk_1, fc1_xboole_0, t53_filter_1, t42_filter_0, t5_borsuk_1, cc6_lattices, t25_funct_1, t16_funct_2, d16_lattices, t113_zfmisc_1, dt_k20_borsuk_1, t34_xboole_1, dt_k7_subset_1, rc4_pre_topc, d13_borsuk_1, t50_borsuk_1, t15_funct_1, rc3_tops_1, fc4_relat_1, t19_lattices, t4_ordinal1, t1_group_6, t39_funct_3, t59_partfun1, t158_funct_1, t43_lattices, redefinition_k10_borsuk_1, t44_relat_1, t1_subset, dt_k1_lattice4, t147_relat_1, t10_partfun1, t47_lattice2, t9_lattice2, t22_funct_1, t43_xboole_1, t81_zfmisc_1, t52_funct_4, t10_relset_1, fc4_tops_1, dt_k1_subset_1, t6_xboole_1, d8_funct_1, fc1_lattice2, d5_xboole_0, t90_tops_1, t38_filter_1, t29_subset_1, dt_k8_borsuk_1, t4_lattice4, t151_funct_1, t52_zfmisc_1, t144_relat_1, dt_k9_lopclset, fc4_subset_1, dt_k1_tops_1, existence_l3_lattices, t53_lattices, dt_k5_lattices, t7_funct_2, fraenkel_a_3_0_borsuk_1, t18_xboole_1, t3_mcart_1, t155_funct_1, d2_group_6, t23_lopclset, t87_filter_0, t16_setwiseo, fc3_relat_1, t96_zfmisc_1, t45_filter_1, t21_lattice2, t19_relat_1, t70_xboole_1, t69_filter_0, redefinition_k13_lopclset, t67_borsuk_1, dt_k2_funct_4, t117_zfmisc_1, t88_tops_1, t61_tops_1, t23_pre_topc, t23_filter_0, t43_zfmisc_1, t47_relat_1, fc9_relat_1, t16_lattice4, t46_lattice4, t68_xboole_1, t19_finset_1, t54_funct_4, existence_m3_lattice4, t25_xboole_1, t2_boole, dt_m1_filter_1, t69_tops_1, t18_filter_0, dt_k3_lattice4, t106_tops_1, t102_tops_1, t5_funct_3, dt_k1_lattice2, t65_partfun1, t29_lopclset, t44_funct_2, fraenkel_a_2_0_lattice4, d10_borsuk_1, d2_funct_3, t117_funct_1, fc11_tops_1, t1_qc_lang1, dt_k4_subset_1, fc6_tops_1, t27_xboole_1, t59_tops_1, t71_xboole_1, t122_zfmisc_1, d13_pre_topc, t83_filter_0, t4_mcart_1, redefinition_k3_lopclset, t50_pre_topc, dt_k1_struct_0, existence_m1_filter_1, t35_lattice4, d6_pre_topc, dt_k16_borsuk_1, t12_pre_topc, t26_lattice4, d11_borsuk_1, t85_filter_0, t82_tops_1, dt_m1_borsuk_1, dt_m1_realset1, t25_pre_topc, cc5_tops_1, t55_funct_4, dt_u2_struct_0, rc2_partfun1, t18_relat_1, fc1_filter_0, fc1_funct_1, t171_relat_1, t45_zfmisc_1, t8_lopclset, t95_zfmisc_1, t63_partfun1, t153_funct_1, t20_funct_3, t15_relset_1, t19_funct_3, t18_funct_3, t14_filter_0, t77_tops_1, t73_tops_1, t56_tops_1, idempotence_k2_lopclset, fraenkel_a_2_0_filter_0, t99_zfmisc_1, l49_lopclset, cc4_lattices, redefinition_k11_filter_0, d8_lopclset, t13_pre_topc, rc3_funct_1, t81_xboole_1, t48_filter_0, d9_lattice4, t6_lopclset, t3_lopclset, t68_borsuk_1, dt_k5_filter_0, dt_k3_filter_0, t32_tops_1, t78_borsuk_1, t69_zfmisc_1, d1_struct_0, t37_xboole_1, cc1_relat_1, rc3_pre_topc, t46_borsuk_1, t36_subset_1, t138_funct_1, t47_filter_1, t17_funct_1, t9_xboole_1, d6_tops_1, t41_zfmisc_1, cc3_tops_1, dt_m2_relset_1, t18_finset_1, t131_zfmisc_1, redefinition_k2_funct_2, idempotence_k5_subset_1, t59_lattice2, t49_zfmisc_1, dt_k1_pre_topc, reflexivity_r1_filter_1, commutativity_k3_xboole_0, t154_funct_1, t29_partfun1, t33_lattice4, t62_funct_2, t55_funct_1, t32_filter_0, dt_k10_filter_1, t70_partfun1, t71_tops_1, dt_k8_lopclset, dt_k4_lopclset, t26_filter_0, t46_pre_topc, fc11_finset_1, t31_lattices, dt_k2_lopclset, rc1_funct_1, t31_relat_1, t168_relat_1, t111_tops_1, redefinition_k6_filter_0, dt_k1_filter_0, t115_zfmisc_1, t80_tops_1, t62_funct_1, t46_lattice2, d3_pre_topc, t65_funct_2, t19_funct_1, t56_setwiseo, dt_m2_lattice4, d11_filter_0, t13_funct_4, t50_tops_1, t29_finset_1, d4_lopclset, dt_k2_binop_1, t137_zfmisc_1, t2_binop_1, t2_partfun1, t34_tops_1, t86_xboole_1, fc5_pre_topc, involutiveness_k3_subset_1, t13_relat_1, t89_xboole_1, t53_filter_0, t25_funct_2, fc2_xboole_0, t16_lopclset, dt_m2_realset1, t9_funct_3, t32_subset_1, rc6_pre_topc, t64_funct_2, t66_tops_1, dt_k12_lopclset, t108_xboole_1, t56_filter_0, t72_filter_0, t24_lopclset, t43_tops_1, fraenkel_a_3_0_filter_0, t46_funct_2, t32_funct_3, t21_funct_4, t15_relat_1, t12_funct_4, t173_relat_1, dt_k6_lopclset, t172_relat_1, t27_relat_1, d16_lattice4, t70_filter_0, t78_funct_4, d1_xboole_0, dt_m1_eqrel_1, t49_funct_1, t65_tops_1, dt_k21_borsuk_1, t46_filter_0, t5_lopclset, t52_pre_topc, t64_relat_1, t138_zfmisc_1, rc6_finseq_1, rc1_tops_1, fraenkel_a_2_0_borsuk_1, t37_filter_0, d14_borsuk_1, t36_filter_1, rc3_lattices, t52_filter_0, t23_funct_1, t130_zfmisc_1, t51_xboole_1, redefinition_k1_filter_1, t57_filter_0, dt_l1_lattices, t14_lopclset, t56_funct_4, t14_relset_1, dt_k11_borsuk_1, t6_mcart_1, t46_zfmisc_1, t31_partfun1, dt_k7_lattices, d15_lattice4, t56_zfmisc_1, t26_borsuk_1, t47_funct_2, t24_finsub_1, t27_relset_1, commutativity_k3_lopclset, d21_borsuk_1, redefinition_k19_borsuk_1, dt_l1_pre_topc, dt_k4_lattice4, t118_zfmisc_1, t55_partfun1, t2_mcart_1, t8_funct_2, fc10_finset_1, t37_funct_3, t19_lopclset, t60_partfun1, existence_m1_realset1, t26_finset_1, t77_borsuk_1, t39_lattice4, t16_relset_1, t38_lattice4, t39_funct_4, t28_lopclset, t49_borsuk_1, fc2_borsuk_1, t6_boole, t12_funct_1, t10_funct_3, t3_funct_2, t18_subset_1, rc2_subset_1, fc9_finset_1, dt_k1_lopclset, fc4_lopclset, existence_l2_lattices, t50_xboole_1, t74_borsuk_1, dt_k6_subset_1, t10_relat_1, t43_pre_topc, t80_borsuk_1, t59_setfam_1, t2_filter_1, t59_filter_0, t26_relset_1, t20_funct_1, t47_lattice4, t16_pre_topc, t41_tops_1, dt_k11_lopclset, t32_partfun1, t22_tops_1, t160_funct_1, t5_subset, t44_filter_1, t1_xboole_1, redefinition_k12_filter_0, dt_k1_funct_4, t86_tops_1, t27_funct_3, t29_relat_1, d14_lattice4, t64_partfun1, t52_relat_1, t77_funct_2, free_g1_pre_topc, t54_borsuk_1, existence_l2_struct_0, t32_lattices, idempotence_k1_filter_1, t55_relat_1, t34_filter_0, t68_partfun1, t5_lattice4, t3_partfun1, t59_setwiseo, t19_filter_0, t52_xboole_1, t44_lattice4, t75_xboole_1, t49_filter_0, t34_relat_1, dt_k10_setwiseo, commutativity_k2_xboole_0, d12_lattices, d17_lattice4, t39_partfun1, t149_funct_1, d2_realset1, t6_lattice2, dt_k13_lopclset, t65_xboole_1, t27_tops_1, t1_zfmisc_1, fc2_tops_1, t53_funct_4, t17_filter_1, t45_funct_2, t53_borsuk_1, t94_zfmisc_1, t8_lattice4, t46_tops_1, t4_xboole_0, t8_tops_1, fc17_finseq_1, t150_relat_1, existence_m1_relset_1, commutativity_k5_subset_1, t79_borsuk_1, t50_lattices, d5_tops_1, dt_l3_lattices, t48_lattice2, t18_pre_topc, t21_filter_1, fraenkel_a_3_1_borsuk_1, t19_relset_1, t64_tops_1, t110_tops_1, t123_zfmisc_1, fc2_subset_1, t79_zfmisc_1, t12_lattice2, t5_funct_2, t176_relat_1, dt_k8_funct_2, redefinition_k5_setwiseo, t18_setwiseo, t75_tops_1, dt_k18_borsuk_1, t24_finset_1, t62_tops_1, t40_funct_2, t57_tops_1, t44_pre_topc, t40_filter_0, t72_partfun1, t27_lattice4, t9_relat_1, t84_lattice2, t2_tops_1, dt_k7_borsuk_1, dt_l2_lattices, t97_zfmisc_1, t121_funct_1, t75_borsuk_1, t2_tarski, t16_funct_1, t14_relat_1, t33_relat_1, dt_k4_filter_0, t33_xboole_1, t75_lattice2, t122_funct_1, t13_setwiseo, t47_lattices, t25_borsuk_1, d20_lattices, d1_filter_1, dt_k15_borsuk_1, t4_filter_0, t2_zfmisc_1, t31_funct_3, t89_filter_0, t114_xboole_1, t1_filter_1, d6_realset1, t39_filter_1, t67_zfmisc_1, t38_filter_0, d1_funct_4, d13_funct_1, t4_cat_1, t98_zfmisc_1, t34_lattice4, fc3_xboole_0, d18_lattices, t70_lattice2, d8_filter_0, t32_xboole_1, t52_subset_1, t60_filter_0, dt_k9_filter_1, t5_ordinal1, t4_boole, t53_xboole_1, d3_lattices, t22_lopclset, t47_borsuk_1, t71_lattice2, t146_funct_1, t84_xboole_1, d2_pre_topc, t125_funct_1, t21_xboole_1, cc5_lattices, d5_pre_topc, t4_subset, d3_lopclset, t34_lopclset, t76_xboole_1, t178_relat_1, t38_subset_1, t53_pre_topc, t81_tops_1, t44_lattices, d2_xboole_0, t30_xboole_1, t18_lopclset, t39_tops_1, dt_k2_funct_1, dt_k8_filter_0, t14_funct_1, dt_k22_borsuk_1, d4_tarski, t56_lattice2, abstractness_v1_pre_topc, t42_filter_1, t61_partfun1, t141_zfmisc_1, t80_xboole_1, t79_xboole_1, t174_relat_1, t41_borsuk_1, d7_realset2, d2_lattice4, t45_lattices, t49_lattice4, t58_funct_1, t25_finset_1, d8_pre_topc, t30_tops_1, t67_xboole_1, d7_filter_0, d2_lopclset, existence_m2_realset1, t52_filter_1, redefinition_k2_lopclset, d7_lopclset, redefinition_k5_setfam_1, t49_tops_1, t58_zfmisc_1, t21_funct_3, t17_funct_2, t85_lattice2, t58_tops_1, t29_xboole_1, t50_funct_4, t75_filter_0, dt_k17_borsuk_1, t13_lattice2, t179_relat_1, t52_tops_1, t72_borsuk_1, t63_tops_1, d10_pre_topc, d9_lopclset, t59_funct_1, t139_zfmisc_1, t32_lopclset, t16_lattice2, t7_boole, fraenkel_a_2_3_borsuk_1, cc1_funct_1, t27_pre_topc, fc9_tops_1, d10_lattice4, fc4_pre_topc, dt_k5_lattice4, rc3_struct_0, fc1_subset_1, t13_finset_1, d1_setwiseo, t3_ordinal1, t4_funct_2, t37_tops_1, dt_g1_pre_topc, dt_k10_borsuk_1, t103_tops_1, d10_setfam_1, t55_filter_0, t50_filter_1, d2_subset_1, t66_zfmisc_1, t33_funct_4, t22_relat_1, dt_k6_borsuk_1, t48_xboole_1, t157_funct_1, t5_setwiseo, d17_lattices, t92_tops_1, dt_k8_filter_1, t37_filter_1, t85_xboole_1, rc1_funct_2, t33_filter_1, d7_tops_1, t34_filter_1, t31_lattice4, t16_subset_1, dt_k2_partfun1, t69_partfun1, t7_ordinal1, t153_relat_1, t41_lopclset, rc2_funct_1, t9_funct_2, t160_relat_1, fc10_relat_1, t31_funct_2, rc1_subset_1, dt_k9_filter_0, t48_funct_1, t90_filter_0, t152_funct_1, t47_funct_1, dt_m1_pre_topc, t31_xboole_1, t4_subset_1, t88_xboole_1, t18_funct_4, t48_lattice4, t68_filter_0, t51_funct_1, t30_funct_4, t22_finset_1, t8_lattice2, d6_lopclset, t21_funct_2, fc3_lopclset, t42_funct_4, t24_xboole_1, d2_tops_1, t116_zfmisc_1, t64_zfmisc_1, t30_filter_0, t27_lopclset, t49_lattices, t65_funct_1, t56_funct_1, t124_zfmisc_1, t6_setwiseo, fraenkel_a_2_2_borsuk_1, t54_xboole_1, t113_funct_2, t71_partfun1, t5_filter_0, t69_xboole_1, d21_lattices, t41_lattices, d7_xboole_0, fc5_relat_1, t151_relat_1, existence_m1_filter_0, t83_xboole_1, t49_filter_1, dt_k3_lattice2, t40_lattice4, t45_relat_1, t2_lattice2, t58_filter_1, t48_lattices, t20_xboole_1, t47_pre_topc, t12_funct_3, dt_k2_lattice4, t70_borsuk_1, t9_filter_0, fc5_borsuk_1, t95_tops_1, t16_zfmisc_1, t40_lattices, t101_zfmisc_1, t17_borsuk_1, t38_funct_3, t55_tops_1, t7_lattice4, t46_filter_1, t82_xboole_1, t93_tops_1, t61_filter_1, t55_xboole_1, t124_funct_1, d9_filter_1, t18_filter_1, t41_funct_4, t22_filter_0, cc2_funct_1, t85_borsuk_1, t120_zfmisc_1, t76_borsuk_1, fraenkel_a_2_1_lattice4, existence_m1_pre_topc, t3_funct_3, t18_funct_1, t5_realset1, t17_finset_1, dt_k8_setfam_1, t4_relset_1, t10_filter_0, t31_subset_1, t3_subset, cc1_relset_1, cc1_eqrel_1, d6_lattice4, t30_lattice4, t12_filter_0, t52_borsuk_1, t55_subset_1, t79_funct_2, t46_funct_1, t41_lattice4, idempotence_k1_funct_4, dt_k6_setfam_1, redefinition_k21_borsuk_1, commutativity_k7_subset_1, t22_lattice4, existence_m1_subset_1, t3_relat_1, t36_borsuk_1, t35_xboole_1, t73_filter_0, redefinition_k4_subset_1, t44_zfmisc_1, t35_funct_3, t155_relat_1, t47_xboole_1, t145_funct_1, t5_lattice2, t44_filter_0, t17_relset_1, t38_tops_1, existence_m2_subset_1, t125_zfmisc_1, t63_borsuk_1, t42_borsuk_1, t30_subset_1, t8_setwiseo, dt_k2_filter_0, dt_k2_funct_2, t14_xboole_1, t44_setfam_1, t11_relset_1, t10_lopclset, d2_filter_0, t11_funct_4, redefinition_k9_lopclset, t5_pre_topc, fc1_finset_1, t15_subset_1, t18_borsuk_1, cc3_lattices, d5_subset_1, t19_lattice2, t72_tops_1, t92_zfmisc_1, t146_relat_1, t9_lattice4, t82_lattice2, d1_filter_0, t15_xboole_1, t11_filter_0, rc2_relat_1, existence_m2_relset_1, t64_filter_0, t48_tops_1, t54_pre_topc, dt_k24_borsuk_1, t114_zfmisc_1, t31_zfmisc_1, t58_partfun1, t60_setwiseo, d1_zfmisc_1, t16_xboole_1, cc2_tops_1, t51_pre_topc, t100_zfmisc_1, t27_filter_0, t26_xboole_1, t63_xboole_1, redefinition_k7_filter_0, t57_setfam_1, t43_funct_2, t1_filter_0, commutativity_k4_subset_1, t62_lattice2, t39_filter_0, dt_k7_lopclset, t11_lattice4, rc2_realset2, dt_k5_subset_1, existence_m2_lattice4, t23_lattice4, dt_k23_borsuk_1, t116_funct_2, d3_lattice4, t25_funct_3, t37_lattice4, t26_subset_1, t65_lattice2, commutativity_k1_filter_1, t6_funct_2, t27_borsuk_1, d4_filter_0, t44_lattice2, t41_subset_1, dt_k12_mcart_1, t157_relat_1, cc3_finsub_1, t96_tops_1, t45_tops_1, t62_setwiseo, d9_pre_topc, t51_filter_0, t142_funct_1, t17_pre_topc, t74_filter_0, t11_lopclset, t51_subset_1, existence_m1_lattice4, t111_xboole_1, d5_filter_0, t15_funct_3, t51_tops_1, t22_xboole_1, t2_funct_3, t60_filter_1, t85_tops_1, t61_lattice2, t84_zfmisc_1, t21_lopclset, t8_xboole_1, t8_realset1, d3_tarski, d1_funct_3, t25_lattice4, rc1_relat_1, t19_setwiseo, t14_setwiseo, t45_lattice2, t36_tops_1, dt_m3_lattice4, t78_xboole_1, t28_xboole_1, t82_borsuk_1, d1_relset_1, t46_subset_1, fc1_struct_0, t62_filter_1, d8_filter_1, t52_lattice2, t78_lattice2, redefinition_k1_struct_0, existence_l1_pre_topc, fc1_lopclset, fraenkel_a_3_1_filter_0, t39_zfmisc_1, d1_realset1, d19_borsuk_1, t5_xboole_0, d15_lattices, t119_zfmisc_1, t13_xboole_1, t60_relat_1, t12_lopclset, t54_funct_1, t40_subset_1, t83_zfmisc_1, t170_relat_1, rc1_lattice4, t77_lattice2, t54_zfmisc_1, t24_lattice2, t19_lattice4, dt_k5_relat_1, t17_subset_1, reflexivity_r1_tarski, t9_funct_1, t6_zfmisc_1, t48_relat_1, t27_finsub_1, t5_mcart_1, t27_finset_1, t52_lattices, t2_xboole_1, fc13_tops_1, t17_funct_4, fraenkel_a_1_0_lopclset, t34_funct_2, rc6_lattices, t67_filter_0, t18_funct_2, t144_funct_1, t121_zfmisc_1, t10_subset_1, t51_funct_4, dt_l2_struct_0, t56_setfam_1, t41_filter_0, rc2_setwiseo, t1_realset1, t38_lopclset, t57_partfun1, t4_xboole_1, d12_funct_1, t9_relset_1, t25_lopclset, dt_g3_lattices, fc6_relat_1, t1_partfun1, t41_xboole_1, t150_funct_1, rc1_pre_topc, t45_borsuk_1, t11_setwiseo, t66_funct_1, d14_lattices, dt_k10_filter_0, dt_k5_lopclset, t54_lattice2, t18_zfmisc_1, t47_filter_0, d7_lattice4, dt_k1_lattices, t49_pre_topc, t90_xboole_1, rc7_pre_topc, t51_relat_1, free_g3_lattices, t20_tops_1, t46_relat_1, t77_filter_0, t30_funct_3, t9_lopclset, d4_xboole_0, t53_tops_1, t48_borsuk_1, t21_lattice4, dt_k5_setfam_1, rc3_finset_1, d6_eqrel_1, rc3_borsuk_1, fc3_pre_topc, dt_k5_setwiseo, commutativity_k5_setwiseo, existence_m1_eqrel_1, fc18_finseq_1, t36_xboole_1, t51_zfmisc_1, t69_lattice2, t47_subset_1, fc2_filter_1, t58_filter_0, t31_tops_1, t47_funct_4, t18_lattice4, dt_m2_subset_1, t40_filter_1, t26_finsub_1, t15_filter_0, t80_zfmisc_1, dt_u1_pre_topc, t54_subset_1, t39_pre_topc, rc1_finset_1, t4_lopclset, d1_lopclset, t64_xboole_1, fc4_borsuk_1, t22_pre_topc, t20_filter_0, t28_finsub_1, t127_zfmisc_1, t123_funct_1, t40_funct_4, t44_subset_1, rc2_tops_1, t49_xboole_1, t7_lopclset, cc1_finset_1, t29_lattices, t16_filter_1, t21_funct_1, t88_filter_0, fc12_finset_1, t51_lattice2, t136_zfmisc_1, t82_filter_0, fc1_relat_1, t77_xboole_1, d6_relat_1, t8_boole, t169_relat_1, rc1_xboole_0, t54_filter_0, t16_funct_3, t1_funct_5, t1_mcart_1, t11_xboole_1, t23_finset_1, t24_partfun1, redefinition_k8_funct_2, fc3_tops_1, t59_filter_1, t47_tops_1, t24_zfmisc_1, t55_lattice2, t68_zfmisc_1, t48_pre_topc, t182_relat_1, d1_borsuk_1, t2_subset, t16_finset_1, fc7_relat_1, t23_finsub_1, t30_finsub_1, t126_zfmisc_1, fc8_relat_1, t40_lopclset, t37_lopclset, rc5_struct_0, t19_filter_1, cc4_tops_1, t46_funct_4, t59_funct_2, t12_xboole_1, t22_funct_3, rc4_borsuk_1, d9_filter_0, t38_funct_2, t33_partfun1, t34_finsub_1, t85_funct_2, d6_borsuk_1, t180_relat_1, t60_funct_1, t37_zfmisc_1, fc2_relat_1, t65_relat_1, t21_relat_1, dt_k6_filter_0, t156_relat_1, d5_borsuk_1, t25_finsub_1, t152_relat_1, dt_k6_lattices, symmetry_r1_xboole_0, t49_funct_4, t134_zfmisc_1, existence_m1_borsuk_1, t25_partfun1, dt_m1_filter_0, t49_relat_1, t161_funct_1, t27_funct_1, t10_realset1, redefinition_k7_borsuk_1, d3_tops_1, t48_funct_4, d1_lattice4, rc1_setwiseo, t15_pre_topc, t33_funct_3, t9_tarski, t34_lattices, t145_relat_1, t51_lattices, t40_tops_1, d10_xboole_0, t74_xboole_1, t7_xboole_1, t115_funct_2, idempotence_k2_xboole_0, t32_finsub_1, t48_subset_1, t28_relat_1, t32_borsuk_1, d4_tops_1, t35_lopclset, t57_filter_1, t32_filter_1, d12_filter_0, t42_lattice4, t50_subset_1, t65_filter_0, t55_borsuk_1, rc2_pre_topc, t46_xboole_1, t71_borsuk_1, t149_relat_1, d15_borsuk_1, redefinition_k20_borsuk_1, t74_tops_1, t33_funct_1, t159_funct_1, t57_funct_1, d19_lattices, t67_partfun1, redefinition_k6_subset_1, t58_setfam_1, t12_relset_1, t14_funct_3, t53_lattice2, existence_l1_struct_0, t5_xboole_1, t45_filter_0, t49_subset_1, t7_tarski, commutativity_k2_lopclset, rc1_partfun1, t71_filter_0, dt_k2_lattices, t3_xboole_0, t28_lattice4, t79_lattice2, dt_k2_setwiseo, t3_boole, redefinition_k2_setwiseo, t13_lopclset, d5_funct_1, t6_ordinal1, t24_funct_3, t20_lopclset, fc1_lattice4, dt_k3_funct_3, redefinition_m2_subset_1, t43_filter_1, t25_relat_1, d1_tops_1, t17_funct_3, t55_filter_1, t6_filter_0, idempotence_k4_subset_1, d14_group_1, t87_xboole_1, d3_filter_0, t24_pre_topc, dt_k3_pre_topc, t41_filter_1, fc14_finset_1, t60_lattice2, t50_filter_0, t26_funct_4, rc4_struct_0, rc5_pre_topc, t39_borsuk_1, dt_k3_lopclset, t49_lattice2, fc13_finset_1, t66_filter_0, t15_funct_4, t43_lattice4, t40_zfmisc_1, d11_lattices, t22_funct_4, rc2_xboole_0, t26_tops_1, t63_lattice2, t55_funct_2, t45_xboole_1, t44_tops_1, d1_pre_topc, dt_k6_pre_topc, t42_lopclset, t8_funct_3, t40_xboole_1, t10_xboole_1, dt_k3_subset_1, t4_funct_3, t6_relat_1, t6_lattice4, t14_lattice2, t159_relat_1, t63_subset_1, t94_tops_1, t42_pre_topc, t26_relat_1, dt_k2_pre_topc, t61_funct_2, t36_funct_4, fc3_lattices, t73_borsuk_1, t33_subset_1, t32_funct_4, t30_partfun1, t65_zfmisc_1, t14_pre_topc, t29_tops_1, fc2_lopclset, t13_filter_0, d3_xboole_0, t38_xboole_1, t19_funct_4, t39_xboole_1, t3_filter_0, t10_lattice4, t20_funct_4, antisymmetry_r2_hidden, t43_lopclset, dt_k1_setwiseo, t68_tops_1, t45_funct_4, d5_lattice4, t21_tops_1, d8_lattice4, t53_relat_1, cc1_pre_topc, t167_relat_1, t69_borsuk_1, t64_lattice2
% 48.42/12.09 % No. of inferences in proof: 2744
% 48.42/12.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11568 ms resp. 10649 ms w/o parsing
% 49.45/12.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.45/12.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------